good reason argument

2 Logic and the Study of Arguments

If we want to study how we ought to reason (normative) we should start by looking at the primary way that we do reason (descriptive): through the use of arguments. In order to develop a theory of good reasoning, we will start with an account of what an argument is and then proceed to talk about what constitutes a “good” argument.

I. Arguments

• Arguments are a set of statements (premises and conclusion).
• The premises provide evidence, reasons, and grounds for the conclusion.
• The conclusion is what is being argued for.
• An argument attempts to draw some logical connection between the premises and the conclusion.
• And in doing so, the argument expresses an inference: a process of reasoning from the truth of the premises to the truth of the conclusion.

Example : The world will end on August 6, 2045. I know this because my dad told me so and my dad is smart.

In this instance, the conclusion is the first sentence (“The world will end…”); the premises (however dubious) are revealed in the second sentence (“I know this because…”).

II. Statements

Conclusions and premises are articulated in the form of statements . Statements are sentences that can be determined to possess or lack truth. Some examples of true-or-false statements can be found below. (Notice that while some statements are categorically true or false, others may or may not be true depending on when they are made or who is making them.)

Examples of sentences that are statements:

• It is below 40°F outside.
• Oklahoma is north of Texas.
• The Denver Broncos will make it to the Super Bowl.
• Russell Westbrook is the best point guard in the league.
• I like broccoli.
• I shouldn’t eat French fries.
• Time travel is possible.
• If time travel is possible, then you can be your own father or mother.

However, there are many sentences that cannot so easily be determined to be true or false. For this reason, these sentences identified below are not considered statements.

• Questions: “What time is it?”
• Commands: “Do your homework.”
• Requests: “Please clean the kitchen.”
• Proposals: “Let’s go to the museum tomorrow.”

Question: Why are arguments only made up of statements?

First, we only believe statements . It doesn’t make sense to talk about believing questions, commands, requests or proposals. Contrast sentences on the left that are not statements with sentences on the right that are statements:

It would be non-sensical to say that we believe the non-statements (e.g. “I believe what time is it?”). But it makes perfect sense to say that we believe the statements (e.g. “I believe the time is 11 a.m.”). If conclusions are the statements being argued for, then they are also ideas we are being persuaded to believe. Therefore, only statements can be conclusions.

Second, only statements can provide reasons to believe.

• Q: Why should I believe that it is 11:00 a.m.? A: Because the clock says it is 11a.m.
• Q: Why should I believe that we are going to the museum tomorrow? A: Because today we are making plans to go.

Sentences that cannot be true or false cannot provide reasons to believe. So, if premises are meant to provide reasons to believe, then only statements can be premises.

III. Representing Arguments

As we concern ourselves with arguments, we will want to represent our arguments in some way, indicating which statements are the premises and which statement is the conclusion. We shall represent arguments in two ways. For both ways, we will number the premises.

In order to identify the conclusion, we will either label the conclusion with a (c) or (conclusion). Or we will mark the conclusion with the ∴ symbol

Example Argument:

There will be a war in the next year. I know this because there has been a massive buildup in weapons. And every time there is a massive buildup in weapons, there is a war. My guru said the world will end on August 6, 2045.

• There has been a massive buildup in weapons.
• Every time there has been a massive buildup in weapons, there is a war.

(c) There will be a war in the next year.

∴ There will be a war in the next year.

Of course, arguments do not come labeled as such. And so we must be able to look at a passage and identify whether the passage contains an argument and if it does, we should also be identify which statements are the premises and which statement is the conclusion. This is harder than you might think!

There is no argument here. There is no statement being argued for. There are no statements being used as reasons to believe. This is simply a report of information.

The following are also not arguments:

Advice: Be good to your friends; your friends will be good to you.

Warnings: No lifeguard on duty. Be careful.

Associated claims: Fear leads to anger. Anger leads to the dark side.

When you have an argument, the passage will express some process of reasoning. There will be statements presented that serve to help the speaker building a case for the conclusion.

IV. How to L ook for A rguments [1]

How do we identify arguments in real life? There are no easy, mechanical rules, and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds “this is because …,” then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterward. Other words in English that might be used to indicate the premises to follow include:

• firstly, secondly, …
• for, as, after all
• assuming that, in view of the fact that
• follows from, as shown / indicated by
• may be inferred / deduced / derived from

Of course whether such words are used to indicate premises or not depends on the context. For example, “since” has a very different function in a statement like “I have been here since noon,” unlike “X is an even number since X is divisible by 4.” In the first instance (“since noon”) “since” means “from.” In the second instance, “since” means “because.”

Conclusions, on the other hand, are often preceded by words like:

• therefore, so, it follows that
• hence, consequently
• suggests / proves / demonstrates that
• entails, implies

Here are some examples of passages that do not contain arguments.

1. When people sweat a lot they tend to drink more water. [Just a single statement, not enough to make an argument.]

2. Once upon a time there was a prince and a princess. They lived happily together and one day they decided to have a baby. But the baby grew up to be a nasty and cruel person and they regret it very much. [A chronological description of facts composed of statements but no premise or conclusion.]

3. Can you come to the meeting tomorrow? [A question that does not contain an argument.]

Do these passages contain arguments? If so, what are their conclusions?

• Cutting the interest rate will have no effect on the stock market this time around, as people have been expecting a rate cut all along. This factor has already been reflected in the market.
• So it is raining heavily and this building might collapse. But I don’t really care.
• Virgin would then dominate the rail system. Is that something the government should worry about? Not necessarily. The industry is regulated, and one powerful company might at least offer a more coherent schedule of services than the present arrangement has produced. The reason the industry was broken up into more than 100 companies at privatization was not operational, but political: the Conservative government thought it would thus be harder to renationalize (The Economist 12/16/2000).
• Bill will pay the ransom. After all, he loves his wife and children and would do everything to save them.
• All of Russia’s problems of human rights and democracy come back to three things: the legislature, the executive and the judiciary. None works as well as it should. Parliament passes laws in a hurry, and has neither the ability nor the will to call high officials to account. State officials abuse human rights (either on their own, or on orders from on high) and work with remarkable slowness and disorganization. The courts almost completely fail in their role as the ultimate safeguard of freedom and order (The Economist 11/25/2000).
• Most mornings, Park Chang Woo arrives at a train station in central Seoul, South Korea’s capital. But he is not commuter. He is unemployed and goes there to kill time. Around him, dozens of jobless people pass their days drinking soju, a local version of vodka. For the moment, middle-aged Mr. Park would rather read a newspaper. He used to be a bricklayer for a small construction company in Pusan, a southern port city. But three years ago the country’s financial crisis cost him that job, so he came to Seoul, leaving his wife and two children behind. Still looking for work, he has little hope of going home any time soon (The Economist 11/25/2000).
• For a long time, astronomers suspected that Europa, one of Jupiter’s many moons, might harbour a watery ocean beneath its ice-covered surface. They were right. Now the technique used earlier this year to demonstrate the existence of the Europan ocean has been employed to detect an ocean on another Jovian satellite, Ganymede, according to work announced at the recent American Geo-physical Union meeting in San Francisco (The Economist 12/16/2000).
• There are no hard numbers, but the evidence from Asia’s expatriate community is unequivocal. Three years after its handover from Britain to China, Hong Kong is unlearning English. The city’s gweilos (Cantonese for “ghost men”) must go to ever greater lengths to catch the oldest taxi driver available to maximize their chances of comprehension. Hotel managers are complaining that they can no longer find enough English-speakers to act as receptionists. Departing tourists, polled at the airport, voice growing frustration at not being understood (The Economist 1/20/2001).

V. Evaluating Arguments

Q: What does it mean for an argument to be good? What are the different ways in which arguments can be good? Good arguments:

• Are persuasive.
• Have premises that provide good evidence for the conclusion.
• Contain premises that are true.
• Reach a true conclusion.
• Provide the audience good reasons for accepting the conclusion.

The focus of logic is primarily about one type of goodness: The logical relationship between premises and conclusion.

An argument is good in this sense if the premises provide good evidence for the conclusion. But what does it mean for premises to provide good evidence? We need some new concepts to capture this idea of premises providing good logical support. In order to do so, we will first need to distinguish between two types of argument.

VI. Two Types of Arguments

The two main types of arguments are called deductive and inductive arguments. We differentiate them in terms of the type of support that the premises are meant to provide for the conclusion.

Deductive Arguments are arguments in which the premises are meant to provide conclusive logical support for the conclusion.

1. All humans are mortal

2. Socrates is a human.

∴ Therefore, Socrates is mortal.

1. No student in this class will fail.

2. Mary is a student in this class.

∴ Therefore, Mary will not fail.

1. A intersects lines B and C.

2. Lines A and B form a 90-degree angle

3. Lines A and C form a 90-degree angle.

∴ B and C are parallel lines.

Inductive arguments are, by their very nature, risky arguments.

Arguments in which premises provide probable support for the conclusion.

Statistical Examples:

1. Ten percent of all customers in this restaurant order soda.

2. John is a customer.

∴ John will not order Soda..

1. Some students work on campus.

2. Bill is a student.

∴ Bill works on campus.

1. Vegas has the Carolina Panthers as a six-point favorite for the super bowl.

∴ Carolina will win the Super Bowl.

VII. Good Deductive Arguments

The First Type of Goodness: Premises play their function – they provide conclusive logical support.

Deductive and inductive arguments have different aims. Deductive argument attempt to provide conclusive support or reasons; inductive argument attempt to provide probable reasons or support. So we must evaluate these two types of arguments.

Deductive arguments attempt to be valid.

To put validity in another way: if the premises are true, then the conclusion must be true.

It is very important to note that validity has nothing to do with whether or not the premises are, in fact, true and whether or not the conclusion is in fact true; it merely has to do with a certain conditional claim. If the premises are true, then the conclusion must be true.

Q: What does this mean?

• The validity of an argument does not depend upon the actual world. Rather, it depends upon the world described by the premises.
• First, consider the world described by the premises. In this world, is it logically possible for the conclusion to be false? That is, can you even imagine a world in which the conclusion is false?

Reflection Questions:

• If you cannot, then why not?
• If you can, then provide an example of a valid argument.

You should convince yourself that validity is not just about the actual truth or falsity of the premises and conclusion. Rather, validity only has to do with a certain logical relationship between the truth of the premise and the truth of the conclusion. So the only possible combination that is ruled out by a valid argument is a set of true premises and false conclusion.

Let’s go back to example #1. Here are the premises:

1. All humans are mortal.

If both of these premises are true, then every human that we find must be a mortal. And this means, that it must be the case that if Socrates is a human, that Socrates is mortal.

Reflection Questions about Invalid Arguments:

• Can you have an invalid argument with a true premise?
• Can you have an invalid argument with true premises and a true conclusion?

The s econd type of goodness for deductive arguments: The premises provide us the right reasons to accept the conclusion.

Soundness V ersus V alidity:

Our original argument is a sound one:

∴ Socrates is mortal.

Question: Can a sound argument have a false conclusion?

VIII. From Deductive Arguments to Inductive Arguments

Question: What happens if we mix around the premises and conclusion?

2. Socrates is mortal.

∴ Socrates is a human.

1. Socrates is mortal

∴ All humans are mortal.

Are these valid deductive arguments?

NO, but they are common inductive arguments.

Other examples :

Suppose that there are two opaque glass jars with different color marbles in them.

1. All the marbles in jar #1 are blue.

2. This marble is blue.

∴ This marble came from jar #1.

1. This marble came from jar #2.

2. This marble is red.

∴ All the marbles in jar #2 are red.

While this is a very risky argument, what if we drew 100 marbles from jar #2 and found that they were all red? Would this affect the second argument’s validity?

IX. Inductive Arguments:

The aim of an inductive argument is different from the aim of deductive argument because the type of reasons we are trying to provide are different. Therefore, the function of the premises is different in deductive and inductive arguments. And again, we can split up goodness into two types when considering inductive arguments:

• The premises provide the right logical support.
• The premises provide the right type of reason.

Logical S upport:

Remember that for inductive arguments, the premises are intended to provide probable support for the conclusion. Thus, we shall begin by discussing a fairly rough, coarse-grained way of talking about probable support by introducing the notions of strong and weak inductive arguments.

A strong inductive argument:

• The vast majority of Europeans speak at least two languages.
• Sam is a European.

∴ Sam speaks two languages.

Weak inductive argument:

• This quarter is a fair coin.

∴ Therefore, the next coin flip will land heads.

• At least one dog in this town has rabies.
• Fido is a dog that lives in this town.

∴ Fido has rabies.

The R ight T ype of R easons. As we noted above, the right type of reasons are true statements. So what happens when we get an inductive argument that is good in the first sense (right type of logical support) and good in the second sense (the right type of reasons)? Corresponding to the notion of soundness for deductive arguments, we call inductive arguments that are good in both senses cogent arguments.

• With which of the following types of premises and conclusions can you have a strong inductive argument?
• With which of the following types of premises and conclusions can you have a cogent inductive argument?

X. Steps for Evaluating Arguments:

• Read a passage and assess whether or not it contains an argument.
• If it does contain an argument, then identify the conclusion and premises.
• If yes, then assess it for soundness.
• If not, then treat it as an inductive argument (step 3).
• If the inductive argument is strong, then is it cogent?

XI. Evaluating Real – World Arguments

An important part of evaluating arguments is not to represent the arguments of others in a deliberately weak way.

For example, suppose that I state the following:

All humans are mortal, so Socrates is mortal.

Is this valid? Not as it stands. But clearly, I believe that Socrates is a human being. Or I thought that was assumed in the conversation. That premise was clearly an implicit one.

So one of the things we can do in the evaluation of argument is to take an argument as it is stated, and represent it in a way such that it is a valid deductive argument or a strong inductive one. In doing so, we are making explicit what one would have to assume to provide a good argument (in the sense that the premises provide good – conclusive or probable – reason to accept the conclusion).

The teacher’s policy on extra credit was unfair because Sally was the only person to have a chance at receiving extra credit.

• Sally was the only person to have a chance at receiving extra credit.
• The teacher’s policy on extra credit is fair only if everyone gets a chance to receive extra credit.

Therefore, the teacher’s policy on extra credit was unfair.

Valid argument

Sally didn’t train very hard so she didn’t win the race.

• Sally didn’t train very hard.
• If you don’t train hard, you won’t win the race.

Therefore, Sally didn’t win the race.

Strong (not valid):

• If you won the race, you trained hard.
• Those who don’t train hard are likely not to win.

Therefore, Sally didn’t win.

Ordinary workers receive worker’s compensation benefits if they suffer an on-the-job injury. However, universities have no obligations to pay similar compensation to student athletes if they are hurt while playing sports. So, universities are not doing what they should.

• Ordinary workers receive worker’s compensation benefits if they suffer an on-the-job injury that prevents them working.
• Student athletes are just like ordinary workers except that their job is to play sports.
• So if student athletes are injured while playing sports, they should also be provided worker’s compensation benefits.
• Universities have no obligations to provide injured student athletes compensation.

Therefore, universities are not doing what they should.

Deductively valid argument

If Obama couldn’t implement a single-payer healthcare system in his first term as president, then the next president will not be able to implement a single-payer healthcare system.

• Obama couldn’t implement a single-payer healthcare system.
• In Obama’s first term as president, both the House and Senate were under Democratic control.
• The next president will either be dealing with the Republican-controlled house and senate or at best, a split legislature.
• Obama’s first term as president will be much easier than the next president’s term in terms of passing legislation.

Therefore, the next president will not be able to implement a single-payer healthcare system.

Strong inductive argument

Sam is weaker than John. Sam is slower than John. So Sam’s time on the obstacle will be slower than John’s.

• Sam is weaker than John.
• Sam is slower than John.
• A person’s strength and speed inversely correlate with their time on the obstacle course.

Therefore, Sam’s time will be slower than John’s.

XII. Diagramming Arguments

All the arguments we’ve dealt with – except for the last two – have been fairly simple in that the premises always provided direct support for the conclusion. But in many arguments, such as the last one, there are often arguments within arguments.

Obama example :

• The next president will either be dealing with the Republican controlled house and senate or at best, a split legislature.

∴ The next president will not be able to implement a single-payer healthcare system.

It’s clear that premises #2 and #3 are used in support of #4. And #1 in combination with #4 provides support for the conclusion.

When we diagram arguments, the aim is to represent the logical relationships between premises and conclusion. More specifically, we want to identify what each premise supports and how.

This represents that 2+3 together provide support for 4

This represents that 4+1 together provide support for 5

When we say that 2+3 together or 4+1 together support some statement, we mean that the logical support of these statements are dependent upon each other. Without the other, these statements would not provide evidence for the conclusion. In order to identify when statements are dependent upon one another, we simply underline the set that are logically dependent upon one another for their evidential support. Every argument has a single conclusion, which the premises support; therefore, every argument diagram should point to the conclusion (c).

Sam Example:

• Sam is less flexible than John.
• A person’s strength and flexibility inversely correlate with their time on the obstacle course.

∴ Therefore, Sam’s time will be slower than John’s.

In some cases, different sets of premises provide evidence for the conclusion independently of one another. In the argument above, there are two logically independent arguments for the conclusion that Sam’s time will be slower than John’s. That Sam is weaker than John and that being weaker correlates with a slower time provide evidence for the conclusion that Sam will be slower than John. Completely independent of this argument is the fact that Sam is less flexible and that being less flexible corresponds with a slower time. The diagram above represent these logical relations by showing that #1 and #3 dependently provide support for #4. Independent of that argument, #2 and #3 also dependently provide support for #4. Therefore, there are two logically independent sets of premises that provide support for the conclusion.

Try diagramming the following argument for yourself. The structure of the argument has been provided below:

• All humans are mortal
• Socrates is human
• So Socrates is mortal.
• If you feed a mortal person poison, he will die.

∴ Therefore, Socrates has been fed poison, so he will die.

• This section is taken from http://philosophy.hku.hk/think/ and is in use under creative commons license. Some modifications have been made to the original content. ↵

Critical Thinking Copyright © 2019 by Brian Kim is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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[A09] Good Arguments

Module: Argument analysis

• A01. What is an argument?
• A02. The standard format
• A03. Validity
• A04. Soundness
• A05. Valid patterns
• A06. Validity and relevance
• A07. Hidden Assumptions
• A08. Inductive Reasoning
• A10. Argument mapping
• A11. Analogical Arguments
• A12. More valid patterns
• A13. Arguing with other people

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§1. What is a good argument?

In this tutorial we shall discuss what a good argument is. The concept of a good argument is of course quite vague. So what we are trying to do here is to give it a somewhat more precise definition. To begin with, make sure that you know what a sound argument is.

Criterion #1 : A good argument must have true premises

This means that if we have an argument with one or more false premises, then it is not a good argument. The reason for this condition is that we want a good argument to be one that can convince us to accept the conclusion. Unless the premises of an argument are all true, we would have no reason to accept to accept its conclusion.

Criterion #2 : A good argument must be either valid or strong

Is validity a necessary condition for a good argument? Certainly many good arguments are valid. Example:

All whales are mammals. All mammals are warm-blooded. So all whales are warm-blooded.

But it is not true that good arguments must be valid. We often accept arguments as good, even though they are not valid. Example:

No baby in the past has ever been able to understand quantum physics. Kitty is going to have a baby soon. So Kitty's baby is not going to be able to understand quantum physics.

This is surely a good argument, but it is not valid. It is true that no baby in the past has ever been able to understand quantum physics. But it does not follow logically that Kitty's baby will not be able to do so. To see that the argument is not valid, note that it is not logically impossible for Kitty's baby to have exceptional brain development so that the baby can talk and learn and understand quantum physics while still being a baby. Extremely unlikely to be sure, but not logically impossible, and this is enough to show that the argument is not valid. But because such possibilities are rather unlikely, we still think that the true premises strongly support the conclusion and so we still think that the argument is a good one.

In other words, a good argument need not be valid. But presumably if it is not valid it must be inductively strong. If an argument is inductively weak, then it cannot be a good argument since the premises do not provide good reasons for accepting the conclusion.

For more information about inductive strength, see the previous tutorial .

Criterion #3 : The premises of a good argument must not beg the question

Notice that criteria #1 and #2 are not sufficient for a good argument. First of all, we certainly don't want to say that circular arguments are good arguments, even if they happen to be sound. Suppose someone offers the following argument:

It is going to rain tomorrow. Therefore, it is going to rain tomorrow.

So far we think that a good argument must (1) have true premises, and (2) be valid or inductively strong. Are these conditions sufficient? The answer is no. Consider this example:

Smoking is bad for your health. Therefore smoking is bad for your health.

This argument is actually sound. The premise is true, and the argument is valid, because the conclusion does follow from the premise! But as an argument surely it is a terrible argument. This is a circular argument where the conclusion also appears as a premise. It is of course not a good argument, because it does not provide independent reasons for supporting the conclusion. So we say that it begs the question .

Here is another example of an argument that begs the question :

Since Mary would not lie to her best friend, and Mary told me that I am indeed her best friend, I must really be Mary's best friend.

Whether this argument is circular depends on your definition of a "circular argument". Some people might not consider this a circular argument in that the conclusion does not appear explicitly as a premise. However, the argument still begs the question and so is not a good argument.

Criterion #4 : The premises of a good argument must be plausible and relevant to the conclusion

Here, plausibility is a matter of having good reasons for believing that the premises are true. As for relevance, this is the requirement that the the subject matter of the premises must be related to that of the conclusion. Why do we need this additional criterion? The reason is that claims and theories can happen to be true even though nobody has got any evidence that they are true. If the premises of an argument happen to be true but there is no evidence indicating that they are, the argument is not going to be pursuasive in convincing people that the conclusion is correct. A good argument, on the other hand, is an argument that a rational person should accept, so a good argument should satisfy the additional criterion mentioned.

§2. Summary

So, here is our final definition of a good argument :

A good argument is an argument that is either valid or strong, and with plausible premises that are true, do not beg the question, and are relevant to the conclusion.

Now that you know what a good argument is, you should be able to explain why these claims are mistaken. Many people who are not good at critical thinking often make these mistakes :

"The conclusion of this argument is true, so some or all the premises are true." "One or more premises of this argument are false, so the conclusion is false." "Since the conclusion of the argument is false, all its premises are false." "The conclusion of this argument does not follow from the premises. So it must be false."

Answer the following questions.

• Does a good argument have to be sound? answer
• Can a good argument be inductively weak? answer

These are some arguments (or just premises) that students have given to support the idea that there is nothing morally wrong with eating meat. Discuss and evaluate these arguments carefully. Think about whether the premises are true, and whether they support the conclusion that it is morally acceptable to eat meat.

• Human beings are part of the food cycle of nature.
• Human beings are able to digest meat.
• It is ok to eat meat because meat is just a kind of food and we need food to survive.
• It is ok to eat meat because lots of people eat meat; because everyone around me eat meat.
• It is ok to eat meat because the government does not stop people from eating meat.
• Many other people eat meat.
• Meat contains protein, and we need protein to survive.
• We are animals, and it is ok for animals to eat animals.
• It is ok to eat meat because I started eating meat when I was a child.
• Meat is more tasty than vegetables.
• It is ok to eat meat because nobody told me that this is wrong.
• I love eating meat.
• It is ok to eat meat because set meals in restaurants have very little vegetables.
• Animals kill each other.
• Maintain the balance of nature - there will be too many animals otherwise.
• We are more powerful than animals.
• I was taught that I should eat meat.
• Human beings are at the top of the food chain.
• Eating meat can help me avoid certain diseases.
• We have special teeth for eating meat.

§3. A technical discussion

This section is a more abstract and difficult. You can skip this if you want.

One interesting but somewhat difficult issue about the definition of a good argument concerns the first requirement that a good argument must have true premises. One might argue that this requirement is too stringent, because we seem to accept many arguments as good arguments, even if we are not completely certain that the premises are true. Or perhaps we had good reasons for the premises, even if it turns out later that we were wrong.

As an example, suppose your friend told you that she is going camping for the whole weekend. She is a trustworthy friend and you have no reason to doubt her. So you accept the following argument as a good argument:

Amie will be camping this weekend. So she will not be able to come to my party.

But suppose the camping trip got cancelled at the last minute, and so Amie came to the party after all. What then should we say about the argument here? Was it a good argument? Surely you were justified in believing the premise, and so someone might argue that it is wrong to require that a good argument must have true premises. It is enough if the premises are highly justified (of course the other conditions must be satisfied as well.)

If we take this position, this implies that when we discover that the camping trip has been cancelled, we are no longer justified in believing the premise, and so at that point the argument ceases to be a good argument.

Here we prefer a different way of describing the situation. We want to say that although in the beginning we had good reasons to think that the argument is a good one, later on we discover that it wasn't a good argument to begin with. In other words, the argument doesn't change from being a good argument to a bad argument. It is just that we change our mind about whether the argument is a good one in light of new information. We think there are are reasons for preferring this way of describing the situation, and it is quite a natural way of speaking.

So there are actually two ways to use the term "good argument". We have adopted one usage here and it is fine if you want to use it differently. We think the ordinary meaning of the term is not precise enough to dictate a particular usage. What is important is to know very clearly how you are using it and what the consequences are as a result.

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Part Three: Evaluating Arguments

Chapter Seven: A Framework for Evaluating

The main aim of education is practical and reflective judgment, a mind trained to be critical everywhere in the use of evidence. —Brand Blanshard, Four Reasonable Men

Standard Evaluating Format

• Complex Arguments
• A Reasonable Objector over Your Shoulder

We now arrive at the portion of the book that is most important for good reasoning, the portion that Parts One and Two have been pointing toward: the evaluation of arguments.

In Part One we saw that good reasoning is ultimately a matter of cultivating the intellectual virtues, including the virtues of critical reflection, empirical inquiry, and intellectual honesty. This requires close attention to arguments, since cultivating each of these virtues is greatly enhanced by skill in clarifying and evaluating arguments. And close attention to arguments is shorthand, really, for close attention to whether arguments have the four merits of clarity, true premises, good logic, and conversational relevance.

In Part Two we saw that clarity is the starting point. This starting point is not only a matter of asking whether an argument is clear, but is also a matter of enhancing the argument’s clarity through the clarifying process. This process includes two general procedures: outlining the argument in standard clarifying format, and, at the same time, paraphrasing the argument for greater clarity. Paraphrasing should accomplish three things: streamlining, specifying, and structuring. And it should be governed by two general principles. The principle of loyalty tells you to imagine that the arguer is looking over your shoulder, checking to be sure that the paraphrased argument reflects the arguer’s intentions. The principle of charity applies if the context does not indicate the arguer’s intentions; it tells you to paraphrase in a way that makes the arguer as reasonable as possible—to paraphrase according to what you probably would have meant had you expressed the same words under similar circumstances.

The whole point of clarifying is to make it simpler to determine whether arguments have the other three merits. The remainder of the book has to do with asking these three questions of clarified arguments: Are the premises true? Is the logic good? And, to a lesser extent, Is the argument conversationally relevant?

7.1 Standard Evaluating Format

Just as there is a standard clarifying format, so is there a standard evaluating format. It systematically links your evaluation to the clarified argument and provides a framework for considering the questions about truth, logic, and conversational relevance. Let’s start with the clarified argument from Scientific American about the air sacs that are spread throughout the bodies of most birds:

• If air sacs of birds play a role in their breathing, then birds are poisoned by carbon monoxide introduced into their air sacs.
• Birds are not poisoned by carbon monoxide introduced into their air sacs.
• ∴ Air sacs of birds do not play a role in their breathing.

Standard evaluating format provides a simple system for discussing the truth of each premise, the logic of the argument, and (where appropriate) the conversational relevance of the argument. Begin with the main heading EVALUATION, and under it provide at least three subheadings: TRUTH, LOGIC, and SOUNDNESS.  (In some cases you will need a fourth subheading, CONVERSATIONAL RELEVANCE.)

Under TRUTH, provide an entry for each premise, and for each premise do two things: state whether you judge the premise to be true, and provide your defense of that evaluation. For the air sac argument, this part of the evaluation would look something like this:

Premise 1. This premise is probably true, assuming large enough quantities of carbon monoxide are involved, since carbon monoxide is known to be poisonous to any animal when breathed in sufficient quantities.

Premise 2. This premise is probably true, since this is reported in Scientific American, known to be a highly reliable publication on topics of this sort, and there is no reason to doubt this particular report.

Under the next subheading, LOGIC, do the same things: state whether you think the logic of the simple argument is good, and provide a defense of that evaluation. The evaluation would continue roughly as follows:

The argument is valid, since it has the form denying the consequent.

It isn’t important at this point in the text that you understand the exact technical meaning of expressions like valid or denying the consequent. For now you only need to know what is intuitively obvious—that expressions like valid, very strong, and fairly strong are ways of saying that the logic is good, while expressions like invalid, fairly weak, and very weak are ways of saying that it is bad.

After this, under the heading SOUNDNESS, provide your summary judgment— sound or unsound —based on the two preceding sections of the evaluation. If you judge that the argument is not sound, state whether this is owing to a problem either with a premise or with the argument’s logic. But if you judge that it is sound, there is no need for further explanation since saying it is sound is the same as saying the premises are true and the logic is good. In our sample air sac case, it would look like this:

The argument is probably sound.

Notice the argument is judged probably sound. Your judgment of the argument’s soundness cannot be any better than the poorest thing said under TRUTH and LOGIC. While under the heading of LOGIC the logic of the air sac argument is judged to be good, under the heading of TRUTH each of the premises is judged merely probably true. Thus, the argument cannot be evaluated as any better than probably sound.

We have not yet provided a place in the format for conversational relevance. This can be an extremely important question, but it will turn out that the majority of the arguments you evaluate will not appear to be defective in this way. My suggestion—which we will follow in this text—is that a fourth subheading, CONVERSATIONAL RELEVANCE, be optional. Include it when an argument is conversationally flawed, and under the heading explain how the argument is thus flawed. But otherwise omit it, simply for the practical reason that it will save you extra writing.

The air sac argument is, so far as I can tell, conversationally relevant. Without any context, there is no good reason to think that it begs the question or misses the point. We could imagine, however, contexts in which it would be conversationally flawed. Suppose, for example, that the same argument had been put forward by a laboratory assistant who was asked by the laboratory director to look into whether air sacs in birds played any role in their breeding. We would in that case add a fourth subheading, as follows:

CONVERSATIONAL RELEVANCE

Even though it is sound, the argument commits the fallacy of missing the point, since the point is to show whether the air sacs play any role in breeding, but the argument only addresses whether they play a role in breathing.

By following this format, you can develop the habit of systematically asking all the right evaluative questions of an argument, and you will always have a straightforward way of presenting your judgments.

Heading: EVALUATION

Subheading: TRUTH. For each premise, state whether you judge it to be true and provide your defense of that judgment.

Subheading: LOGIC. State whether you judge the logic to be successful and provide your defense of that judgment.

Subheading: SOUNDNESS. State whether you judge the argument to be sound; then, if it is not sound, state whether this is owing to a problem with a premise or with the logic.

Subheading (optional): CONVERSATIONAL RELEVANCE. If and only if the argument is flawed in this way, state whether it commits the fallacy of begging the question or missing the point, and explain how.

Exercises Chapter 7, set (a)

Given the brief evaluations provided for truth and logic, provide, in standard form, the correct evaluation of the argument’s soundness.

Sample exercise (1).

TRUTH. Premise 1 is probably true. I can’t decide about premise 2. LOGIC. The argument is valid.

Sample answer (1).

SOUNDNESS. I can’t decide whether the argument is sound, since I can’t decide about the truth of one of the premises.

Sample exercise (2).

TRUTH. Premise 1 is certainly true. LOGIC. The argument is fairly weak logically.

Sample answer (2).

SOUNDNESS. The argument is fairly unsound, since the logic is fairly weak.

• TRUTH. Premise 1 is probably false. I can’t decide about premise 2. LOGIC. The argument is invalid.
• TRUTH. Premise 1 is probably false. LOGIC. The argument is extremely weak.
• TRUTH. Premise 1 is certainly false. I can’t decide about premise 2. LOGIC. The argument is valid.
• TRUTH. Premise 1 is certainly true. LOGIC. The argument is valid.
• TRUTH. Premise 1 is probably true. I can’t decide about premise 2. Premise 3 is certainly true. LOGIC. The argument is fairly strong.
• TRUTH. Premise 1 is probably true. Premise 2 is probably true. Premise 3 is certainly true. LOGIC. The argument is very strong.

7.1.1 The Conclusion

You may have noticed there is no place in this format for evaluating whether the main conclusion of any argument is itself true. This may initially strike you as a serious oversight. But it is not. What we are evaluating here is not the truth of the conclusion, but the quality of the reasoning for the conclusion. Suppose you decided that an argument was utterly unsound, yet at the same time suspected that the conclusion was true. That would be no problem. Recall that for any true statement, it is possible to offer a bad argument in the attempt to support the statement. (If it then turned out that you were especially interested in such a conclusion, it would be up to you to see if you could come up with a better argument for it.) On the other hand, suppose you had a strong hunch that a conclusion was false, even though the argument itself appeared to be sound. This would give you good reason to check more carefully for a flaw in the argument, one that may have initially escaped your notice. Or you could end up changing your mind and accepting the initially implausible conclusion.

7.2 Complex Arguments

There is no important difference between evaluating a simple argument and a complex one. If the argument is complex—that is, if it is a series of linked simple arguments—then, after the clarification of the complex argument, evaluate separately each simple argument that makes up the complex argument. Instead of the heading EVALUATION, use the heading EVALUATION OF ARGUMENT TO N, where n identifies the relevant subconclusion or conclusion. To illustrate, suppose other air sac experiments by Professor Soum, reported in the same Scientific American story, had independently narrowed down the role of air sacs in birds to either flight-enhancement or breathing-enhancement. Suppose further that the air sac argument had been the first part of a larger argument that was designed to settle this issue, concluding thus:

Therefore, since air sacs in birds are known to play a role in either flight or breathing, we can conclude that they play a role in flight.

The complex argument would be clarified thus (adding premise 4 and a new conclusion):

• Air sacs of birds play a role in their breathing or air sacs in birds play a role in their flight.
• ∴ Air sacs of birds play a role in their flight.

The evaluation, framed in standard evaluation format, would then look like this:

EVALUATION OF ARGUMENT TO 3

Premise 2. This premise is probably true, since this is reported in Scientific American, known to be a highly reliable publication on topics of this sort, and there is no special reason to doubt this particular report.

The argument is valid, since it has the form of denying the consequent.

EVALUATION OF ARGUMENT TO C

Premise 3 is probably true, since it is supported by an argument that we have seen is probably sound (see evaluation of argument to 3).

Premise 4 is probably true, since (according to my hypothetical addition to the actual story, for the sake of this illustration) the experiments are reported in Scientific American, known to be a highly reliable publication on topics of this sort, and there is no reason to doubt this particular report.

The argument is valid, since it has the form of the process of elimination.

The evaluation of the first simple argument remains exactly the same, except for expanding the heading to say EVALUATION OF THE ARGUMENT TO 3. And we add to it the evaluation of the second simple argument—the evaluation of the argument to C . Premise 3 is the subconclusion of the complex argument—so it is both the conclusion of the argument to 3 and a premise in the argument to C . When evaluating its truth (under the heading EVALUATION OF THE ARGUMENT TO C) it is good to point out that the premise is supported by an argument that you have just evaluated as probably sound.

7.2.1 When a Simple Argument within the Complex Argument Is Unsound

In a complex argument, when one simple argument is sound it has an important effect on your entire evaluation. When you evaluate the subconclusion as a premise in the next simple argument, the soundness of the preceding simple argument serves as a good defense for judging its subconclusion to be true.

But this ripple effect does not naturally occur if the simple argument is unsound. Obviously, its unsoundness would not be something to appeal to in defense of the truth of the subconclusion. But—note this carefully—neither would it be something to appeal to in defense of the falsity of the subconclusion. Any statement, whether true or false, can have an unsound argument offered for it.

This presents an interesting problem: in a complex argument, you can evaluate a simple argument as unsound without its affecting your evaluation of the next simple argument. Thus, in a complex argument, you may evaluate as perfectly sound the argument to the main conclusion, even though the previous simple arguments have been unsound. This is as it should be. But at the same time, since the arguer has presented the complex argument as a whole, there should be some way of indicating earlier problems when you evaluate later simple arguments.

The solution is this: in a complex argument, when one simple argument is unsound and the next one is sound, qualify your evaluation of it as sound but not shown . In this way, you indicate that even though the simple argument is, in your judgment, sound, the arguer has failed to carry out the job of showing it to be sound by the previous simple arguments.

Here is an easy-to-understand example:

You have to be extremely good-looking to get hired as a lifeguard. Not many people are that good-looking, so it’s very tough to land such a job. For that reason, even though it would be great to work on the beach, most people should probably try to find some other sort of summer job.

This argument can be clarified as follows:

• If someone qualifies for a job as a lifeguard, then that person is extremely good-looking.
• Not many people are extremely good-looking.
• ∴ Not many people qualify for a job as a lifeguard.
• If not many people qualify for a particular job, then most people should try for some other sort of job.
• ∴ Most people should try for some other summer job than that of a lifeguard.

The subconclusion— Not many people qualify for a job as a lifeguard —seems clearly to be true. And even though the simple argument offered in its support is a bad one (premise 1, despite evidence you might gather from Baywatch reruns, is surely false), the simple argument from premises 3 and 4 to the main conclusion is a pretty good one. A very brief evaluation might take this rough form:

Premise 1. This premise is certainly false; it isn’t looks, but experience and ability, which qualify you for a job as a lifeguard.

Premise 2. This premise is very probably true. My observations are that most people are average-looking (it may even be that average-looking just means the way most people look ).

The argument is valid, since it has the form of singular denying the consequent.

The argument is unsound, due to the falsity of premise 1.

Premise 3 is certainly true. Most people need a lifeguard just because they aren’t qualified to be one. Qualifying to be a lifeguard requires that you be in excellent physical shape, that you be able to swim well, and that you have extensive training. (Before completing the evaluation, note that even though the argument to 3 has just been evaluated as unsound, I have nevertheless defended here the truth of 3—but for entirely different reasons than those offered in the argument to 3.)

Premise 4 is probably true. Under most circumstances, it doesn’t make good practical sense for people to apply for a job if their chances of getting it are extremely low.

The argument is valid, since it has the form of singular affirming the antecedent.

The argument is probably sound, but is not shown to be so by the rest of the argument.

Note that the argument to C is judged as probably sound (since the poorest thing said about it under TRUTH and LOGIC is that its premises are probably true ). But, to reflect the unsoundness of the simple argument used to lead into it, it is noted that it was not shown to be sound by the preceding simple argument.

Exercises Chapter 7, set (b)

Briefly describe the general conditions under which each of the following evaluations would apply.

• Probably sound.
• Sound but not shown.
• Can’t decide whether it is sound.
• Unsound but not shown.
• True but not shown.
• Logically successful but not shown.
• Logically successful because the preceding simple argument has been evaluated as sound.

7.3 A Reasonable Objector Over Your Shoulder

Whenever you write anything, it is crucially important that you know who your audience is. You may be writing for introductory students, your professor, your parents, a customer, a friend, your professional colleagues, or the general public. Different writing is designed for different audiences. And this applies to argument evaluations. Often they are directed at the arguer, whom you may hope to prove wrong. When doing the exercises in this text, you will be aiming them to your professor, who will grade your paper. When you do them on your job, you may be aiming them to a potential customer, whom you may hope to convince of the flaws in your competitor’s product.

But in the background, your primary audience should always be you. You should be aiming to arrive at the best evaluation you can for your own sake —the evaluation that is most likely to result in your arriving at knowledge and the one most likely to cultivate the habits that would continue to be conducive to your arriving at knowledge. In short, always evaluate arguments with a view to being the most honest, critically reflective, and inquisitive thinker you can be.

It may not always be easy to think in this way when evaluating an argument. It can be much easier to think in terms of an opponent who must be won over. And this can be turned to your advantage. Recall that an important guideline for clarifying is to imagine the arguer looking over your shoulder, checking your paraphrase for loyalty to the arguer’s intentions. I now recommend that you be similarly accompanied while evaluating the argument. In evaluating, though, imagine that looking over your shoulder is a reasonable person who disagrees with your evaluation. This reasonable objector has roughly the same evidence that you have and possesses the intellectual virtues of honesty, critical reflection, and inquiry. What reasons are most likely to persuade this person to accept your evaluation? What objection is this person most likely to raise? Be sure to express your defense in a way that defeats—or ultimately agrees with—the objections of this hypothetical adversary. In this way, you are more likely to exemplify the intellectual virtues yourself.

7.4 Summary of Chapter Seven

Frame your evaluation of every argument in the standard evaluation format, thereby ensuring that you appropriately present and defend your evaluation of the truth of every premise, the success of the argument’s logic, and, when necessary, the conversational relevance of the argument. The key judgment in every case is whether the argument is sound—that is, whether it is successful with respect to both truth and logic. Failure in either respect makes the argument unsound; and the poorest judgment in either respect should be reflected in your evaluation of the argument’s soundness. (Thus, for example, an argument that is logically successful and with a premise you have judged to be probably true can, at best, be probably sound.)

When the argument is complex, separately evaluate each component simple argument. If one of the simple arguments other than the argument to the main conclusion is unsound, and if a later simple argument is sound, be sure the earlier failure is reflected by noting that even the sound argument has not been shown to be sound in the preceding portion of the complex argument.

While thinking about and writing your evaluation, imagine that a reasonable objector—an intellectually virtuous person who has roughly the same evidence you have but disagrees with you—is watching over your shoulder and must be persuaded by your evaluation.

7.5 Guidelines for Chapter Seven

• Evaluate the clarified argument in standard evaluating format.
• Your evaluation of the argument’s soundness should be no better than the poorest evaluation you have provided of its logic and of the truth of its premises.
• If you have judged an argument to be sound, but you find that you still have doubts about the truth of the conclusion, carefully examine the argument again. You may initially have overlooked a flaw.
• Evaluate separately each simple argument that serves as a component of a complex argument.
• In a complex argument, if one simple argument is unsound and a later one is sound, qualify your evaluation of the sound one by saying that it is sound but not shown. This applies only to complex arguments.
• While writing your evaluation, imagine there is a reasonable objector looking over your shoulder, one whom you must persuade.

7.6 Glossary for Chapter Seven

Reasonable objector —someone who has approximately the same information you have, who exhibits the virtues of honesty, critical reflection, and inquiry, yet who disagrees with your evaluation. Imagine that this is your audience for every evaluation you write.

Sound but not shown —evaluation to use under the SOUNDNESS subheading in a complex argument when one simple argument is sound but a preceding simple argument, on which it depends, is unsound. Using this terminology reflects the fact that even though this simple argument happens to be sound, the arguer has failed to show it to be so, by virtue of having supported it with an unsound argument.

Evaluation to use under the SOUNDNESS subheading in a complex argument when one simple argument is sound but a preceding simple argument, on which it depends, is unsound. Using this terminology reflects the fact that even though this simple argument happens to be sound, the arguer has failed to show it to be so, by virtue of having supported it with an unsound argument.

Someone who has approximately the same information you have, who exhibits the virtues of honesty, critical reflection, and inquiry, yet who disagrees with your evaluation. Imagine that this is your audience for every evaluation you write.

A Guide to Good Reasoning: Cultivating Intellectual Virtues Copyright © 2020 by David Carl Wilson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Part I: Propositional Logic

3. Good Arguments

3.1  a historical example.

An important example of excellent reasoning can be found in the case of the medical advances of the Nineteenth Century physician, Ignaz Semmelweis.  Semmelweis was an obstetrician at the Vienna General Hospital.  Built on the foundation of a poor house, and opened in 1784, the General Hospital is still operating today.  Semmelweis, during his tenure as assistant to the head of one of two maternity clinics, noticed something very disturbing.  The hospital had two clinics, separated only by a shared anteroom, known as the First and the Second Clinics.  The mortality rate for mothers delivering babies in the First Clinic, however, was nearly three times as bad as the mortality for mothers in the Second Clinic (9.9 % average versus 3.4% average).  The same was true for the babies born in the clinics:  the mortality rate in the First Clinic was 6.1% versus 2.1% at the Second Clinic. [5]   In nearly all these cases, the deaths were caused by what appeared to be the same illness, commonly called “childbed fever”.  Worse, these numbers actually understated the mortality rate of the First Clinic, because sometimes very ill patients were transferred to the general treatment portion of the hospital, and when they died, their death was counted as part of the mortality rate of the general hospital, not of the First Clinic.

Semmelweis set about trying to determine why the First Clinic had the higher mortality rate.  He considered a number of hypotheses, many of which were suggested by or believed by other doctors.

One hypothesis was that cosmic-atmospheric-terrestrial influences caused childbed fever.  The idea here was that some kind of feature of the atmosphere would cause the disease.  But, Semmelweis observed, the First and Second Clinics were very close to each other, had similar ventilation, and shared a common anteroom.  So, they had similar atmospheric conditions.  He reasoned:  If childbed fever is caused by cosmic-atmospheric-terrestrial influences, then the mortality rate would be similar in the First and Second Clinics.  But the mortality rate was not similar in the First and Second Clinics.  So, the childbed fever was not caused by cosmic-atmospheric-terrestrial influences.

Another hypothesis was that overcrowding caused the childbed fever.  But, if overcrowding caused the childbed fever, then the more crowded of the two clinics should have the higher mortality rate.  But, the Second Clinic was more crowded (in part because, aware of its lower mortality rate, mothers fought desperately to be put there instead of in the First Clinic).  It did not have a higher mortality rate.  So, the childbed fever was not caused by overcrowding.

Another hypothesis was that fear caused the childbed fever.  In the Second Clinic, the priest delivering last rites could walk directly to a dying patient’s room.  For reasons of the layout of the rooms, the priest delivering last rites in the First Clinic walked by all the rooms, ringing a bell announcing his approach.  This frightened patients; they could not tell if the priest was coming for them.  Semmelweis arranged a different route for the priest and asked him to silence his bell.  He reasoned:  if the higher rate of childbed fever was caused by fear of death resulting from the priest’s approach, then the rate of childbed fever should decline if people could not tell when the priest was coming to the Clinic.  But it was not the case that the rate of childbed fever declined when people could not tell if the priest was coming to the First Clinic.  So, the higher rate of childbed fever in the First Clinic was not caused by fear of death resulting from the priest’s approach.

In the First Clinic, male doctors were trained; this was not true in the Second Clinic.  These male doctors performed autopsies across the hall from the clinic, before delivering babies.  Semmelweis knew of a doctor who cut himself while performing an autopsy, and who then died a terrible death not unlike that of the mothers who died of childbed fever.  Semmelweis formed a hypothesis.  The childbed fever was caused by something on the hands of the doctors, something that they picked up from corpses during autopsies, but that infected the women and infants.  He reasoned that:  if the fever was caused by cadaveric matter on the hands of the doctors, then the mortality rate would drop when doctors washed their hands with chlorinated water before delivering babies.  He forced the doctors to do this.  The result was that the mortality rate dropped to a rate below that even of the Second Clinic.

Semmelweis concluded that the best explanation of the higher mortality rate was this “cadaveric matter” on the hands of doctors.  He was the first person to see that washing of hands with sterilizing cleaners would save thousands of lives.  It is hard to overstate how important this contribution is to human well being.  Semmelweis’s fine reasoning deserves our endless respect and gratitude.

But how can we be sure his reasoning was good?  Semmelweis was essentially considering a series of arguments.  Let us turn to the question:  how shall we evaluate arguments?

3.2  Arguments

Our logical language now allows us to say conditional and negation statements.  That may not seem like much, but our language is now complex enough for us to develop the idea of using our logic not just to describe things, but also to reason about those things.

We will think of reasoning as providing an argument.  Here, we use the word “argument” not in the sense of two or more people criticizing each other, but rather in the sense we mean when we say, “Pythagoras’s argument”.  In such a case, someone is using language to try to convince us that something is true.  Our goal is to make this notion very precise, and then identify what makes an argument good.

We need to begin by making the notion of an argument precise.  Our logical language so far contains only sentences.  An argument will, therefore, consist of sentences.  In a natural language, we use the term “argument” in a strong way, which includes the suggestion that the argument should be good.  However, we want to separate the notion of a good argument from the notion of an argument, so we can identify what makes an argument good, and what makes an argument bad.  To do this, we will start with a minimal notion of what an argument is.  Here is the simplest, most minimal notion:

Argument:  an ordered list of sentences; we call one of these sentences the “conclusion”, and we call the other sentences “premises”.

This is obviously very weak.  (There is a famous Monty Python skit where one of the comedians ridicules the very idea that such a thing could be called an argument.)  But for our purposes, this is a useful notion because it is very clearly defined, and we can now ask, what makes an argument good?

The everyday notion of an argument is that it is used to convince us to believe something.  The thing that we are being encouraged to believe is the conclusion.  Following our definition of “argument”, the reasons that the person gives will be what we are calling “premises”.  But belief  is a psychological notion.  We instead are interested only in truth.  So, we can reformulate this intuitive notion of what an argument should do, and think of an argument as being used to show that something is true.  The premises of the argument are meant to show us that the conclusion is true.

What then should be this relation between the premises and the conclusion?  Intuitive notions include that the premises should support the conclusion, or corroborate the conclusion, or make the conclusion true.  But “support” and “corroborate” sound rather weak, and “make” is not very clear.  What we can use in their place is a stronger standard: let us say as a first approximation that if the premises are true, the conclusion is true.

But even this seems weak, on reflection.  For, the conclusion could be true by accident, for reasons unrelated to our premises.  Remember that we define the conditional as true if the antecedent and consequent are true.  But this could happen by accident.  For example, suppose I say, “If Tom wears blue then he will get an A on the exam”.  Suppose also that Tom both wears blue and Tom gets an A on the exam.  This makes the conditional true, but (we hope) the color of his clothes really had nothing to do with his performance on the exam.  Just so, we want our definition of “good argument” to be such that it cannot be an accident that the premises and conclusion are both true.

A better and stronger standard would be that, necessarily, given true premises, the conclusion is true.

This points us to our definition of a good argument.  It is traditional to call a good argument “valid.”

Valid argument:  an argument for which, necessarily, if the premises are true, then the conclusion is true.

This is the single most important principle in this book.  Memorize it.

A bad argument is an argument that is not valid.  Our name for this will be an “invalid argument”.

Sometimes, a dictionary or other book will define or describe a “valid argument” as an argument that follows the rules of logic.  This is a hopeless way to define “valid”, because it is circular in a pernicious way:  we are going to create the rules of our logic in order to ensure that they construct valid arguments.  We cannot make rules of logical reasoning until we know what we want those rules to do, and what we want them to do is to create valid arguments.  So “valid” must be defined before we can make our reasoning system.

Experience shows that if a student is to err in understanding this definition of “valid argument”, he or she will typically make the error of assuming that a valid argument has all true premises.  This is not required.  There are valid arguments with false premises and a false conclusion.  Here’s one:

If Miami is the capital of Kansas, then Miami is in Canada.  Miami is the capital of Kansas.  Therefore, Miami is in Canada.

This argument has at least one false premise:  Miami is not the capital of Kansas.  And the conclusion is false:  Miami is not in Canada.  But the argument is valid:  if the premises were both true, the conclusion would have to be true.  (If that bothers you, hold on a while and we will convince you that this argument is valid because of its form alone.  Also, keep in mind always that “if…then…” is interpreted as meaning the conditional.)

Similarly, there are invalid arguments with true premises, and with a true conclusion.  Here’s one:

If Miami is the capital of Ontario, then Miami is in Canada.  Miami is not the capital of Ontario.  Therefore, Miami is not in Canada.

(If you find it confusing that this argument is invalid, look at it again after you finish reading this chapter.)

Validity is about the relationship between the sentences in the argument.  It is not a claim that those sentences are true.

Another variation of this confusion seems to arise when we forgot to think carefully about the conditional.  The definition of valid is not “All the premises are true, so the conclusion is true.”  If you don’t see the difference, consider the following two sentences.  “If your house is on fire, then you should call the fire department.”  In this sentence, there is no claim that your house is on fire.  It is rather advice about what you should do if your house is on fire.  In the same way, the definition of valid argument does not tell you that the premises are true.  It tells you what follows if they are true.  Contrast now, “Your house is on fire, so you should call the fire department”.  This sentence delivers very bad news.  It is not a conditional at all.  What it really means is, “Your house is on fire and you should call the fire department”.  Our definition of valid is not, “All the premises are true and the conclusion is true”.

Finally, another common mistake is to confuse true  and valid .  In the sense that we are using these terms in this book, only sentences can be true or false, and only arguments can be valid and invalid.  When discussing and using our logical language, it is nonsense to say, “a true argument”, and it is nonsense to say, “a valid sentence”.

Someone new to logic might wonder, why would we want a definition of “good argument” that does not guarantee that our conclusion is true?  The answer is that logic is an enormously powerful tool for checking arguments, and we want to be able to identify what the good arguments are, independently of the particular premises that we use in the argument.  For example, there are infinitely many particular arguments that have the same form as the valid argument given above.  There are infinitely many particular arguments that have the same form as the invalid argument given above.  Logic lets us embrace all the former arguments at once, and reject all those bad ones at once.

Furthermore, our propositional logic will not be able to tell us whether an atomic sentence is true.  If our argument is about rocks, we must ask the geologist if the premises are true.  If our argument is about history, we must ask the historian if the premises are true.  If our argument is about music, we must ask the music theorist if the premises are true.  But the logician can tell the geologist, the historian, and the musicologist whether her arguments are good or bad, independent of the particular premises.

We do have a common term for a good argument that has true premises.  This is called “sound”.  It is a useful notion when we are applying our logic.  Here is our definition:

Sound argument:  a valid argument with true premises.

A sound argument must have a true conclusion, given the definition of “valid”.

3.3  Checking arguments semantically

Every element of our definition of “valid” is clear except for one.  We know what “if…then…” means.  We defined the semantics of the conditional in chapter 2.  We have defined “argument”, “premise”, and “conclusion”.  We take true and false as primitives.  But what does “necessarily” mean?

We define a valid argument as one where, necessarily, if the premises are true, then the conclusion is true.  It would seem the best way to understand this is to say, there is no situation in which the premises are true but the conclusion is false.  But then, what are these “situations”?  Fortunately, we already have a tool that looks like it could help us:  the truth table.

Remember that in the truth table, we put on the bottom left side all the possible combinations of truth values of some set of atomic sentences.  Each row of the table then represents a kind of way the world could be.  Using this as a way to understand “necessarily”, we could rephrase our definition of valid to something like this, “In any kind of situation in which all the premises are true, the conclusion is true.”

Let’s try it out.  We will need to use truth tables in a new way:  to check an argument.  That will require having not just one sentence, but several on the truth table.  Consider an argument that looks like it should be valid.

If Jupiter is more massive than Earth, then Jupiter has a stronger gravitational field than Earth.  Jupiter is more massive than Earth.  In conclusion, Jupiter has a stronger gravitational field than Earth.

This looks like it has the form of a valid argument, and it looks like an astrophysicist would tell us it is sound.  Let’s translate it to our logical language using the following translation key.  (We’ve used up our letters, so I’m going to start over.  We’ll do that often:  assume we are starting a new language each time we translate a new set of problems or each time we consider a new example.)

P :  Jupiter is more massive than Earth

Q :  Jupiter has a stronger gravitational field than Earth.

This way of writing out sentences of logic and sentences of English we can call a “translation key”.  We can use this format whenever we want to explain what our sentences mean in English.

Using this key, our argument would be formulated

That short line is not part of our language, but rather is a handy tradition.  When quickly writing down arguments, we write the premises, and then write the conclusion last, and draw a short line above the conclusion.

This is an argument:  it is an ordered list of sentences, the first two of which are premises and the last of which is the conclusion.

To make a truth table, we identify all the atomic sentences that constitute these sentences.  These are P  and Q .  There are four possible kinds of ways the world could be that matter to us then:

We’ll write out the sentences, in the order of premises and then conclusion.

Now we can fill in the columns for each sentence, identifying the truth value of the sentence for that kind of situation.

We know how to fill in the column for the conditional because we can refer back to the truth table used to define the conditional, to determine what its truth value is when the first part and second part are true; and so on.   P  is true in those kinds of situations where P  is true, and P  is false in those kinds of situations where P  is false.  And the same is so for Q .

Now, consider all those kinds of ways the world could be such that all the premises are true.  Only the first row of the truth table is one where all the premises are true.  Note that the conclusion is true in that row.  That means, in any kind of situation in which all the premises are true, the conclusion will be true.  Or, equivalently: necessarily, if all the premises are true, then the conclusion is true.

Consider in contrast the second argument above, the invalid argument with all true premises and a true conclusion.  We’ll use the following translation key.

R :  Miami is the capital of Ontario

S :  Miami is in Canada

And our argument is thus

Here is the truth table.

Note that there are two kinds of ways that the world could be in which all of our premises are true.  These correspond to the third and fourth row of the truth table.  But for the third row of the truth table, the premises are true but the conclusion is false.  Yes, there is a kind of way the world could be in which all the premises are true and the conclusion is true; that is shown in the fourth row of the truth table.  But we are not interested in identifying arguments that will have true conclusions if we are lucky.  We are interested in valid arguments.  This argument is invalid.  There is a kind of way the world could be such that all the premises are true and the conclusion is false.  We can highlight this.

Hopefully it becomes clear why we care about validity.  Any argument of the form, (P→Q)  and P , therefore Q , is valid.  We do not have to know what P  and Q  mean to determine this. Similarly, any argument of the form, (R→S)  and ¬R , therefore ¬S , is invalid.  We do not have to know what R  and S  mean to determine this.  So logic can be of equal use to the astronomer and the financier, the computer scientist or the sociologist.

3.4 Returning to our historical example

We described some (not all) of the hypotheses that Semmelweis tested when he tried to identify the cause of childbed fever, so that he could save thousands of women and infants.  Let us symbolize these and consider his reasoning.

The first case we considered was one where he reasoned:  If childbed fever is caused by cosmic-atmospheric-terrestrial influences, then the mortality rate would be similar in the First and Second Clinics.  But the mortality rate was not similar in the First and Second Clinics.  So, the childbed fever is not caused by cosmic-atmospheric-terrestrial influences.

Here is a key to symbolize the argument.

T:   Childbed fever is caused by cosmic-atmospheric-terrestrial influences.

U:   The mortality rate is similar in the First and Second Clinics.

This would mean the argument is:

Is this argument valid?  We can check using a truth table.

The last row is the only row where all the premises are true.  For this row, the conclusion is true.  Thus, for all the kinds of ways the world could be in which the premises are true, the conclusion is also true.  This is a valid argument.  If we accept his premises, then we should accept that childbed fever was not caused by cosmic-atmospheric-terrestrial influences.

The second argument we considered was the concern that fear caused the higher mortality rates, particularly the fear of the priest coming to deliver last rites.  Semmelweis reasoned that if the higher rate of childbed fever is caused by fear of death resulting from the priest’s approach, then the rate of childbed fever should decline if people cannot discern when the priest is coming to the Clinic.  Here is a key:

V:   the higher rate of childbed fever is caused by fear of death resulting from the priest’s approach.

W:   the rate of childbed fever will decline if people cannot discern when the priest is coming to the Clinic.

But when Semmelweis had the priest silence his bell, and take a different route, so that patients could not discern that he was coming to the First Clinic, he found no difference in the mortality rate; the First Clinic remained far worse than the second clinic.  He concluded that the higher rate of childbed fever was not caused by fear of death resulting from the priest’s approach.

Again, we see that Semmelweis’s reasoning was good.  He showed that it was not the case that the higher rate of childbed fever was caused by fear of death resulting from the Priest’s approach.

What about Semmelweis’s positive conclusion, that the higher mortality rate was caused by some contaminant from the corpses that doctors had autopsied just before they assisted in a delivery?  To understand this step in his method, we need to reflect a moment on the scientific method and its relation to logic.

3.5  Other kinds of arguments 1:  Scientific reasoning

Valid arguments, and the methods that we are developing, are sometimes called “deductive reasoning”.  This is the kind of reasoning in which necessarily our conclusions is true if our premises are true; these arguments can be shown to be good by way of our logical reasoning alone.  There are other kinds of reasoning, and understanding this may help clarify the relation of logic to other endeavors.  Two important, and closely related, alternatives to deductive reasoning are scientific reasoning and statistical generalizations.  We’ll discuss statistical generalizations in the next section.

Scientific method relies upon logic, but science is not reducible to logic:  scientists do empirical research.  That is, they examine and test phenomena in the world.  This is a very important difference from pure logic.  To understand how this difference results in a distinct method, let us review Semmelweis’s important discovery.

The details and nature of scientific reasoning are somewhat controversial.  I am going to provide here a basic—many philosophers would say, oversimplified—account of scientific reasoning.  My goal is to indicate the relation between logic and the kind of reasoning Semmelweis may have used.

As we noted, Semmelweis learned about the death of a colleague, Professor Jakob Kolletschka.  Kolletschka had been performing an autopsy, and he cut his finger.  Shortly thereafter, Kolletschka died with symptoms like those of childbed fever.  Semmelweis reasoned that something on the corpse caused the disease; he called this “cadaveric matter”.  In the First Clinic, where the mortality rate of women and babies was high, doctors were doing autopsies and then delivering babies immediately after.  If he could get this cadaveric matter off the hands of the doctors, the rate of childbed fever should fall.

So, he reasoned thus:  if the fever is caused by cadaveric matter on the hands of the doctors, then the mortality rate will drop when doctors wash their hands with chlorinated water before delivering babies.  He forced the doctors to do this.  The result was that the mortality rate dropped a very great deal, at times to below 1%.

Here is a key:

P:   The fever is caused by cadaveric matter on the hands of the doctors.

Q:   The mortality rate will drop when doctors wash their hands with chlorinated water before delivering babies.

And the argument appears to be something like this (as we will see, this isn’t quite the right way to put it, but for now…):

From this, it looks like Semmelweis has used an invalid argument!

However, an important feature of scientific reasoning must be kept in mind.  There is some controversy over the details of the scientific method, but the most basic view goes something like this.  Scientists formulate hypotheses about the possible causes or features of a phenomenon.  They make predictions based on these hypotheses, and then they perform experiments to test those predictions.  The reasoning here uses the conditional:  if the hypotheses is true, then the particular prediction will be true.  If the experiment shows that the prediction is false, then the scientist rejects the hypothesis. [6]   But if the prediction proved to be true, then the scientist has shown that the hypothesis may be true—at least, given the information we glean from the conditional and the consequent alone.

This is very important.  Scientific conclusions are about the physical world, they are not about logic.  This means that scientific claims are not necessarily true, in the sense of “necessarily” that we used in our definition of “valid”.  Instead, science identifies claims that may be true, or (after some progress) are very likely to be true, or (after very much progress) are true.

Scientists keep testing their hypotheses, using different predictions and experiments.  Very often, they have several competing hypotheses that have, so far, survived testing.  To decide between these, they can use a range of criteria.  In order of their importance, these include:  choose the hypothesis with the most predictive power (the one that correctly predicts more kinds of phenomena); choose the hypothesis that will be most productive of other scientific theories; choose the hypothesis consistent with your other accepted hypotheses; choose the simplest hypothesis.

What Semmelweis showed was that it could be true that cadaveric matter caused the childbed fever.  This hypothesis predicted more than any other hypothesis that the doctors had, and so for that reason alone this was the very best hypothesis.  “But,” you might reason, “doesn’t that mean his conclusion was true?  And don’t we know now, given all that we’ve learned, that his conclusion must be true?”  No.  He was far ahead of other doctors, and his deep insights were of great service to all of humankind.  But the scientific method continued to refine Semmelweis’s ideas.  For example, later doctors introduced the idea of microorganisms as the cause of childbed fever, and this refined and improved Semmelweis’s insights:  it was not because the cadaveric matter came from corpses that it caused the disease; it was because the cadaveric matter contained particular micro-organisms that it caused the disease.  So, further scientific progress showed his hypothesis could be revised and improved.

To review and summarize, with the scientific method:

• We develop a hypothesis about the causes or nature of a phenomenon.
• We predict what (hopefully unexpected) effects are a consequence of this hypothesis.
• We check with experiments to see if these predictions come true:
• If the predictions prove false, we reject the hypothesis; [7]
• If the predictions prove true, we conclude that the hypothesis could be true.  We continue to test the hypothesis by making other predictions (that is, we return to step 2).

This means that a hypothesis that does not make testable predictions (that is, a hypothesis that cannot possibly be proven false) is not a scientific hypothesis.  Such a hypothesis is called “unfalsifiable” and we reject it as unscientific.

This method can result in more than one hypothesis being shown to be possibly true.  Then, we chose between competing hypotheses by using criteria like the following (here ordered by their relative importance; “theory” can be taken to mean a collection of one or more hypotheses):

• Predictive power: the more that a hypothesis can successfully predict, the better it is.
• Productivity:  a hypothesis that suggests more new directions for research is to be preferred.
• Coherence with Existing Theory: if two hypotheses predict the same amount and are equally productive, then the hypothesis that coheres with (does not contradict) other successful theories is preferable to one that does contradict them.
• Simplicity: if two hypotheses are equally predictive, productive, and coherent with existing theories, then the simpler hypothesis is preferable.

Out of respect to Ignaz Semmelweis we should tell the rest of his story, although it means we must end on a sad note.  Semmelweis’s great accomplishment was not respected by his colleagues, who resented being told that their lack of hygiene was causing deaths.  He lost his position at the First Clinic, and his successors stopped the program of washing hands in chlorinated water.  The mortality rate leapt back to its catastrophically high levels.  Countless women and children died.  Semmelweis continued to promote his ideas, and this caused growing resentment.  Eventually, several doctors in Vienna—not one of them a psychiatrist—secretly signed papers declaring Semmelweis insane.  We do not know whether Semmelweis was mentally ill at this time.  These doctors took him to an asylum on the pretense of having him visit in his capacity as a doctor; when he arrived, the guards seized Semmelweis.  He struggled, and the guards at the asylum beat him severely, put him in a straightjacket, and left him alone in a locked room.  Neglected in isolation, the wounds from his beating became infected and he died a week later.

It was years before Semmelweis’s views became widely accepted and his accomplishment properly recognized.  His life teaches many lessons, including unfortunately that even the most educated among us can be evil, petty, and willfully ignorant.  Let us repay Semmelweis, as those in his own time did not, by remembering and praising his scientific acumen and humanity.

3.6 Other kinds of arguments 2:  Statistical reasoning

Here we can say a few words about statistical generalizations—our goal being only to provide a contrast with deductive reasoning.

In one kind of statistical generalization, we have a population of some kind that we want to make general claims about.  A population could be objects or events.  So, a population can be a group of organisms, or a group of weather events.  “Population” just means all the events or all the things we want to make a generalization about.  Often however it is impossible to examine every object or event in the population, so what we do is gather a sample.  A sample is some portion of the population.  Our hope is that the sample is representative of the population:  that whatever traits are shared by the members of the sample are also shared by the members of the population.

For a sample to representative, it must be random and large enough.  “Random” in this context means that the sample was not chosen in any way that might distinguish members of the sample from the population, other than being members of the population.  In other words, every member of the population was equally likely to be in the sample.  “Large enough” is harder to define.  Statisticians have formal models describing this, but suffice to say we should not generalize about a whole population using just a few members.

Here’s an example.  We wonder if all domestic dogs are descended from wolves.  Suppose we have some genetic test to identify if an organism was a descendent of wolves.  We cannot give the test to all domestic dogs—this would be impractical and costly and unnecessary.  We pick a random sample of domestic dogs that is large enough, and we test them.  For the sample to be random, we need to select it without allowing any bias to influence our selection; all that should matter is that these are domestic dogs, and each member of the population must have an equal chance of being in the sample.  Consider the alternative:  if we just tested one family of dogs—say, dogs that are large—we might end up selecting dogs that differed from others in a way that matters to our test.  For example, maybe large dogs are descended from wolves, but small dogs are not.  Other kinds of bias can creep in less obviously.  We might just sample dogs in our local community, and it might just be that people in our community prefer large dogs, and again we would have a sample bias.  So, we randomly select dogs, and give them the genetic test.

Suppose the results were positive.  We reason that if all the members of the randomly selected and large enough sample (the tested dogs) have the trait, then it is very likely that all the members of the population (all dogs) have the trait.  Thus: we could say that it appears very likely that all dogs have the trait.  (This likelihood can be estimated, so that we can also sometimes say how likely it is that all members of the population have the trait.)

This kind of reasoning obviously differs from a deductive argument very substantially.  It is a method of testing claims about the world, it requires observations, and its conclusion is likely instead of being certain.

But such reasoning is not unrelated to logic.  Deductive reasoning is the foundation of these and all other forms of reasoning.  If one must reason using statistics in this way, one relies upon deductive methods always at some point in one’s arguments.  There was a conditional at the penultimate step of our reasoning, for example (we said “if all the members of the randomly selected and large enough sample have the trait, then it is very likely that all the members of the population have the trait”).  Furthermore, the foundations of these methods (the most fundamental descriptions of what these methods are) are given using logic and mathematics.  Logic, therefore, can be seen as the study of the most fundamental form of reasoning, which will be used in turn by all other forms of reasoning, including scientific and statistical reasoning.

3.7  Problems

• Make truth tables to show that the following arguments are valid.  Circle or highlight the rows of the truth table that show the argument is valid (that is, all the rows where all the premises are true).  Note that you will need eight rows in the truth table for problems d-f, and sixteen rows in the truth table for problems g and h.
• Premises:   (P→Q) , ¬Q . Conclusion:   ¬P .
• Premises:   ¬P . Conclusion: (P→Q) .
• Premises:   Q . Conclusion: (P→Q) .
• Premises:   (P→Q) , (Q→R) . Conclusion:   (P→R) .
• Premises:   (P → Q) , (Q → R) , P . Conclusion:   R .
• Premises:   (P → Q) , (Q → R) , ¬ R . Conclusion:   ¬ P .
• Premises:   (P→Q) , (Q→R) , (R→S) , P . Conclusion:   S .
• Premises:   (P→Q) , (Q→R) , (R→S) . Conclusion:   (P→S) .
• Make truth tables to show the following arguments are invalid. Circle or highlight the rows of the truth table that show the argument is invalid (that is, any row where all the premises are true but the conclusion is false).
• Premises:   (P→Q) . Conclusion:   P .
• Premises:   (P→Q) . Conclusion:   Q .
• Premises:   P . Conclusion:   (P→Q) .
• Premises:   (P→Q) , Q . Conclusion:   P .
• Premises:   ¬Q . Conclusion: (P→Q) .
• Premises:  (P→Q) . Conclusion: (Q→P) .
• Premises:   (P→Q) , (Q→R) , ¬P . Conclusion:   ¬R .
• Premises:   (P→Q) , (Q→R) , R . Conclusion:   P .
• Premises:   (P→Q) , (Q→R) . Conclusion:   (R→P) .
• Premises:   (P→Q) , (Q→R) , (R→S) . Conclusion:   (S→P) .
• In normal colloquial English, write your own valid argument with at least two premises. Your argument should just be a paragraph (not an ordered list of sentences or anything else that looks like logic).  Translate it into propositional logic and use a truth table to show it is valid.
• In normal colloquial English, write your own invalid argument with at least two premises.  Translate it into propositional logic and use a truth table to show it is invalid.
• For each of the following, state whether the argument described could be: valid, invalid, sound, unsound.
• An argument with false premises and a false conclusion.
• An argument with true premises and a false conclusion.
• An argument with false premises and a true conclusion.
• An argument with true premises and a true conclusion.

[5]  All the data cited here comes from Carter (1983) and additional biographical information comes from Carter and Carter (2008).  These books are highly recommended to anyone interested in the history of science or medicine.

[6]  It would be more accurate to say, if the prediction proves false, the scientist must reject either the hypothesis or some other premise of her reasoning.  For example, her argument may include the implicit premise that her scientific instruments were operating correctly.  She might instead reject this premise that her instruments are working correctly, change one of her instruments, and try again to test the hypothesis.  See Duhem (1991).  Or, to return to the case of Semmelweis, he might wonder whether he sufficiently established that there were no differences in the atmosphere between the two clinics; or he might wonder whether he sufficiently muffled the Priest’s approach; or whether he recorded his results accurately; and so on.  As noted, my account of scientific reasoning here is simplified.

[7]  Or, as noted in note 6, we reject some other premise of the argument.

A Concise Introduction to Logic Copyright © 2017 by Craig DeLancey is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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An Introduction to Reasoning

1 Reasoning and Argument

Section 1: introduction.

We spend a lot of time trying to figure things out, and we do so primarily by means of reason.  For example, we try to predict what will happen, explain what has already occurred, generalize from our experiences, and extrapolate from what we know.  While we are sometimes interested in abstract questions, most of the time we put our reasoning skills to work on entirely practical matters.  We have goals, plans, and interests, and being able to accurately predict, explain, generalize on, and extrapolate from, our experiences are crucial skills for achieving our goals.  Indeed, we all know how to reason.  We do it all the time, and it is something we are relatively good at doing.  Nevertheless, reasoning is also something that we can improve on, and sharpening our skills can have dramatic effects on our beliefs and decisions. In this chapter we will start by defining reasoning and explaining how it relates to arguments.  We will then briefly introduce two important skills: argument analysis and argument evaluation.  Along the way, we will begin building a vocabulary for thinking about and developing these skills.

Section 2: What is Reasoning?

We reason all the time, but what are we doing exactly?  This answer might not be immediately obvious, so let’s begin with some straightforward cases to see what they have in common.

• Solving a math problem
• Figuring out why your phone won’t work correctly
• Deciding who to vote for
• Working out why your friend is angry with you
• Determining whether you can afford to buy a new car

What do these have in common?  We could pick out a number of features, but we will focus on two in particular.  First, in each case our thinking is driving toward a specific outcome or conclusion (e.g. “my phone won’t work because…”, or “the answer is…”, etc.).  Second, in each one of these cases this conclusion will be based on reasons.  That is, we will arrive at a specific conclusion because we think we have good reasons for doing so.  Let us take a closer look at each of these features.

Reasoning is a mental process that ends with a conclusion.  Sometimes this conclusion is a newly formed belief.  You might, for example, be asked to find the average of 88, 69, 94, and 77 and arrive at the new belief that the average of these numbers is 82.  Alternatively, you might troubleshoot your phone and arrive at the new belief that the operating system wasn’t properly installed. While reasoning always leads to a conclusion, that conclusion need not be a new belief.  In some cases, these processes lead us to be more (or less) confident in beliefs we already hold.  We can see both kinds of conclusion at work in the following example.

Ex. 1: Talia wakes up one morning to discover that her car is missing.  As she thinks about it she quickly concludes that her brother has probably borrowed it.  Her reasons for drawing this conclusion are that he i) knows where her spare set of keys are, ii) has borrowed it without asking in the past, and iii) is supposed to pick up a cake at a bakery across town today.  Just after she has come to this conclusion the phone rings.  It is one of Talia’s friends who mentions that she saw Talia’s car parked at the bakery across town.

In the first part of Ex. 1 Talia is reasoning to a new belief, namely that her brother has borrowed her car.  When her friend calls, she gets a new piece of information.  However, this information does not lead her to any new belief; after all, this information is an additional reason for thinking that her brother has borrowed the car, and she already believes that.  Instead, as a result of this news, she is even more confident that her brother has borrowed the car.  In light of this distinction, we will say that reasoning is a process that leads to a change in a person’s system of belief, and we will understand a person’s system of belief to include not only their beliefs, but also the relationships between those beliefs, and the confidence with which they are held.

The second defining feature of reasoning is that it is a process whereby we change our system of beliefs because we have reasons for doing so.  In general, to have reasons for drawing some conclusion is to have some group of existing beliefs that indicate in one way or another that the conclusion in question is true.  In the example above, Talia has a variety of existing beliefs about her brother and his circumstances, and she takes this information to point toward the fact that her brother has borrowed the car.

Importantly, our reasons can indicate the truth of the conclusion to different degrees.  When we take ourselves to have solved a math problem correctly, for example, we take ourselves to have shown that the conclusion is correct.  This is a bit different from Talia’s reasoning—she probably wouldn’t say that her reasons show or prove that her brother borrowed the car.  Nonetheless, she thinks that her reasons are good enough to draw the conclusion.  In general, reasons can support conclusions with different degrees of strength, and it should be no surprise that we have many different ways of talking about this support.  We can say, for example, that when we reason we take our existing beliefs to indicate , give good reason for , offer evidence on behalf of, establish , warrant, or demonstrate a change to our system of beliefs.  These differences will be important later, but for now we will simply say that when we reason, we take our existing beliefs to justify a particular change in our system of belief.

Now that we have taken a brief look at the reasoning process, we can return to the question we began with and define reasoning as follows:

Reasoning is the process whereby a person changes their system of belief on the basis of reasons which they take to justify this change.

Section 3: Types of Reasoning

We have just arrived at a definition of reasoning, but it is important to note that this definition captures only one kind of reasoning.  Over the last 20-30 years, psychologists and cognitive scientists have come to the conclusion that we use a variety of different methods and mechanisms to update our system of beliefs.  Some of these methods involve conscious directed attention, but many do not.  Here is the basic idea: many of the things that humans do are automatic and do not involve conscious control.  We do not, for example, need to tell ourselves to breathe or blink (although we can).  Moreover, it is not just physical activity that can be automatic; mental activities can occur automatically as well.  Take recognition for example.  You do not decide to recognize people—it is something you automatically do.  The same goes for laughing.  You do not need to think about laughing—it is often an automatic reaction (though sometimes events can become funny as you think about them).  Cognitive scientists and psychologists now think that, in addition, there are a variety of automatic and semi-automatic reasoning processes.  These processes update our systems of belief in ways that are often outside of any conscious effort or awareness.

In order to get a sense for different kinds of reasoning processes, consider the following example. [1]   In answering this question make sure to note the first answer that comes to mind.  Then stop and think about it a little more.

Ex. 2: A bat and ball cost $1.10 in total.  The bat costs $1.00 more than the ball.  How much does the ball cost? First Answer that Occurs to You: _________________. Considered Answer:_________________.

Most people read this question and a particular answer just pops into their heads.  This answer appears immediately to them, without any particular effort.  However, if you take a closer look at this automatic answer, you will see that it can’t be right, and figuring out the actual answer to this question takes some work (follow this note if you need some help). [2]   The way the question in Ex. 2 is structured triggers in many people an automatic reasoning mechanism which gives an answer that our conscious reasoning system subsequently recognizes as wrong.

In this case, a largely automatic process leads us to make a mistake.  But this is not always the case; in fact, we rely on reasoning processes like this all of the time.  As we navigate through the world we automatically and reliably respond to our environment, and we will see that these kinds of reasoning processes naturally generate intuitive reactions to, and impressions of, people, places, circumstances, and ideas (among other things).  These intuitions and impressions contribute to our system of belief, and can thereby inform successive conscious forms of reasoning.

In this book, we will primarily address consciously directed reasoning, since this is the kind of reasoning over which we have the most control.  Nonetheless, we cannot ignore other types of reasoning processes.  These processes are pervasive features of our thinking and inform our conscious judgments and decisions both positively and negatively. Given this, it is important to know when to be skeptical of the impressions and intuitions that these processes give us.  As such, if we want to think more clearly and make better choices, we will have to take these kinds of processes into account.  Since we will be primarily discussing directed conscious reasoning, let us simply refer to this as “reasoning” in line with the definition given at the end of section 2.  When we need to talk about automatic reasoning processes we will explicitly identify them.

Section 4: From Reasoning to Argument

In thinking about reasoning more generally, we will focus our attention primarily on the investigation of arguments.  In order to illustrate the difference between reasoning and argument, we will need to start by talking in more detail about beliefs.  Normally, we would agree that two people can share a belief.  Consider, for example, the fact that both Maria and Jackson are enrolled in Economics 101, and so share the belief that the course is taught on Tuesdays and Thursdays from 2-3:15.  In what sense do they share this belief?  As we’ve seen, a belief is part of an individual’s system of belief, and so is a psychological state of that individual.  Maria’s beliefs are hers, and Jackson’s are his, and this means that in an important sense, Maria and Jackson do not have the same belief.  Rather, they share the belief insofar as their distinct beliefs are about the same thing, or have the same content.  The sharable content of a belief is called a proposition , and we will say that Maria and Jackson believe the same proposition, namely that Economics 101 is on Tuesdays and Thursdays from 2-3:15.   Making the distinction between a belief and its content is useful, at least in part, because it allows us to talk about the truth of the proposition without talking about any individual person.

This is relevant because there is a similar distinction between reasoning and argument.  Suppose that Maria and Jackson are sitting in their Economics class; at 2:05 they both look out the window and see their friend Logan, who is also enrolled in the course, speeding away from the building on his bike.  They both conclude that Logan is not coming to class.  Let’s compare their thinking.  On the one hand, Maria and Jackson have engaged in distinct reasoning processes.  After all, Maria’s reasoning had led her to update her system of belief, and Jackson’s reasoning has led him to update his.  Nevertheless, there is something common to their distinct reasoning processes.  They have both updated their systems of belief to include the same proposition, namely ‘Logan is not coming to class,’ on the basis of the same reasons, namely their respective beliefs in the propositions that ‘It is 2:05’ and ‘Logan is speeding away from the building’.  These distinct reasoning processes share the same content, and we will call the content of a process of reasoning, an argument.  That is, we will say that an argument is a collection of propositions in which one is purportedly justified by the others.  When we reason, we take our existing belief that one or more propositions are true (our reasons), to justify our belief that some other proposition is also true (our conclusion).  That is, we reason by means of arguments. Like the distinction between beliefs and propositions, drawing the distinction between reasoning and argument is useful because it allows us to evaluate a reasoning processes independently of who is engaging in it.

Section 5: Arguments and their Parts

When it comes to arguments, it is important to make two terminological distinctions.  First, the term ‘argument’ as it is defined above differs from another common sense of the term.  We often use the term ‘an argument’ to refer to a disagreement or a dispute.  This is not how we will be using the term.  Here is an example of a dispute that is not an argument as this book uses the term.

Ex. 3: Maria: Eating meat is irresponsible and unnecessary. Jackson: Are you crazy?  No it is not.

Why isn’t this disagreement an example of an argument?  The answer, in short, is because neither person has tried to justify what they are saying.  Presumably each person has reasons for thinking they are right, but as conversation stands all that has been publically expressed is a disagreement.  Compare Ex. 3 to the following.

Ex. 4: I bet the Phillies will win their game tonight since they are on a hot streak.

Ex. 5: I needed to get at least 90% of the points in this class to earn an A-.  Because I got 84%, I didn’t earn an A-.

Ex. 6: The choice for dinner is either lasagna or pizza.  The pizza is too gross to even consider eating.  I guess it’s lasagna for me!

Examples 4-6 are all arguments since, in each case, a reason is offered on behalf of a conclusion.  As these examples of argumentation show, arguments are common in everyday thinking and need not concern abstract or theoretical topics (although they certainly may).

A second terminological note is that all arguments have two parts—the premises and the conclusion.  The premises of an argument give reasons or evidence on behalf of the conclusion; put otherwise, premises are the pieces of information that back-up or justify the conclusion. The conclusion , on the other hand, is the proposition for which reasons or evidence are given, it is that proposition which is backed-up or justified.  We can label the parts of the arguments above accordingly:

Ex. 4: Premise—The Phillies are on a hot streak Conclusion—The Phillies will win their game tonight.

Ex. 5: Premise—I needed to have gotten at least 90% of the points in this class to get an A- Premise—I got 84% Conclusion—I won’t get an A-

Ex. 6: Premise—My choices are either lasagna or pizza. Premise—There is no way I can eat the pizza—it is always gross. Conclusion—I will be having lasagna.

With these terminological issues out of the way we can focus on arguments themselves.  First, although we reason by means of arguments, it is important to recognize that we often think and reason about arguments as well.  Here is an example:

Ex. 7: Maria says “I don’t buy the argument that since voting is a restricted activity, we should require IDs at the polls.”

Maria is considering the following argument:

Premise: Voting is a restricted activity. Conclusion: We should require IDs at the polls.

In this instance Maria is talking about an argument, but not making one herself.  Maria is claiming that one reason people sometimes give for thinking that we should require IDs at the polls is not, to her mind, a good one.

This raises a second point.  Arguments can be good or bad.  When we come to believe a conclusion on the basis of the premises we do so because we have judged that the premises justify or establish the conclusion.  But we can be wrong about this.  Sometimes arguments that we take to be good, are not.  In general terms, good arguments are arguments in which the premises establish their conclusion, whereas bad arguments are those in which the premises do not.  Correspondingly, we reason well when our beliefs are based on good arguments and we reason poorly when they are not.  Thus, in order to improve our reasoning, we will have to learn how to properly evaluate arguments.  Doing so is a two-step process.  Most obviously, we will need to learn how to distinguish between good arguments and bad ones.  This information is useless, however, if we cannot accurately identify and analyze arguments.  Put otherwise, you cannot accurately assess whether an argument is good or bad, if you don’t know what the premises are, and how they are related to the conclusion.  Let us take an introductory look at these two steps.

Section 6: An Introduction to Spotting Arguments

There are a number of words that authors and speakers use to indicate that they are making an argument.  We will call these words indicator words , since they typically indicate the presence of an argument.  Some words and phrases, like ‘since’, ‘because’, ‘for’, ‘on account of’, and ‘given that…’, specifically indicate the presence of a premise.

Ex. 8: There is no way the Spartans will make the playoffs this year, since they are 6 games back with less than two weeks to go.

Ex. 9: Given the suspect’s blood/alcohol level at the time of the accident, it is clear that she was driving over the legal limit.

Other words and phrases specifically indicate the presence of an argument’s conclusion: ‘thus’, ‘therefore’, ‘hence’, ‘so’, ‘consequently’.

Ex. 10: Malik doesn’t have any brothers or sisters; hence he is an only child.

Ex. 11: The number 8 is even; consequently , it is not a prime number.

We need to keep two qualifications in mind.  First, these brief lists include the most common indicator words, but there are many ways that authors and speakers can indicate the presence of an argument without using these terms.  Thus, we cannot merely memorize the terms above and be done with it.  Second, unfortunately indicator words do not always indicate the presence of an argument.  Consider the following:

Ex. 12: The marching band hasn’t gotten anything less than a #1 at contest since 2015.

In this case, the term ‘since’ is being used to refer to time, not to a premise.  Given that indicator words are not 100% reliable as indications of argumentation, we cannot infer that we have an argument merely because one of our indicator words shows up.  As we will see, we need to pay attention to the contexts in which these words are used.

There are a couple of common obstacles to spotting arguments we should note at the outset.  The first has to do with conditional claims.  As noted, an argument amounts to a set of propositions in which one proposition is supported by the others.  Propositions report a fact about the world and are either true or false, e.g. ‘Dogs are mammals’, ‘Yosemite is in California’, ‘Jordan’s mom is a lawyer’.  Presumably you get the point, but there is one kind of proposition that people often find confusing: conditionals.  What is a conditional?  To start off, let’s look at some examples:

Ex. 13: You are legally eligible to purchase alcoholic beverages in this state only if you are 21 years of age or older.

Ex. 14: If the candle is lit, then oxygen is present.

Ex. 15: You are not permitted to play poker at the Platinum table if you are not willing to bet at least $20 per hand.

What do all of these propositions have in common?  While we might identify a number of features, the most important for our purposes is that each expresses a relationship between two things.  More specifically, each tells us that one thing is dependent or conditional in some way on another thing: a burning candle depends on oxygen, playing at the Platinum table is conditional on betting $20 per hand, and so forth.  In very general terms, this is what a conditional is—a proposition that says that one thing is dependent on another (more on this later though).  Part of what makes thinking about conditionals difficult is that we are used to thinking about objects and their characteristics, but less so about the relations between them.  Nevertheless, relations are just as much a part of the world as anything else.

There is a lot to say about conditionals, but for the time being we will focus on two noteworthy features of conditionals in particular.  First, as you can see there are many ways that conditionals can be expressed, though it is very common to use the word ‘if’.  Second, because conditional claims express a relation between two or more things, they commonly appear in arguments about the things they relate.   You might conclude, for example, that you are not permitted to play poker at the Platinum table, since you aren’t willing to bet $20 per hand, and this is a requirement for playing at that table.

A second obstacle to spotting arguments has to do with opinions.   Suppose somebody says “teens really shouldn’t be watching R-rated movies, since for the most part they  are not mature enough to handle the psychological and emotional effects of mature content.”  Is this an argument?  Many people are tempted to say ‘no’—this is just an opinion.  When we use ‘opinion’ in this way, we are identifying an idea or claim as particularly controversial, uncertain, or debatable.  Understood in this sense the claim that “teens really shouldn’t be watching R-rated movies” is an opinion, whereas something like “The bookshelf weighs 80 lbs.” is not.  After all, the weight of the bookshelf should not be controversial or debatable—we can use objective and commonly agreed upon methods to determine its weight.

We need to be aware, however, that whether a statement is controversial or debatable is not relevant to whether there is an argument present.  Recall that anytime a speaker or author gives a reason to believe a conclusion, they have given an argument—regardless whether anything the author has said or written is controversial, uncertain, or debatable.  In the example above, the speaker uses the word ‘since’ to indicate the presence of a premise, and consequently, the presence of an argument.  So: whether somebody’s claim is an opinion won’t tell us anything about whether they have offered an argument.  In fact, often controversial, uncertain, and debatable claims are precisely the sort of thing that people offer arguments for!

Section 7: Evaluating Arguments

Last, let us turn to the most important topic this book will take up: argument evaluation.  To evaluate an argument is to decide whether it is good or bad.  We have an intuitive ability to evaluate arguments—we can usually distinguish good arguments from bad ones just by looking at them.  This native ability is not, however, infallible; in fact, there are certain contexts and kinds of cases where we tend to make mistakes.  Thus it is important to ask: what is the difference between a good argument and a bad one?  Put otherwise, we need to know what makes a good argument, good, and a bad argument, bad.  Let us start with an example.

Ex. 16: Premise: The largest city in the U.S. is located in Nebraska. Premise: New York City is the largest city in the U.S. Conclusion:  So, New York City is located in Nebraska.

Clearly this is a bad argument.  The problem is that one of its premises is false—we know that the largest city in the U.S. is not in the state of Nebraska.  This example shows one way in which an argument can be bad: when it has false premises.  Let us say the following:

An argument is factually correct when (and only when) all of its premises are true.  It is factually incorrect otherwise.

Thus, the argument in Ex. 16 is factually incorrect because not all of its premises are true.  In addition, whether an argument is factually correct or not is solely a matter of whether the premises are true—an argument with all true premises but a false conclusion is still factually correct.  Factual correctness is not, however, the only feature of an argument relevant to its evaluation.  Consider the following case.

Ex. 17: Premise: Selena passed her driver’s license exam. Conclusion: So, Selena will pass her calculus exam.

Let us say that it is true that Selena passed her driver’s license exam.  Even so, clearly this is a bad argument.  This is a poor argument because the premise does not support the truth of the conclusion.  That is, the premise, though true, does not give us good or sufficient reason to believe the conclusion is true.  We will refer to this feature of arguments as logical strength and say:

An argument is logically strong when (and only when) the premises—if true—provide strong support for the truth of the conclusion.  An argument is logically weak otherwise.

It is crucial to see that these features of arguments are independent of one another.  An argument may be factually incorrect, but logically strong (see, e.g. Ex. 16), factually correct, but logically weak (Ex. 17), both correct and strong, or both incorrect and weak.  In light of these distinctions we can distinguish good arguments from bad ones in the following way.  Let us say that:

An argument is good, henceforth sound , when (and only when) it is both factually correct and logically strong.  An argument is unsound otherwise.

Ideally, all of our reasoning would proceed by means of sound arguments.  However, we are always working with limited information, and this means that we all sometimes endorse unsound arguments.  Nevertheless, as we will see in this text, we can take steps to limit these kinds of cases.

Exercise Set 1A :

Directions: For each of the following passages, determine whether either speaker is giving an argument or whether the speakers are merely having a dispute.

A: We should go to Drew’s place tonight.

B: Um, no.  We should avoid Drew’s place like the plague.

A: Obama is our worst president!

B: What are you talking about?  Our “worst president”?  Do you even know what that means?

A: Many peer-reviewed studies have shown that asbestos is a carcinogen.

B: These studies can’t be right, since my uncle worked in an asbestos mine for 40 years and didn’t get cancer.

A: Minneapolis has about the same population as Indianapolis.

B: No it doesn’t, my dad told me that Indianapolis is much bigger.

Exercise Set 1B :

Directions: For each of the following passages, determine whether there is an indicator word(s) present and if so, identify it.

People who can’t speak Russian are excluded from this opportunity, so you can’t come.

The first inhabitants of the island were Dutch settlers.  The next wave of settlers were mainly from Italy and Greece.

There are two main reasons for rejecting this option—first, it is immoral; second, it doesn’t achieve what we are actually trying to do!

Seeing as it has air conditioning, I think you should count yourself lucky to live in that dorm.

Exercise Set 1C:

Directions: Determine whether each of the following arguments is sound or not.  If unsound, then say whether it is factually incorrect, logically weak, or both.

Premise: There are exactly 52 states that make up the United States.

Conclusion: So, if I’ve only been to 50 states, then I haven’t been to them all.

Premise: All squares are rectangles.

Premise: No rectangles are circles.

Conclusion: So some squares are circles.

Premise: The word ‘since’ always indicates the presence of an argument.

Conclusion: So, the claim “ the marching band hasn’t gotten anything less than a #1 at contest since 2015 ” is an argument.

Premise: If an argument is sound, then it is logically strong.

Premise: If an argument is logically strong, then the premises—if true—provide  strong support for the truth of the conclusion.

Conclusion: So, if an argument is sound, then the premises—if true—provide strong support for the truth of the conclusion.

Exercise Set 1D:

Our systems of belief change all the time.  Give a brief example of a time your system of belief changed.

What is the difference between reasoning and argument as we are using the terms in this book.

List 1 true conditional claim.  List 1 false conditional claim.

Describe the experience of playing scrabble, or bananagrams, or some other similar word game.  How might automatic reasoning processes be at work in this kind of experience?

• Frederick, Shane. (2005) “Cognitive Reflection and Decision Making.” Journal of Economic Perspectives 19 (4), 25-42. ↵
• On first glance most people think the answer is that the ball costs $.10.  However, that can’t be right.  The bat costs $1.00 more than the ball, so if the ball costs $.10, the bat costs $1.10, and together they cost $1.20. ↵

Arguments in Context Copyright © 2021 by Thaddeus Robinson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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2 Evaluating Arguments

Nathan Smith

One particularly relevant application of logic is assessing the relative strength of philosophical claims. While the topics covered by philosophers are fascinating, it is often difficult to determine which positions on these topics are the right ones. Many students are led to think that philosophy is just a matter of opinion. After all, who could claim to know the final answer to philosophical questions?

It’s not likely that anyone will ever know the final answer to deep philosophical questions. Yet there are clearly better and worse answers; and philosophy can help us distinguish them. This chapter will give you some tools to begin to distinguish which positions on philosophical topics are well-founded and which are not. When a person makes a claim about a philosophical subject, you should ask, “What are the arguments to support that claim?” Once you have identified an argument, you can use these tools to assess whether it’s a good or bad one, whether the evidence and reasoning really support the claim or not.

In broad terms, there are two features of arguments that make them good: (1) the structure of the argument and (2) the truth of the evidence provided by the argument. Logic deals more directly with the structure of arguments. When we examine the logic of arguments, we are interested in whether the arguments have the right architecture, whether the evidence provided is the right sort of evidence to support the conclusion drawn. However, once we try to evaluate the truth of the conclusion, we need to know whether the evidence is true. We’ll look at both of these considerations in what follows.

Inference and Implication: Why Conclusions Follow from Premises

An argument is a connected series of propositions, some of which are called premises and at least one of which is a conclusion. The premises provide the reasons or evidence that supports the conclusion. From the point of view of the reader, an argument is meant to persuade the reader that, once the premises are accepted as true, the conclusion follows from them. If the reader accepts the premises, then she ought to accept the conclusion. The act of reasoning that connects the premises to the conclusion is called an inference . A good argument supports a rational inference to the conclusion, a bad argument supports no rational inference to the conclusion. [1]

Consider the following example:

• All human beings are mortal.
• Socrates is a human being.
• [latex]/ \therefore[/latex] Socrates is mortal.

This argument asserts that Socrates is mortal. It does so by appealing to the fact that Socrates is a human being, together with the idea that all human beings are mortal. There is clearly a strong connection between the premises and conclusion. Imagine a reader who accepts both premises but denies the conclusion. This person would have to believe that Socrates is a human being and that all human beings are mortal, but still deny that Socrates is mortal. How could such a person maintain that belief? It just doesn’t seem rational to believe the premises but deny the conclusion!

Now consider the following argument:

• I saw a black cat today.
• My knee is aching.
• [latex]/ \therefore[/latex] It is going to rain.

Suppose that it does, in fact, rain and the person who advances this argument believes that it is going to rain. Is that person justified in their belief that it will rain? Not based on the argument presented here! In this argument, there is a very weak connection between the premises and the conclusion. So, even if the conclusion turns out to be true, there is no reason why a reader ought to accept the conclusion given these premises (there may be other reasons for thinking it is going to rain that are not provided here, of course). The point is that these premises do not provide the right sort of evidence to justify the conclusion.

So far, I have described the connection between premises and conclusion in terms of the psychological demand placed on a reader of the argument. However, we can describe this connection from another perspective. We can say that the premises of an argument logically imply a conclusion. Either way of speaking is correct. What they assert is that good arguments present a strong connection between the truth of the premises and the truth of the conclusion. In the next few sections, we will examine three different types of logical connection, each with its own rules for evaluation. Sometimes logical implication is guaranteed (as in the case of deductive arguments ), sometimes the logical connection only ensures the conclusion is probable (as with inductive and abductive arguments ).

Deductive Arguments

Deductive arguments are the most common type of argument in philosophy, and for good reason. Deductive arguments attempt to demonstrate that the conclusion follows necessarily from the premises. As long as the premises of a good deductive argument are true, the conclusion is true as a matter of logic. This means that if I know the premises are true, I know with one-hundred percent certainty that the conclusion is also true! This may be hard to believe; after all, how can we be absolutely certain about anything? But notice what I am saying: I am not saying that we know the conclusion is true with one-hundred percent certainty. I am saying that we can be one-hundred percent certain the conclusion is true, on the condition that the premises are true. If one of the premises is false, then the conclusion is not guaranteed.

Here are two examples of good deductive arguments. They are both valid and have true premises. A valid argument is an argument whose premises guarantee the truth of the conclusion. That is, if the premises are true, then it is impossible for the conclusion to be false. A valid deductive argument whose premises are all true is called a sound argument .

• If it rained outside, then the streets will be wet.
• It rained outside.
• [latex]/ \therefore[/latex] The streets are wet.
•  Either the world ended on December 12, 2012 or it continues today.
• The world did not end on December 12, 2012.
• [latex]/ \therefore[/latex] The world continues today.

Hopefully, you can see that these arguments present a close connection between the premises and conclusion. It seems impossible to deny the conclusion while accepting that the premises are all true. This is what makes them valid deductive arguments. To show what happens when similar arguments employ false premises, consider the following examples:

•  If Russia wins the 2018 FIFA World Cup, then Russia is the reigning FIFA world champion [in 2019].
• Russia won the 2018 FIFA World Cup.
• [latex]/ \therefore[/latex] Russia is the reigning FIFA world champion [in 2019].
• Either snow is cold or snow is dry.
• Snow is not cold.
• [latex]/ \therefore[/latex] Snow is dry.

You may recognize that these arguments have the same structure as the previous two arguments. That is, each expresses the same connection between the premises and conclusion, and they are all deductively valid. However, these latter two arguments have at least one false premise and this false premise is the reason why these otherwise valid arguments reach a false conclusion. In the case of these arguments, the structure is good, but the evidence is bad.

Deductive arguments are either valid or invalid because of the form or structure of the argument. They are sound or unsound based on the form, plus the content. You might become familiar with some of the common forms of arguments (many of them have names) and once you do, you will be able to tell when a deductive argument is invalid.

Now let’s look at some invalid deductive arguments. These are arguments that have the wrong structure or form. Perhaps you have heard a playful argument like the following:

• Grass is green.
• Money is green.
• [latex]/ \therefore[/latex] Grass is money.

Here is another example of the same argument:

• All tigers are felines.
• All lions are felines.
• [latex]/ \therefore[/latex] All tigers are lions.

These arguments are examples of the fallacy of the undistributed middle term . The name is not important, but you may recognize what is going on here. The two types of objects in each conclusion are each a member of some third type, but they are not members of each other. So, the premises are all true, but the conclusions are false. If you encounter an argument with this structure, you will know that it is invalid.

But what do you do if you cannot immediately recognize when an argument is invalid? Philosophers look for counterexamples. A counterexample is a scenario in which the premises of the argument are true while the conclusion is clearly false. This automatically shows that it is possible for the argument’s premises to be true and the conclusion false. So, a counterexample demonstrates that the argument is invalid. After all, validity requires that if the premises are all true, the conclusion cannot possibly be false. Consider the following argument, which is an example of a fallacy called affirming the consequent :

• The streets are wet.
• [latex]/ \therefore[/latex] It rained outside.

Can you imagine a scenario where the premises are true, but the conclusion is false?

What if a water main broke and flooded the streets? Then the streets would be wet, but it may not have rained. It would still remain true that if it had rained, the streets would be wet, but in this scenario even if it didn’t rain, the streets would still be wet. So, the scenario where a water main breaks demonstrates this argument is invalid.

The counterexample method can also be applied to arguments where there is no clear scenario that makes the premises true and the conclusion false, but we will have to apply it a little differently. In these cases, we need to imagine another argument that has exactly the same structure as the argument in question but uses propositions that more easily produce a counterexample. Suppose I made the following argument:

• Most people who live near the coast know how to swim.
• Mary lives near the coast.
• [latex]/ \therefore[/latex] Mary knows how to swim.

I don’t know if Mary knows how to swim, but I do know that this argument does not provide sufficient reasons for us to know that Mary knows how to swim. I can demonstrate this by imagining another argument with the same structure as this argument, but the premises of this argument are clearly true while its conclusion is false:

• Most months in the calendar year have at least 30 days.
• February is a month in the calendar year.
• [latex]/ \therefore[/latex] February has at least 30 days.

To review, deductive arguments purport to lead to a conclusion that must be true if all the premises are true. But there are many ways a deductive argument can go wrong. In order to evaluate a deductive argument, we must answer the following questions:

• Are the premises true? If the premises are not true, then even if the argument is valid, the conclusion is not guaranteed to be true.
• Is the form of the argument a valid form? Does this argument have the exact same structure as one of the invalid arguments noted in this chapter or elsewhere in this book? [2]
• Can you come up with a counterexample for the argument? If you can imagine a case in which the premises are true but the conclusion is false, then you have demonstrated that the argument is invalid.

Inductive Arguments

Almost all of the formal logic taught to philosophy students is deductive. This is because we have a very well-established formal system, called first-order logic, that explains deductive validity. [3] Conversely, most of the inferences we make on a daily basis are inductive or abductive. The problem is that the logic governing inductive and abductive inferences is significantly more complex and more difficult to formalize than deductive inferences.

The chief difference between deductive arguments and inductive or abductive arguments is that while the former arguments aim to guarantee the truth of the conclusion, the latter arguments only aim to ensure that the conclusion is more probable . Even the conclusions of the best inductive and abductive arguments may still turn out to be false. Consequently, we do not refer to these arguments as valid or invalid. Instead, arguments with good inductive and abductive inferences are strong ; bad ones are weak . Similarly, strong inductive or abductive arguments with true premises are called cogent .

Here’s a table to help you remember these distinctions:

Inductive inferences typically involve an appeal to past experience in order to infer some further claim directly related to that experience. In its classic formulation, inductive inferences move from observed instances to unobserved instances, reasoning that what is not yet observed will resemble what has been observed before. Generalizations, statistical inferences, and forecasts about the future are all examples of inductive inference. [4] A classic example is the following:

• The Sun rose today.
• The Sun rose yesterday.
• The Sun has risen every day of human history.
• [latex]/ \therefore[/latex] The Sun will rise tomorrow.

You might wonder why this conclusion is merely probable. Is there anything more certain than the fact that the Sun will rise tomorrow? Well, not much. But at some point in the future, the Sun, like all other stars, will die out and its light will become so faint that there will be no sunrise on the Earth. More radically, imagine an asteroid disrupting the Earth’s rotation so that it fails to spin in coordination with our 24-hour clocks—in this case, the Sun would also fail to rise tomorrow. Finally, any inference about the future must always contain a degree of uncertainty because we cannot be certain that the future will resemble the past. So, even though the inference is very strong, it does not provide us with one-hundred percent certainty.

Consider the following, very similar inference, from the perspective of a chicken:

• When the farmer came to the coop yesterday, he brought us food.
• When the farmer came to the coop the day before, he brought us food.
• Every day that I can remember, the farmer has come to the coop to bring us food.
• [latex]/ \therefore[/latex] When the farmer comes today, he will bring food.

From a chicken’s perspective, this inference looks equally as strong as the previous one. But this chicken will be surprised on that fateful day when the farmer comes to the coop with a hatchet to butcher her! From the chicken’s perspective, the inference may appear strong, but from the farmer’s perspective, it’s fatally flawed. The chicken’s inference shares some similarities with the following example:

• A recent poll of over 5,000 people in the USA found that 85% of them are members of the National Rifle Association.
• The poll found that 98% of respondents were strongly or very strongly opposed to any firearms regulation.
• [latex]/ \therefore[/latex] Support of gun rights is very strong in the USA.

While the conclusion of this argument may be true and certainly appears to be supported by the premises, there is a key weakness that undermines the argument. You may suspect that these polling numbers present unusually high support for guns, even in the USA. [5] So, you may suspect that something is wrong with the data. But if I tell you that this poll was taken outside of a gun show, then you should realize that data may be correct, but the sample is clearly flawed. This reveals something important about inductive inferences. Inductive inferences depend on whether the sample set of experiences from which the conclusion is inferred are representative of the whole population described in the conclusion. In the cases of the chicken and gun rights, we are provided with a sample of experiences that are not representative of the populations in the conclusion. If we want to generalize about chicken farmer behavior, we need to sample the range of behaviors a farmer engages in. One chicken may not have enough data points to make a generalization about farmer behavior. Similarly, if we want to make a claim about the gun control preferences in the USA, we need to have a sample that represents all Americans, not just those who attend gun shows. The sample of experiences in a strong inductive argument must be representative of the conclusion that is drawn from it.

To review, strong inductive inferences lead to conclusions that are made more likely by the premises, but not guaranteed to be true. They are typically used to make generalizations, infer statistical probabilities, and make forecasts about the future. To evaluate an inductive inference, you should use the following guidelines:

• Are the premises true? Just like deductive arguments, inductive arguments require true premises to infer that the conclusion is likely to be true.
• Are the examples cited in the premises a large enough sample? The larger the sample, the greater the likelihood it is representative of the population as a whole, and thus the more likely inductive inferences made on the basis of it will be strong.

Abductive Arguments

Abductive arguments produce conclusions that attempt to explain the phenomena found in the premises. From a commonsense point of view, we can think of abductive inferences as “reading between the lines,” “using context clues,” or “putting two and two together.” We typically use these phrases to describe an inference to an explanation that is not explicitly provided. This is why abductive arguments are often called an “inference to the best explanation.” From a scientific perspective, abduction is a critical part of hypothesis formation. Whereas the classic “scientific method” teaches that science is deductive and that the purpose of experimentation is to test a hypothesis (by confirming or disconfirming the hypothesis), it is not always clear how scientists arrive at a hypothesis. Abduction provides an explanation for how scientists generate likely hypotheses for experimental testing.

Even though Sherlock Holmes is famous for declaring, in the course of his investigations, “Deduction, my dear Watson,” he probably should have said “Abduction”! Consider the following inference:

• The victim’s body has multiple stab wounds on its right side.
• There was evidence of a struggle between the murderer and the victim.
• [latex]/ \therefore[/latex] The murderer was left-handed.

You should recognize that the conclusion is not guaranteed by the premises, and so it is not a deductive argument. Additionally, the argument is not inductive, because the conclusion isn’t simply an extension from past experiences. This argument attempts to provide the best explanation for the evidence in the premises. In a struggle, two people are most likely to be standing face to face. Also, the killer probably attacked with his or her dominant hand. It would be unnatural for a right-handed person to stab with their left hand or to stab a person facing them on that person’s right side. So, the fact that the murderer is left-handed provides the most likely explanation for the stab wounds.

You use these sorts of inferences regularly. For instance, suppose that when you come home from work, you notice that the door to your apartment is unlocked and various items from the refrigerator are out on the counter. You might infer that your roommate is home. Of course, this explanation is not guaranteed to be true. For instance, you may have forgotten to lock the door and put away your food in your haste to get out the door. Abductive inferences attempt to reason to the most likely conclusion, not one that is guaranteed to be true.

What makes an abductive inference strong or weak? Good explanations ought to take account of all the available evidence. If the conclusion leaves some evidence unexplained, then it is probably not a strong argument. Additionally, extraordinary claims require extraordinary evidence. If an explanation requires belief in some entirely novel or supernatural entity, or generally requires us to revise deeply held beliefs, then we ought to demand that the evidence for this explanation is very solid. Finally, when assessing alternative explanations, we should heed the advice of “Ockham’s Razor.” William of Ockham argued that given any two explanations, the simpler one is more likely to be true. In other words, we should be skeptical of explanations that require complex mechanics, extensive caveats and exceptions, or an extremely precise set of circumstances, in order to be true. [6]

Consider the following arguments with identical premises:

•  There have been hundreds of stories about strange objects in the night sky.
• There is some video evidence of these strange objects.
• Some people have recalled encounters with extraterrestrial life forms.
• There are no peer-reviewed scientific accounts of extraterrestrial life forms visiting earth.
• [latex]/ \therefore[/latex] There must be a vast conspiracy denying the existence of aliens.
• There have been hundreds of stories about strange objects in the night sky.
• [latex]/ \therefore[/latex] The stories, videos, and recollections are probably the result of confusion, confabulation or exaggeration, or are outright falsifications.

Which is the more likely explanation?

To review, abductive inferences assert a conclusion that the premises do not guarantee, but which aims to provide the most likely explanation for the phenomena detailed in the premises. To assess the strength of an abductive inference, use the following guidelines:

• Is all the relevant evidence provided? If critical pieces of information are missing, then it may not be possible to know what the right explanation is.
• Does the conclusion explain all of the evidence provided? If the conclusion fails to account for some of the evidence, then it may not be the best explanation.
• Extraordinary claims require extraordinary evidence! If the conclusion asserts something novel, surprising, or contrary to standard explanations, then the evidence should be equally compelling.
• Use Ockham’s Razor; recognize that the simpler of two explanations is likely the correct one.

Exercise One

For each argument decide whether it is deductive, inductive or abductive. If it contains more than one type of inference, indicate which.

• Every human being has a heart,
• If something has a heart, then it has a liver
• [latex]/ \therefore[/latex] Every human being has a liver

Answer: This is a deductive argument because it is attempting to show that it’s impossible for the conclusion to be false if the premises are true.

• Chickens from my farm have gone missing,
• My farm is in the British countryside,
• [latex]/ \therefore[/latex] There are foxes killing my chickens
• All flamingos are pink birds,
• All flamingos are fire breathing creatures,
• [latex]/ \therefore[/latex] Some pink birds are fire breathing creatures
• Every Friday so far this year the cafeteria has served fish and chips,
• If the cafeteria’s serving fish and chips and I want fish and chips then I should bring in £4,
• If the cafeteria isn’t serving fish and chips then I shouldn’t bring in £4,
• I always want fish and chips,
• [latex]/ \therefore[/latex] I should bring in £4 next Friday
• If Bob Dylan or Italo Calvino were awarded the Nobel Prize in Literature, then the choices made by the Swedish Academy would be respectable,
• The choices made by the Swedish Academy are not respectable,
• [latex]/ \therefore[/latex] Neither Bob Dylan nor Italo Calvino have been awarded the Nobel Prize in Literature
• In all the games that the Boston Red Sox have played so far this season they have been better than their opposition,
• If a team plays better than their opposition in every game then they win the World Series
• [latex]/ \therefore[/latex] The Boston Red Sox will win the league
• There are lights on in the front room and there are noises coming from upstairs,
• If there are noises coming from upstairs then Emma is in the house,
• [latex]/ \therefore[/latex] Emma is in the house

Exercise Two

Give examples of arguments that have each of the following properties:

• Valid, and has at least one false premise and a false conclusion
• Valid, and has at least one false premise and a true conclusion
• Invalid, and has at least one false premise and a false conclusion
• Invalid, and has at least one false premise and a true conclusion
• Invalid, and has true premises and a true conclusion
• Invalid, and has true premises and a false conclusion
• Strong, but invalid [Hint: Think about inductive arguments.]
• This does not mean that bad arguments cannot be psychologically persuasive. In fact, people are often persuaded by bad arguments. However, a good philosophical assessment of an argument ought to rely purely on the rationality of its inferences. ↵
• Chapters 3 and 4 of this Introduction address types of fallacies. Fallacies are just systematic mistakes made within arguments. You can learn more examples of invalid argument forms in these chapters. ↵
• Chapter 3 introduces formal logic. ↵
• You may notice that the inference from the previous section about Mary being able to swim could be rephrased as a kind of inductive argument. If it is true that most people who live near the coast can swim and Mary lives near the coast, then it follows that Mary probably can swim. This demonstrates an important difference between deductive and inductive arguments. ↵
• See, for instance, recent Gallup polling: 2019. “Guns.” http://news.gallup.com/poll/1645/guns.aspx. ↵
• While Ockham’s Razor is a good rule of thumb in evaluating explanations, there is considerable debate among philosophers of science about whether simplicity it is a feature of good scientific explanations or not. ↵

A psychological act that links premises to a conclusion in an argument.

One proposition P logically implies another Q if whenever P is true, Q is also true. Arguments in which the premises logically imply the conclusion are known as valid arguments.

An argument that aims to be valid.

An argument that moves from observed instances of a certain phenomenon to unobserved instances of the same phenomenon.

An argument that attempts to provide the best explanation possible of certain other phenomena as its conclusion. Also known as inference to the best explanation .

An argument in which it is impossible for the premises to be true and the conclusion false.

A valid argument with actually true premises . Thus, if an argument is sound, its conclusion must be true.

A counterexample is a scenario in which the premises of the argument are true while the conclusion is false. If an argument has a counterexample, it is not valid.

An inductive or abductive argument in which the premises make the conclusion likely to be true.

An inductive or abductive argument in which the premises fail to make the conclusion likely to be true.

A strong inductive or abductive argument with true premises. If an argument is cogent, then its conclusion is likely to be true.

Evaluating Arguments Copyright © 2020 by Nathan Smith is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• 9 Ways to Construct a Compelling Argument

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But especially in the circumstances that we’re deeply convinced of the rightness of our points, putting them across in a compelling way that will change other people’s mind is a challenge. If you feel that your opinion is obviously right, it’s hard work even to understand why other people might disagree. Some people reach this point and don’t bother to try, instead concluding that those who disagree with them must be stupid, misled or just plain immoral. And it’s almost impossible to construct an argument that will persuade someone if you’re starting from the perspective that they’re either dim or evil. In the opposite set of circumstances – when you only weakly believe your perspective to be right – it can also be tricky to construct a good argument. In the absence of conviction, arguments tend to lack coherence or force. In this article, we take a look at how you can put together an argument, whether for an essay, debate speech or social media post, that is forceful, cogent and – if you’re lucky – might just change someone’s mind.

1. Keep it simple

Almost all good essays focus on a single powerful idea, drawing in every point made back to that same idea so that even someone skim-reading will soon pick up the author’s thesis. But when you care passionately about something, it’s easy to let this go. If you can see twenty different reasons why you’re right, it’s tempting to put all of them into your argument, because it feels as if the sheer weight of twenty reasons will be much more persuasive than just focusing on one or two; after all, someone may be able rebut a couple of reasons, but can they rebut all twenty? Yet from the outside, an argument with endless different reasons is much less persuasive than one with focus and precision on a small number of reasons. The debate in the UK about whether or not to stay in the EU was a great example of this. The Remain campaign had dozens of different reasons. Car manufacturing! Overfishing! Cleaner beaches! Key workers for the NHS! Medical research links! Economic opportunities! The difficulty of overcoming trade barriers! The Northern Irish border! Meanwhile, the Leave campaign boiled their argument down to just one: membership of the EU means relinquishing control. Leaving it means taking back control. And despite most expectations and the advice of most experts, the simple, straightforward message won. Voters struggled to remember the many different messages put out by the Remain campaign, as compelling as each of those reasons might have been; but they remembered the message about taking back control.

2. Be fair on your opponent

One of the most commonly used rhetorical fallacies is the Strawman Fallacy. This involves constructing a version of your opponent’s argument that is much weaker than the arguments they might use themselves, in order than you can defeat it more easily. For instance, in the area of crime and punishment, you might be arguing in favour of harsher prison sentences, while your opponent argues in favour of early release where possible. A Strawman would be to say that your opponent is weak on crime, wanting violent criminals to be let out on to the streets without adequate punishment or deterrence, to commit the same crimes again. In reality, your opponent’s idea might exclude violent criminals, and focus on community-based restorative justice that could lead to lower rates of recidivism. To anyone who knows the topic well, if your argument includes a Strawman, then you will immediately have lost credibility by demonstrating that either you don’t really understand the opposing point of view, or that you simply don’t care about rebutting it properly. Neither is persuasive. Instead, you should be fair to your opponent and represent their argument honestly, and your readers will take you seriously as a result

3. Avoid other common fallacies

It’s worth taking the time to read about logical fallacies and making sure that you’re not making them, as argument that rest of fallacious foundations can be more easily demolished. (This may not apply on social media, but it does in formal debating and in writing essays). Some fallacies are straightforward to understand, such as the appeal to popularity (roughly “everyone agrees with me, so I must be right!”), but others are a little trickier. Take “begging the question”, which is often misunderstood. It gets used to mean “raises the question” (e.g. “this politician has defended terrorists, which raises the question – can we trust her?”), but the fallacy it refers to is a bit more complicated. It’s when an argument rests on the assumption that its conclusions are true. For example, someone might argue that fizzy drinks shouldn’t be banned in schools, on the grounds that they’re not bad for students’ health. How can we know that they’re not bad for students’ health? Why, if they were, they would be banned in schools! When put in a condensed form like this example, the flaw in this approach is obvious, but you can imagine how you might fall for it over the course of a whole essay – for instance, paragraphs arguing that teachers would have objected to hyperactive students, parents would have complained, and we can see that none of this has happened because they haven’t yet been banned. With more verbosity, a bad argument can be hidden, so check that you’re not falling prey to it in your own writing.

4. Make your assumptions clear

Every argument rests on assumptions. Some of these assumptions are so obvious that you’re not going to be aware that you’re making them – for instance, you might make an argument about different economic systems that rests on the assumption that reducing global poverty is a good thing. While very few people would disagree with you on that, in general, if your assumption can be proven false, then the entire basis of your argument is undermined. A more controversial example might be an argument that rests on the assumption that everyone can trust the police force – for instance, if you’re arguing for tougher enforcement of minor offences in order to prevent them from mounting into major ones. But in countries where the police are frequently bribed, or where policing has obvious biases, such enforcement could be counterproductive. If you’re aware of such assumptions underpinning your argument, tackle them head on by making them clear and explaining why they are valid; so you could argue that your law enforcement proposal is valid in the particular circumstances that you’re suggesting because the police force there can be relied on, even if it wouldn’t work everywhere.

5. Rest your argument on solid foundations

If you think that you’re right in your argument, you should also be able to assemble a good amount of evidence that you’re right. That means putting the effort in and finding something that genuinely backs up what you’re saying; don’t fall back on dubious statistics or fake news . Doing the research to ensure that your evidence is solid can be time-consuming, but it’s worthwhile, as then you’ve removed another basis on which your argument could be challenged. What happens if you can’t find any evidence for your argument? The first thing to consider is whether you might be wrong! If you find lots of evidence against your position, and minimal evidence for it, it would be logical to change your mind. But if you’re struggling to find evidence either way, it may simply be that the area is under-researched. Prove what you can, including your assumptions, and work from there.

6. Use evidence your readers will believe

So far we’ve focused on how to construct an argument that is solid and hard to challenge; from this point onward, we focus on what it takes to make an argument persuasive. One thing you can do is to choose your evidence with your audience in mind. For instance, if you’re writing about current affairs, a left-wing audience will find an article from the Guardian to be more persuasive (as they’re more likely to trust its reporting), while a right-wing audience might be more swayed by the Telegraph. This principle doesn’t just hold in terms of politics. It can also be useful in terms of sides in an academic debate, for instance. You can similarly bear in mind the demographics of your likely audience – it may be that an older audience is more skeptical of footnotes that consist solely of web addresses. And it isn’t just about statistics and references. The focus of your evidence as a whole can take your probable audience into account; for example, if you were arguing that a particular drug should be banned on health grounds and your main audience was teenagers, you might want to focus more on the immediate health risks, rather than ones that might only appear years or decades later.

7. Avoid platitudes and generalisations, and be specific

A platitude is a phrase used to the point of meaninglessness – and it may not have had that much meaning to begin with. If you find yourself writing something like “because family life is all-important” to support one of your claims, you’ve slipped into using platitudes. Platitudes are likely to annoy your readers without helping to persuade them. Because they’re meaningless and uncontroversial statements, using them doesn’t tell your reader anything new. If you say that working hours need to be restricted because family ought to come first, you haven’t really given your reader any new information. Instead, bring the importance of family to life for your reader, and then explain just how long hours are interrupting it. Similarly, being specific can demonstrate the grasp you have on your subject, and can bring it to life for your reader. Imagine that you were arguing in favour of nationalising the railways, and one of your points was that the service now was of low quality. Saying “many commuter trains are frequently delayed” is much less impactful than if you have the full facts to hand, e.g. “in Letchworth Garden City, one key commuter hub, half of all peak-time trains to London were delayed by ten minutes or more.”

8. Understand the opposing point of view

As we noted in the introduction, you can’t construct a compelling argument unless you understand why someone might think you were wrong, and you can come up with reasons other than them being mistaken or stupid. After all, we almost all target them same end goals, whether that’s wanting to increase our understanding of the world in academia, or increase people’s opportunities to flourish and seek happiness in politics. Yet we come to divergent conclusions. In his book The Righteous Mind , Jonathan Haidt explores the different perspectives of people who are politically right or left-wing. He summarises the different ideals people might value, namely justice, equality, authority, sanctity and loyalty, and concludes that while most people see that these things have some value, different political persuasions value them to different degrees. For instance, someone who opposes equal marriage might argue that they don’t oppose equality – but they do feel that on balance, sanctity is more important. An argument that focuses solely on equality won’t sway them, but an argument that addresses sanctity might.

9. Make it easy for your opponent to change their mind

It’s tricky to think of the last time you changed your mind about something really important. Perhaps to preserve our pride, we frequently forget that we ever believed something different. This survey of British voters’ attitudes to the Iraq war demonstrates the point beautifully. 54% of people supporting invading Iraq in 2003; but twelve years on, with the war a demonstrable failure, only 37% were still willing to admit that they had supported it at the time. The effect in the USA was even more dramatic. It would be tempting for anyone who genuinely did oppose the war at the time to be quite smug towards anyone who changed their mind, especially those who won’t admit it. But if changing your mind comes with additional consequences (e.g. the implication that you were daft ever to have believed something, even if you’ve since come to a different conclusion), then the incentive to do so is reduced. Your argument needs to avoid vilifying people who have only recently come around to your point of view; instead, to be truly persuasive, you should welcome them.

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2: Evaluating Arguments

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One particularly relevant application of logic is assessing the relative strength of philosophical claims. While the topics covered by philosophers are fascinating, it is often difficult to determine which positions on these topics are the right ones. Many students are led to think that philosophy is just a matter of opinion. After all, who could claim to know the final answer to philosophical questions?

It’s not likely that anyone will ever know the final answer to deep philosophical questions. Yet there are clearly better and worse answers; and philosophy can help us distinguish them. This chapter will give you some tools to begin to distinguish which positions on philosophical topics are well-founded and which are not. When a person makes a claim about a philosophical subject, you should ask, “What are the arguments to support that claim?” Once you have identified an argument, you can use these tools to assess whether it’s a good or bad one, whether the evidence and reasoning really support the claim or not.

In broad terms, there are two features of arguments that make them good: (1) the structure of the argument and (2) the truth of the evidence provided by the argument. Logic deals more directly with the structure of arguments. When we examine the logic of arguments, we are interested in whether the arguments have the right architecture, whether the evidence provided is the right sort of evidence to support the conclusion drawn. However, once we try to evaluate the truth of the conclusion, we need to know whether the evidence is true. We’ll look at both of these considerations in what follows.

Inference and Implication: Why Conclusions Follow from Premises

An argument is a connected series of propositions, some of which are called premises and at least one of which is a conclusion. The premises provide the reasons or evidence that supports the conclusion. From the point of view of the reader, an argument is meant to persuade the reader that, once the premises are accepted as true, the conclusion follows from them. If the reader accepts the premises, then she ought to accept the conclusion. The act of reasoning that connects the premises to the conclusion is called an inference . A good argument supports a rational inference to the conclusion, a bad argument supports no rational inference to the conclusion. [1]

Consider the following example:

• All human beings are mortal.
• Socrates is a human being.

This argument asserts that Socrates is mortal. It does so by appealing to the fact that Socrates is a human being, together with the idea that all human beings are mortal. There is clearly a strong connection between the premises and conclusion. Imagine a reader who accepts both premises but denies the conclusion. This person would have to believe that Socrates is a human being and that all human beings are mortal, but still deny that Socrates is mortal. How could such a person maintain that belief? It just doesn’t seem rational to believe the premises but deny the conclusion!

Now consider the following argument:

• I saw a black cat today.
• My knee is aching.

Suppose that it does, in fact, rain and the person who advances this argument believes that it is going to rain. Is that person justified in their belief that it will rain? Not based on the argument presented here! In this argument, there is a very weak connection between the premises and the conclusion. So, even if the conclusion turns out to be true, there is no reason why a reader ought to accept the conclusion given these premises (there may be other reasons for thinking it is going to rain that are not provided here, of course). The point is that these premises do not provide the right sort of evidence to justify the conclusion.

So far, I have described the connection between premises and conclusion in terms of the psychological demand placed on a reader of the argument. However, we can describe this connection from another perspective. We can say that the premises of an argument logically imply a conclusion. Either way of speaking is correct. What they assert is that good arguments present a strong connection between the truth of the premises and the truth of the conclusion. In the next few sections, we will examine three different types of logical connection, each with its own rules for evaluation. Sometimes logical implication is guaranteed (as in the case of deductive arguments ), sometimes the logical connection only ensures the conclusion is probable (as with inductive and abductive arguments ).

Deductive Arguments

Deductive arguments are the most common type of argument in philosophy, and for good reason. Deductive arguments attempt to demonstrate that the conclusion follows necessarily from the premises. As long as the premises of a good deductive argument are true, the conclusion is true as a matter of logic. This means that if I know the premises are true, I know with one-hundred percent certainty that the conclusion is also true! This may be hard to believe; after all, how can we be absolutely certain about anything? But notice what I am saying: I am not saying that we know the conclusion is true with one-hundred percent certainty. I am saying that we can be one-hundred percent certain the conclusion is true, on the condition that the premises are true. If one of the premises is false, then the conclusion is not guaranteed.

Here are two examples of good deductive arguments. They are both valid and have true premises. A valid argument is an argument whose premises guarantee the truth of the conclusion. That is, if the premises are true, then it is impossible for the conclusion to be false. A valid deductive argument whose premises are all true is called a sound argument .

• If it rained outside, then the streets will be wet.
• It rained outside.
• Either the world ended on December 12, 2012 or it continues today.
• The world did not end on December 12, 2012.

Hopefully, you can see that these arguments present a close connection between the premises and conclusion. It seems impossible to deny the conclusion while accepting that the premises are all true. This is what makes them valid deductive arguments. To show what happens when similar arguments employ false premises, consider the following examples:

• If Russia wins the 2018 FIFA World Cup, then Russia is the reigning FIFA world champion [in 2019].
• Russia won the 2018 FIFA World Cup.
• Either snow is cold or snow is dry.
• Snow is not cold.

You may recognize that these arguments have the same structure as the previous two arguments. That is, each expresses the same connection between the premises and conclusion, and they are all deductively valid. However, these latter two arguments have at least one false premise and this false premise is the reason why these otherwise valid arguments reach a false conclusion. In the case of these arguments, the structure is good, but the evidence is bad.

Deductive arguments are either valid or invalid because of the form or structure of the argument. They are sound or unsound based on the form, plus the content. You might become familiar with some of the common forms of arguments (many of them have names) and once you do, you will be able to tell when a deductive argument is invalid.

Now let’s look at some invalid deductive arguments. These are arguments that have the wrong structure or form. Perhaps you have heard a playful argument like the following:

• Grass is green.
• Money is green.

Here is another example of the same argument:

• All tigers are felines.
• All lions are felines.

These arguments are examples of the fallacy of the undistributed middle term . The name is not important, but you may recognize what is going on here. The two types of objects in each conclusion are each a member of some third type, but they are not members of each other. So, the premises are all true, but the conclusions are false. If you encounter an argument with this structure, you will know that it is invalid.

But what do you do if you cannot immediately recognize when an argument is invalid? Philosophers look for counterexamples. A counterexample is a scenario in which the premises of the argument are true while the conclusion is clearly false. This automatically shows that it is possible for the argument’s premises to be true and the conclusion false. So, a counterexample demonstrates that the argument is invalid. After all, validity requires that if the premises are all true, the conclusion cannot possibly be false. Consider the following argument, which is an example of a fallacy called affirming the consequent :

• The streets are wet.

Can you imagine a scenario where the premises are true, but the conclusion is false?

What if a water main broke and flooded the streets? Then the streets would be wet, but it may not have rained. It would still remain true that if it had rained, the streets would be wet, but in this scenario even if it didn’t rain, the streets would still be wet. So, the scenario where a water main breaks demonstrates this argument is invalid.

The counterexample method can also be applied to arguments where there is no clear scenario that makes the premises true and the conclusion false, but we will have to apply it a little differently. In these cases, we need to imagine another argument that has exactly the same structure as the argument in question but uses propositions that more easily produce a counterexample. Suppose I made the following argument:

• Most people who live near the coast know how to swim.
• Mary lives near the coast.

I don’t know if Mary knows how to swim, but I do know that this argument does not provide sufficient reasons for us to know that Mary knows how to swim. I can demonstrate this by imagining another argument with the same structure as this argument, but the premises of this argument are clearly true while its conclusion is false:

• Most months in the calendar year have at least 30 days.
• February is a month in the calendar year.

To review, deductive arguments purport to lead to a conclusion that must be true if all the premises are true. But there are many ways a deductive argument can go wrong. In order to evaluate a deductive argument, we must answer the following questions:

• Are the premises true? If the premises are not true, then even if the argument is valid, the conclusion is not guaranteed to be true.
• Is the form of the argument a valid form? Does this argument have the exact same structure as one of the invalid arguments noted in this chapter or elsewhere in this book? [2]
• Can you come up with a counterexample for the argument? If you can imagine a case in which the premises are true but the conclusion is false, then you have demonstrated that the argument is invalid.

Inductive Arguments

Almost all of the formal logic taught to philosophy students is deductive. This is because we have a very well-established formal system, called first-order logic, that explains deductive validity. [3] Conversely, most of the inferences we make on a daily basis are inductive or abductive. The problem is that the logic governing inductive and abductive inferences is significantly more complex and more difficult to formalize than deductive inferences.

The chief difference between deductive arguments and inductive or abductive arguments is that while the former arguments aim to guarantee the truth of the conclusion, the latter arguments only aim to ensure that the conclusion is more probable . Even the conclusions of the best inductive and abductive arguments may still turn out to be false. Consequently, we do not refer to these arguments as valid or invalid. Instead, arguments with good inductive and abductive inferences are strong ; bad ones are weak . Similarly, strong inductive or abductive arguments with true premises are called cogent .

Here’s a table to help you remember these distinctions:

Inductive inferences typically involve an appeal to past experience in order to infer some further claim directly related to that experience. In its classic formulation, inductive inferences move from observed instances to unobserved instances, reasoning that what is not yet observed will resemble what has been observed before. Generalizations, statistical inferences, and forecasts about the future are all examples of inductive inference. [4] A classic example is the following:

• The Sun rose today.
• The Sun rose yesterday.
• The Sun has risen every day of human history.

You might wonder why this conclusion is merely probable. Is there anything more certain than the fact that the Sun will rise tomorrow? Well, not much. But at some point in the future, the Sun, like all other stars, will die out and its light will become so faint that there will be no sunrise on the Earth. More radically, imagine an asteroid disrupting the Earth’s rotation so that it fails to spin in coordination with our 24-hour clocks—in this case, the Sun would also fail to rise tomorrow. Finally, any inference about the future must always contain a degree of uncertainty because we cannot be certain that the future will resemble the past. So, even though the inference is very strong, it does not provide us with one-hundred percent certainty.

Consider the following, very similar inference, from the perspective of a chicken:

• When the farmer came to the coop yesterday, he brought us food.
• When the farmer came to the coop the day before, he brought us food.
• Every day that I can remember, the farmer has come to the coop to bring us food.

From a chicken’s perspective, this inference looks equally as strong as the previous one. But this chicken will be surprised on that fateful day when the farmer comes to the coop with a hatchet to butcher her! From the chicken’s perspective, the inference may appear strong, but from the farmer’s perspective, it’s fatally flawed. The chicken’s inference shares some similarities with the following example:

• A recent poll of over 5,000 people in the USA found that 85% of them are members of the National Rifle Association.
• The poll found that 98% of respondents were strongly or very strongly opposed to any firearms regulation.

While the conclusion of this argument may be true and certainly appears to be supported by the premises, there is a key weakness that undermines the argument. You may suspect that these polling numbers present unusually high support for guns, even in the USA. [5] So, you may suspect that something is wrong with the data. But if I tell you that this poll was taken outside of a gun show, then you should realize that data may be correct, but the sample is clearly flawed. This reveals something important about inductive inferences. Inductive inferences depend on whether the sample set of experiences from which the conclusion is inferred are representative of the whole population described in the conclusion. In the cases of the chicken and gun rights, we are provided with a sample of experiences that are not representative of the populations in the conclusion. If we want to generalize about chicken farmer behavior, we need to sample the range of behaviors a farmer engages in. One chicken may not have enough data points to make a generalization about farmer behavior. Similarly, if we want to make a claim about the gun control preferences in the USA, we need to have a sample that represents all Americans, not just those who attend gun shows. The sample of experiences in a strong inductive argument must be representative of the conclusion that is drawn from it.

To review, strong inductive inferences lead to conclusions that are made more likely by the premises, but not guaranteed to be true. They are typically used to make generalizations, infer statistical probabilities, and make forecasts about the future. To evaluate an inductive inference, you should use the following guidelines:

• Are the premises true? Just like deductive arguments, inductive arguments require true premises to infer that the conclusion is likely to be true.
• Are the examples cited in the premises a large enough sample? The larger the sample, the greater the likelihood it is representative of the population as a whole, and thus the more likely inductive inferences made on the basis of it will be strong.

Abductive Arguments

Abductive arguments produce conclusions that attempt to explain the phenomena found in the premises. From a commonsense point of view, we can think of abductive inferences as “reading between the lines,” “using context clues,” or “putting two and two together.” We typically use these phrases to describe an inference to an explanation that is not explicitly provided. This is why abductive arguments are often called an “inference to the best explanation.” From a scientific perspective, abduction is a critical part of hypothesis formation. Whereas the classic “scientific method” teaches that science is deductive and that the purpose of experimentation is to test a hypothesis (by confirming or disconfirming the hypothesis), it is not always clear how scientists arrive at a hypothesis. Abduction provides an explanation for how scientists generate likely hypotheses for experimental testing.

Even though Sherlock Holmes is famous for declaring, in the course of his investigations, “Deduction, my dear Watson,” he probably should have said “Abduction”! Consider the following inference:

• The victim’s body has multiple stab wounds on its right side.
• There was evidence of a struggle between the murderer and the victim.

You should recognize that the conclusion is not guaranteed by the premises, and so it is not a deductive argument. Additionally, the argument is not inductive, because the conclusion isn’t simply an extension from past experiences. This argument attempts to provide the best explanation for the evidence in the premises. In a struggle, two people are most likely to be standing face to face. Also, the killer probably attacked with his or her dominant hand. It would be unnatural for a right-handed person to stab with their left hand or to stab a person facing them on that person’s right side. So, the fact that the murderer is left-handed provides the most likely explanation for the stab wounds.

You use these sorts of inferences regularly. For instance, suppose that when you come home from work, you notice that the door to your apartment is unlocked and various items from the refrigerator are out on the counter. You might infer that your roommate is home. Of course, this explanation is not guaranteed to be true. For instance, you may have forgotten to lock the door and put away your food in your haste to get out the door. Abductive inferences attempt to reason to the most likely conclusion, not one that is guaranteed to be true.

What makes an abductive inference strong or weak? Good explanations ought to take account of all the available evidence. If the conclusion leaves some evidence unexplained, then it is probably not a strong argument. Additionally, extraordinary claims require extraordinary evidence. If an explanation requires belief in some entirely novel or supernatural entity, or generally requires us to revise deeply held beliefs, then we ought to demand that the evidence for this explanation is very solid. Finally, when assessing alternative explanations, we should heed the advice of “Ockham’s Razor.” William of Ockham argued that given any two explanations, the simpler one is more likely to be true. In other words, we should be skeptical of explanations that require complex mechanics, extensive caveats and exceptions, or an extremely precise set of circumstances, in order to be true. [6]

Consider the following arguments with identical premises:

• There have been hundreds of stories about strange objects in the night sky.
• There is some video evidence of these strange objects.
• Some people have recalled encounters with extraterrestrial life forms.
• There are no peer-reviewed scientific accounts of extraterrestrial life forms visiting earth.

Which is the more likely explanation?

To review, abductive inferences assert a conclusion that the premises do not guarantee, but which aims to provide the most likely explanation for the phenomena detailed in the premises. To assess the strength of an abductive inference, use the following guidelines:

• Is all the relevant evidence provided? If critical pieces of information are missing, then it may not be possible to know what the right explanation is.
• Does the conclusion explain all of the evidence provided? If the conclusion fails to account for some of the evidence, then it may not be the best explanation.
• Extraordinary claims require extraordinary evidence! If the conclusion asserts something novel, surprising, or contrary to standard explanations, then the evidence should be equally compelling.
• Use Ockham’s Razor; recognize that the simpler of two explanations is likely the correct one.

Exercise One

For each argument decide whether it is deductive, inductive or abductive. If it contains more than one type of inference, indicate which.

• Every human being has a heart,
• If something has a heart, then it has a liver

Answer: This is a deductive argument because it is attempting to show that it’s impossible for the conclusion to be false if the premises are true.

• Chickens from my farm have gone missing,
• My farm is in the British countryside,
• All flamingos are pink birds,
• All flamingos are fire breathing creatures,
• Every Friday so far this year the cafeteria has served fish and chips,
• If the cafeteria’s serving fish and chips and I want fish and chips then I should bring in £4,
• If the cafeteria isn’t serving fish and chips then I shouldn’t bring in £4,
• I always want fish and chips,
• If Bob Dylan or Italo Calvino were awarded the Nobel Prize in Literature, then the choices made by the Swedish Academy would be respectable,
• The choices made by the Swedish Academy are not respectable,
• In all the games that the Boston Red Sox have played so far this season they have been better than their opposition,
• If a team plays better than their opposition in every game then they win the World Series
• There are lights on in the front room and there are noises coming from upstairs,
• If there are noises coming from upstairs then Emma is in the house,

Exercise Two

Give examples of arguments that have each of the following properties:

• Valid, and has at least one false premise and a false conclusion
• Valid, and has at least one false premise and a true conclusion
• Invalid, and has at least one false premise and a false conclusion
• Invalid, and has at least one false premise and a true conclusion
• Invalid, and has true premises and a true conclusion
• Invalid, and has true premises and a false conclusion
• Strong, but invalid [Hint: Think about inductive arguments.]
• This does not mean that bad arguments cannot be psychologically persuasive. In fact, people are often persuaded by bad arguments. However, a good philosophical assessment of an argument ought to rely purely on the rationality of its inferences. ↵
• Chapters 3 and 4 of this Introduction address types of fallacies. Fallacies are just systematic mistakes made within arguments. You can learn more examples of invalid argument forms in these chapters. ↵
• Chapter 3 introduces formal logic. ↵
• You may notice that the inference from the previous section about Mary being able to swim could be rephrased as a kind of inductive argument. If it is true that most people who live near the coast can swim and Mary lives near the coast, then it follows that Mary probably can swim. This demonstrates an important difference between deductive and inductive arguments. ↵
• See, for instance, recent Gallup polling: 2019. “Guns.” http://news.gallup.com/poll/1645/guns.aspx . ↵
• While Ockham’s Razor is a good rule of thumb in evaluating explanations, there is considerable debate among philosophers of science about whether simplicity it is a feature of good scientific explanations or not. ↵

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• How to write an argumentative essay | Examples & tips

How to Write an Argumentative Essay | Examples & Tips

Published on July 24, 2020 by Jack Caulfield . Revised on July 23, 2023.

An argumentative essay expresses an extended argument for a particular thesis statement . The author takes a clearly defined stance on their subject and builds up an evidence-based case for it.

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Table of contents

When do you write an argumentative essay, approaches to argumentative essays, introducing your argument, the body: developing your argument, concluding your argument, other interesting articles, frequently asked questions about argumentative essays.

You might be assigned an argumentative essay as a writing exercise in high school or in a composition class. The prompt will often ask you to argue for one of two positions, and may include terms like “argue” or “argument.” It will frequently take the form of a question.

The prompt may also be more open-ended in terms of the possible arguments you could make.

Argumentative writing at college level

At university, the vast majority of essays or papers you write will involve some form of argumentation. For example, both rhetorical analysis and literary analysis essays involve making arguments about texts.

In this context, you won’t necessarily be told to write an argumentative essay—but making an evidence-based argument is an essential goal of most academic writing, and this should be your default approach unless you’re told otherwise.

Examples of argumentative essay prompts

At a university level, all the prompts below imply an argumentative essay as the appropriate response.

Your research should lead you to develop a specific position on the topic. The essay then argues for that position and aims to convince the reader by presenting your evidence, evaluation and analysis.

• Don’t just list all the effects you can think of.
• Do develop a focused argument about the overall effect and why it matters, backed up by evidence from sources.
• Don’t just provide a selection of data on the measures’ effectiveness.
• Do build up your own argument about which kinds of measures have been most or least effective, and why.
• Don’t just analyze a random selection of doppelgänger characters.
• Do form an argument about specific texts, comparing and contrasting how they express their thematic concerns through doppelgänger characters.

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An argumentative essay should be objective in its approach; your arguments should rely on logic and evidence, not on exaggeration or appeals to emotion.

There are many possible approaches to argumentative essays, but there are two common models that can help you start outlining your arguments: The Toulmin model and the Rogerian model.

Toulmin arguments

The Toulmin model consists of four steps, which may be repeated as many times as necessary for the argument:

• Make a claim
• Provide the grounds (evidence) for the claim
• Explain the warrant (how the grounds support the claim)
• Discuss possible rebuttals to the claim, identifying the limits of the argument and showing that you have considered alternative perspectives

The Toulmin model is a common approach in academic essays. You don’t have to use these specific terms (grounds, warrants, rebuttals), but establishing a clear connection between your claims and the evidence supporting them is crucial in an argumentative essay.

Say you’re making an argument about the effectiveness of workplace anti-discrimination measures. You might:

• Claim that unconscious bias training does not have the desired results, and resources would be better spent on other approaches
• Cite data to support your claim
• Explain how the data indicates that the method is ineffective
• Anticipate objections to your claim based on other data, indicating whether these objections are valid, and if not, why not.

Rogerian arguments

The Rogerian model also consists of four steps you might repeat throughout your essay:

• Discuss what the opposing position gets right and why people might hold this position
• Highlight the problems with this position
• Present your own position , showing how it addresses these problems
• Suggest a possible compromise —what elements of your position would proponents of the opposing position benefit from adopting?

This model builds up a clear picture of both sides of an argument and seeks a compromise. It is particularly useful when people tend to disagree strongly on the issue discussed, allowing you to approach opposing arguments in good faith.

Say you want to argue that the internet has had a positive impact on education. You might:

• Acknowledge that students rely too much on websites like Wikipedia
• Argue that teachers view Wikipedia as more unreliable than it really is
• Suggest that Wikipedia’s system of citations can actually teach students about referencing
• Suggest critical engagement with Wikipedia as a possible assignment for teachers who are skeptical of its usefulness.

You don’t necessarily have to pick one of these models—you may even use elements of both in different parts of your essay—but it’s worth considering them if you struggle to structure your arguments.

Regardless of which approach you take, your essay should always be structured using an introduction , a body , and a conclusion .

Like other academic essays, an argumentative essay begins with an introduction . The introduction serves to capture the reader’s interest, provide background information, present your thesis statement , and (in longer essays) to summarize the structure of the body.

Hover over different parts of the example below to see how a typical introduction works.

The spread of the internet has had a world-changing effect, not least on the world of education. The use of the internet in academic contexts is on the rise, and its role in learning is hotly debated. For many teachers who did not grow up with this technology, its effects seem alarming and potentially harmful. This concern, while understandable, is misguided. The negatives of internet use are outweighed by its critical benefits for students and educators—as a uniquely comprehensive and accessible information source; a means of exposure to and engagement with different perspectives; and a highly flexible learning environment.

The body of an argumentative essay is where you develop your arguments in detail. Here you’ll present evidence, analysis, and reasoning to convince the reader that your thesis statement is true.

In the standard five-paragraph format for short essays, the body takes up three of your five paragraphs. In longer essays, it will be more paragraphs, and might be divided into sections with headings.

Each paragraph covers its own topic, introduced with a topic sentence . Each of these topics must contribute to your overall argument; don’t include irrelevant information.

This example paragraph takes a Rogerian approach: It first acknowledges the merits of the opposing position and then highlights problems with that position.

Hover over different parts of the example to see how a body paragraph is constructed.

A common frustration for teachers is students’ use of Wikipedia as a source in their writing. Its prevalence among students is not exaggerated; a survey found that the vast majority of the students surveyed used Wikipedia (Head & Eisenberg, 2010). An article in The Guardian stresses a common objection to its use: “a reliance on Wikipedia can discourage students from engaging with genuine academic writing” (Coomer, 2013). Teachers are clearly not mistaken in viewing Wikipedia usage as ubiquitous among their students; but the claim that it discourages engagement with academic sources requires further investigation. This point is treated as self-evident by many teachers, but Wikipedia itself explicitly encourages students to look into other sources. Its articles often provide references to academic publications and include warning notes where citations are missing; the site’s own guidelines for research make clear that it should be used as a starting point, emphasizing that users should always “read the references and check whether they really do support what the article says” (“Wikipedia:Researching with Wikipedia,” 2020). Indeed, for many students, Wikipedia is their first encounter with the concepts of citation and referencing. The use of Wikipedia therefore has a positive side that merits deeper consideration than it often receives.

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An argumentative essay ends with a conclusion that summarizes and reflects on the arguments made in the body.

No new arguments or evidence appear here, but in longer essays you may discuss the strengths and weaknesses of your argument and suggest topics for future research. In all conclusions, you should stress the relevance and importance of your argument.

Hover over the following example to see the typical elements of a conclusion.

The internet has had a major positive impact on the world of education; occasional pitfalls aside, its value is evident in numerous applications. The future of teaching lies in the possibilities the internet opens up for communication, research, and interactivity. As the popularity of distance learning shows, students value the flexibility and accessibility offered by digital education, and educators should fully embrace these advantages. The internet’s dangers, real and imaginary, have been documented exhaustively by skeptics, but the internet is here to stay; it is time to focus seriously on its potential for good.

If you want to know more about AI tools , college essays , or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!

• Ad hominem fallacy
• Post hoc fallacy
• Appeal to authority fallacy
• False cause fallacy
• Sunk cost fallacy

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An argumentative essay tends to be a longer essay involving independent research, and aims to make an original argument about a topic. Its thesis statement makes a contentious claim that must be supported in an objective, evidence-based way.

An expository essay also aims to be objective, but it doesn’t have to make an original argument. Rather, it aims to explain something (e.g., a process or idea) in a clear, concise way. Expository essays are often shorter assignments and rely less on research.

At college level, you must properly cite your sources in all essays , research papers , and other academic texts (except exams and in-class exercises).

Add a citation whenever you quote , paraphrase , or summarize information or ideas from a source. You should also give full source details in a bibliography or reference list at the end of your text.

The exact format of your citations depends on which citation style you are instructed to use. The most common styles are APA , MLA , and Chicago .

The majority of the essays written at university are some sort of argumentative essay . Unless otherwise specified, you can assume that the goal of any essay you’re asked to write is argumentative: To convince the reader of your position using evidence and reasoning.

In composition classes you might be given assignments that specifically test your ability to write an argumentative essay. Look out for prompts including instructions like “argue,” “assess,” or “discuss” to see if this is the goal.

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Moral Reasoning

While moral reasoning can be undertaken on another’s behalf, it is paradigmatically an agent’s first-personal (individual or collective) practical reasoning about what, morally, they ought to do. Philosophical examination of moral reasoning faces both distinctive puzzles – about how we recognize moral considerations and cope with conflicts among them and about how they move us to act – and distinctive opportunities for gleaning insight about what we ought to do from how we reason about what we ought to do.

Part I of this article characterizes moral reasoning more fully, situates it in relation both to first-order accounts of what morality requires of us and to philosophical accounts of the metaphysics of morality, and explains the interest of the topic. Part II then takes up a series of philosophical questions about moral reasoning, so understood and so situated.

1.1 Defining “Moral Reasoning”

1.2 empirical challenges to moral reasoning, 1.3 situating moral reasoning, 1.4 gaining moral insight from studying moral reasoning, 1.5 how distinct is moral reasoning from practical reasoning in general, 2.1 moral uptake, 2.2 moral principles, 2.3 sorting out which considerations are most relevant, 2.4 moral reasoning and moral psychology, 2.5 modeling conflicting moral considerations, 2.6 moral learning and the revision of moral views, 2.7 how can we reason, morally, with one another, other internet resources, related entries, 1. the philosophical importance of moral reasoning.

This article takes up moral reasoning as a species of practical reasoning – that is, as a type of reasoning directed towards deciding what to do and, when successful, issuing in an intention (see entry on practical reason ). Of course, we also reason theoretically about what morality requires of us; but the nature of purely theoretical reasoning about ethics is adequately addressed in the various articles on ethics . It is also true that, on some understandings, moral reasoning directed towards deciding what to do involves forming judgments about what one ought, morally, to do. On these understandings, asking what one ought (morally) to do can be a practical question, a certain way of asking about what to do. (See section 1.5 on the question of whether this is a distinctive practical question.) In order to do justice to the full range of philosophical views about moral reasoning, we will need to have a capacious understanding of what counts as a moral question. For instance, since a prominent position about moral reasoning is that the relevant considerations are not codifiable, we would beg a central question if we here defined “ morality ” as involving codifiable principles or rules. For present purposes, we may understand issues about what is right or wrong, or virtuous or vicious, as raising moral questions.

Even when moral questions explicitly arise in daily life, just as when we are faced with child-rearing, agricultural, and business questions, sometimes we act impulsively or instinctively rather than pausing to reason, not just about what to do, but about what we ought to do. Jean-Paul Sartre described a case of one of his students who came to him in occupied Paris during World War II, asking advice about whether to stay by his mother, who otherwise would have been left alone, or rather to go join the forces of the Free French, then massing in England (Sartre 1975). In the capacious sense just described, this is probably a moral question; and the young man paused long enough to ask Sartre’s advice. Does that mean that this young man was reasoning about his practical question? Not necessarily. Indeed, Sartre used the case to expound his skepticism about the possibility of addressing such a practical question by reasoning. But what is reasoning?

Reasoning, of the sort discussed here, is active or explicit thinking, in which the reasoner, responsibly guided by her assessments of her reasons (Kolodny 2005) and of any applicable requirements of rationality (Broome 2009, 2013), attempts to reach a well-supported answer to a well-defined question (Hieronymi 2013). For Sartre’s student, at least such a question had arisen. Indeed, the question was relatively definite, implying that the student had already engaged in some reflection about the various alternatives available to him – a process that has well been described as an important phase of practical reasoning, one that aptly precedes the effort to make up one’s mind (Harman 1986, 2).

Characterizing reasoning as responsibly conducted thinking of course does not suffice to analyze the notion. For one thing, it fails to address the fraught question of reasoning’s relation to inference (Harman 1986, Broome 2009). In addition, it does not settle whether formulating an intention about what to do suffices to conclude practical reasoning or whether such intentions cannot be adequately worked out except by starting to act. Perhaps one cannot adequately reason about how to repair a stone wall or how to make an omelet with the available ingredients without actually starting to repair or to cook (cf. Fernandez 2016). Still, it will do for present purposes. It suffices to make clear that the idea of reasoning involves norms of thinking. These norms of aptness or correctness in practical thinking surely do not require us to think along a single prescribed pathway, but rather permit only certain pathways and not others (Broome 2013, 219). Even so, we doubtless often fail to live up to them.

Our thinking, including our moral thinking, is often not explicit. We could say that we also reason tacitly, thinking in much the same way as during explicit reasoning, but without any explicit attempt to reach well-supported answers. In some situations, even moral ones, we might be ill-advised to attempt to answer our practical questions by explicit reasoning. In others, it might even be a mistake to reason tacitly – because, say, we face a pressing emergency. “Sometimes we should not deliberate about what to do, and just drive” (Arpaly and Schroeder 2014, 50). Yet even if we are not called upon to think through our options in all situations, and even if sometimes it would be positively better if we did not, still, if we are called upon to do so, then we should conduct our thinking responsibly: we should reason.

Recent work in empirical ethics has indicated that even when we are called upon to reason morally, we often do so badly. When asked to give reasons for our moral intuitions, we are often “dumbfounded,” finding nothing to say in their defense (Haidt 2001). Our thinking about hypothetical moral scenarios has been shown to be highly sensitive to arbitrary variations, such as in the order of presentation. Even professional philosophers have been found to be prone to such lapses of clear thinking (e.g., Schwitzgebel & Cushman 2012). Some of our dumbfounding and confusion has been laid at the feet of our having both a fast, more emotional way of processing moral stimuli and a slow, more cognitive way (e.g., Greene 2014). An alternative explanation of moral dumbfounding looks to social norms of moral reasoning (Sneddon 2007). And a more optimistic reaction to our confusion sees our established patterns of “moral consistency reasoning” as being well-suited to cope with the clashing input generated by our fast and slow systems (Campbell & Kumar 2012) or as constituting “a flexible learning system that generates and updates a multidimensional evaluative landscape to guide decision and action” (Railton, 2014, 813).

Eventually, such empirical work on our moral reasoning may yield revisions in our norms of moral reasoning. This has not yet happened. This article is principally concerned with philosophical issues posed by our current norms of moral reasoning. For example, given those norms and assuming that they are more or less followed, how do moral considerations enter into moral reasoning, get sorted out by it when they clash, and lead to action? And what do those norms indicate about what we ought to do do?

The topic of moral reasoning lies in between two other commonly addressed topics in moral philosophy. On the one side, there is the first-order question of what moral truths there are, if any. For instance, are there any true general principles of morality, and if so, what are they? At this level utilitarianism competes with Kantianism, for instance, and both compete with anti-theorists of various stripes, who recognize only particular truths about morality (Clarke & Simpson 1989). On the other side, a quite different sort of question arises from seeking to give a metaphysical grounding for moral truths or for the claim that there are none. Supposing there are some moral truths, what makes them true? What account can be given of the truth-conditions of moral statements? Here arise familiar questions of moral skepticism and moral relativism ; here, the idea of “a reason” is wielded by many hoping to defend a non-skeptical moral metaphysics (e.g., Smith 2013). The topic of moral reasoning lies in between these two other familiar topics in the following simple sense: moral reasoners operate with what they take to be morally true but, instead of asking what makes their moral beliefs true, they proceed responsibly to attempt to figure out what to do in light of those considerations. The philosophical study of moral reasoning concerns itself with the nature of these attempts.

These three topics clearly interrelate. Conceivably, the relations between them would be so tight as to rule out any independent interest in the topic of moral reasoning. For instance, if all that could usefully be said about moral reasoning were that it is a matter of attending to the moral facts, then all interest would devolve upon the question of what those facts are – with some residual focus on the idea of moral attention (McNaughton 1988). Alternatively, it might be thought that moral reasoning is simply a matter of applying the correct moral theory via ordinary modes of deductive and empirical reasoning. Again, if that were true, one’s sufficient goal would be to find that theory and get the non-moral facts right. Neither of these reductive extremes seems plausible, however. Take the potential reduction to getting the facts right, first.

Contemporary advocates of the importance of correctly perceiving the morally relevant facts tend to focus on facts that we can perceive using our ordinary sense faculties and our ordinary capacities of recognition, such as that this person has an infection or that this person needs my medical help . On such a footing, it is possible to launch powerful arguments against the claim that moral principles undergird every moral truth (Dancy 1993) and for the claim that we can sometimes perfectly well decide what to do by acting on the reasons we perceive instinctively – or as we have been trained – without engaging in any moral reasoning. Yet this is not a sound footing for arguing that moral reasoning, beyond simply attending to the moral facts, is always unnecessary. On the contrary, we often find ourselves facing novel perplexities and moral conflicts in which our moral perception is an inadequate guide. In addressing the moral questions surrounding whether society ought to enforce surrogate-motherhood contracts, for instance, the scientific and technological novelties involved make our moral perceptions unreliable and shaky guides. When a medical researcher who has noted an individual’s illness also notes the fact that diverting resources to caring, clinically, for this individual would inhibit the progress of my research, thus harming the long-term health chances of future sufferers of this illness , he or she comes face to face with conflicting moral considerations. At this juncture, it is far less plausible or satisfying simply to say that, employing one’s ordinary sensory and recognitional capacities, one sees what is to be done, both things considered. To posit a special faculty of moral intuition that generates such overall judgments in the face of conflicting considerations is to wheel in a deus ex machina . It cuts inquiry short in a way that serves the purposes of fiction better than it serves the purposes of understanding. It is plausible instead to suppose that moral reasoning comes in at this point (Campbell & Kumar 2012).

For present purposes, it is worth noting, David Hume and the moral sense theorists do not count as short-circuiting our understanding of moral reasoning in this way. It is true that Hume presents himself, especially in the Treatise of Human Nature , as a disbeliever in any specifically practical or moral reasoning. In doing so, however, he employs an exceedingly narrow definition of “reasoning” (Hume 2000, Book I, Part iii, sect. ii). For present purposes, by contrast, we are using a broader working gloss of “reasoning,” one not controlled by an ambition to parse out the relative contributions of (the faculty of) reason and of the passions. And about moral reasoning in this broader sense, as responsible thinking about what one ought to do, Hume has many interesting things to say, starting with the thought that moral reasoning must involve a double correction of perspective (see section 2.4 ) adequately to account for the claims of other people and of the farther future, a double correction that is accomplished with the aid of the so-called “calm passions.”

If we turn from the possibility that perceiving the facts aright will displace moral reasoning to the possibility that applying the correct moral theory will displace – or exhaust – moral reasoning, there are again reasons to be skeptical. One reason is that moral theories do not arise in a vacuum; instead, they develop against a broad backdrop of moral convictions. Insofar as the first potentially reductive strand, emphasizing the importance of perceiving moral facts, has force – and it does have some – it also tends to show that moral theories need to gain support by systematizing or accounting for a wide range of moral facts (Sidgwick 1981). As in most other arenas in which theoretical explanation is called for, the degree of explanatory success will remain partial and open to improvement via revisions in the theory (see section 2.6 ). Unlike the natural sciences, however, moral theory is an endeavor that, as John Rawls once put it, is “Socratic” in that it is a subject pertaining to actions “shaped by self-examination” (Rawls 1971, 48f.). If this observation is correct, it suggests that the moral questions we set out to answer arise from our reflections about what matters. By the same token – and this is the present point – a moral theory is subject to being overturned because it generates concrete implications that do not sit well with us on due reflection. This being so, and granting the great complexity of the moral terrain, it seems highly unlikely that we will ever generate a moral theory on the basis of which we can serenely and confidently proceed in a deductive way to generate answers to what we ought to do in all concrete cases. This conclusion is reinforced by a second consideration, namely that insofar as a moral theory is faithful to the complexity of the moral phenomena, it will contain within it many possibilities for conflicts among its own elements. Even if it does deploy some priority rules, these are unlikely to be able to cover all contingencies. Hence, some moral reasoning that goes beyond the deductive application of the correct theory is bound to be needed.

In short, a sound understanding of moral reasoning will not take the form of reducing it to one of the other two levels of moral philosophy identified above. Neither the demand to attend to the moral facts nor the directive to apply the correct moral theory exhausts or sufficiently describes moral reasoning.

In addition to posing philosophical problems in its own right, moral reasoning is of interest on account of its implications for moral facts and moral theories. Accordingly, attending to moral reasoning will often be useful to those whose real interest is in determining the right answer to some concrete moral problem or in arguing for or against some moral theory. The characteristic ways we attempt to work through a given sort of moral quandary can be just as revealing about our considered approaches to these matters as are any bottom-line judgments we may characteristically come to. Further, we may have firm, reflective convictions about how a given class of problems is best tackled, deliberatively, even when we remain in doubt about what should be done. In such cases, attending to the modes of moral reasoning that we characteristically accept can usefully expand the set of moral information from which we start, suggesting ways to structure the competing considerations.

Facts about the nature of moral inference and moral reasoning may have important direct implications for moral theory. For instance, it might be taken to be a condition of adequacy of any moral theory that it play a practically useful role in our efforts at self-understanding and deliberation. It should be deliberation-guiding (Richardson 2018, §1.2). If this condition is accepted, then any moral theory that would require agents to engage in abstruse or difficult reasoning may be inadequate for that reason, as would be any theory that assumes that ordinary individuals are generally unable to reason in the ways that the theory calls for. J.S. Mill (1979) conceded that we are generally unable to do the calculations called for by utilitarianism, as he understood it, and argued that we should be consoled by the fact that, over the course of history, experience has generated secondary principles that guide us well enough. Rather more dramatically, R. M. Hare defended utilitarianism as well capturing the reasoning of ideally informed and rational “archangels” (1981). Taking seriously a deliberation-guidance desideratum for moral theory would favor, instead, theories that more directly inform efforts at moral reasoning by we “proletarians,” to use Hare’s contrasting term.

Accordingly, the close relations between moral reasoning, the moral facts, and moral theory do not eliminate moral reasoning as a topic of interest. To the contrary, because moral reasoning has important implications about moral facts and moral theories, these close relations lend additional interest to the topic of moral reasoning.

The final threshold question is whether moral reasoning is truly distinct from practical reasoning more generally understood. (The question of whether moral reasoning, even if practical, is structurally distinct from theoretical reasoning that simply proceeds from a proper recognition of the moral facts has already been implicitly addressed and answered, for the purposes of the present discussion, in the affirmative.) In addressing this final question, it is difficult to overlook the way different moral theories project quite different models of moral reasoning – again a link that might be pursued by the moral philosopher seeking leverage in either direction. For instance, Aristotle’s views might be as follows: a quite general account can be given of practical reasoning, which includes selecting means to ends and determining the constituents of a desired activity. The difference between the reasoning of a vicious person and that of a virtuous person differs not at all in its structure, but only in its content, for the virtuous person pursues true goods, whereas the vicious person simply gets side-tracked by apparent ones. To be sure, the virtuous person may be able to achieve a greater integration of his or her ends via practical reasoning (because of the way the various virtues cohere), but this is a difference in the result of practical reasoning and not in its structure. At an opposite extreme, Kant’s categorical imperative has been taken to generate an approach to practical reasoning (via a “typic of practical judgment”) that is distinctive from other practical reasoning both in the range of considerations it addresses and its structure (Nell 1975). Whereas prudential practical reasoning, on Kant’s view, aims to maximize one’s happiness, moral reasoning addresses the potential universalizability of the maxims – roughly, the intentions – on which one acts. Views intermediate between Aristotle’s and Kant’s in this respect include Hare’s utilitarian view and Aquinas’ natural-law view. On Hare’s view, just as an ideal prudential agent applies maximizing rationality to his or her own preferences, an ideal moral agent’s reasoning applies maximizing rationality to the set of everyone’s preferences that its archangelic capacity for sympathy has enabled it to internalize (Hare 1981). Thomistic, natural-law views share the Aristotelian view about the general unity of practical reasoning in pursuit of the good, rightly or wrongly conceived, but add that practical reason, in addition to demanding that we pursue the fundamental human goods, also, and distinctly, demands that we not attack these goods. In this way, natural-law views incorporate some distinctively moral structuring – such as the distinctions between doing and allowing and the so-called doctrine of double effect’s distinction between intending as a means and accepting as a by-product – within a unified account of practical reasoning (see entry on the natural law tradition in ethics ). In light of this diversity of views about the relation between moral reasoning and practical or prudential reasoning, a general account of moral reasoning that does not want to presume the correctness of a definite moral theory will do well to remain agnostic on the question of how moral reasoning relates to non-moral practical reasoning.

2. General Philosophical Questions about Moral Reasoning

To be sure, most great philosophers who have addressed the nature of moral reasoning were far from agnostic about the content of the correct moral theory, and developed their reflections about moral reasoning in support of or in derivation from their moral theory. Nonetheless, contemporary discussions that are somewhat agnostic about the content of moral theory have arisen around important and controversial aspects of moral reasoning. We may group these around the following seven questions:

• How do relevant considerations get taken up in moral reasoning?
• Is it essential to moral reasoning for the considerations it takes up to be crystallized into, or ranged under, principles?
• How do we sort out which moral considerations are most relevant?
• In what ways do motivational elements shape moral reasoning?
• What is the best way to model the kinds of conflicts among considerations that arise in moral reasoning?
• Does moral reasoning include learning from experience and changing one’s mind?
• How can we reason, morally, with one another?

The remainder of this article takes up these seven questions in turn.

One advantage to defining “reasoning” capaciously, as here, is that it helps one recognize that the processes whereby we come to be concretely aware of moral issues are integral to moral reasoning as it might more narrowly be understood. Recognizing moral issues when they arise requires a highly trained set of capacities and a broad range of emotional attunements. Philosophers of the moral sense school of the 17th and 18th centuries stressed innate emotional propensities, such as sympathy with other humans. Classically influenced virtue theorists, by contrast, give more importance to the training of perception and the emotional growth that must accompany it. Among contemporary philosophers working in empirical ethics there is a similar divide, with some arguing that we process situations using an innate moral grammar (Mikhail 2011) and some emphasizing the role of emotions in that processing (Haidt 2001, Prinz 2007, Greene 2014). For the moral reasoner, a crucial task for our capacities of moral recognition is to mark out certain features of a situation as being morally salient. Sartre’s student, for instance, focused on the competing claims of his mother and the Free French, giving them each an importance to his situation that he did not give to eating French cheese or wearing a uniform. To say that certain features are marked out as morally salient is not to imply that the features thus singled out answer to the terms of some general principle or other: we will come to the question of particularism, below. Rather, it is simply to say that recognitional attention must have a selective focus.

What will be counted as a moral issue or difficulty, in the sense requiring moral agents’ recognition, will again vary by moral theory. Not all moral theories would count filial loyalty and patriotism as moral duties. It is only at great cost, however, that any moral theory could claim to do without a layer of moral thinking involving situation-recognition. A calculative sort of utilitarianism, perhaps, might be imagined according to which there is no need to spot a moral issue or difficulty, as every choice node in life presents the agent with the same, utility-maximizing task. Perhaps Jeremy Bentham held a utilitarianism of this sort. For the more plausible utilitarianisms mentioned above, however, such as Mill’s and Hare’s, agents need not always calculate afresh, but must instead be alive to the possibility that because the ordinary “landmarks and direction posts” lead one astray in the situation at hand, they must make recourse to a more direct and critical mode of moral reasoning. Recognizing whether one is in one of those situations thus becomes the principal recognitional task for the utilitarian agent. (Whether this task can be suitably confined, of course, has long been one of the crucial questions about whether such indirect forms of utilitarianism, attractive on other grounds, can prevent themselves from collapsing into a more Benthamite, direct form: cf. Brandt 1979.)

Note that, as we have been describing moral uptake, we have not implied that what is perceived is ever a moral fact. Rather, it might be that what is perceived is some ordinary, descriptive feature of a situation that is, for whatever reason, morally relevant. An account of moral uptake will interestingly impinge upon the metaphysics of moral facts, however, if it holds that moral facts can be perceived. Importantly intermediate, in this respect, is the set of judgments involving so-called “thick” evaluative concepts – for example, that someone is callous, boorish, just, or brave (see the entry on thick ethical concepts ). These do not invoke the supposedly “thinner” terms of overall moral assessment, “good,” or “right.” Yet they are not innocent of normative content, either. Plainly, we do recognize callousness when we see clear cases of it. Plainly, too – whatever the metaphysical implications of the last fact – our ability to describe our situations in these thick normative terms is crucial to our ability to reason morally.

It is debated how closely our abilities of moral discernment are tied to our moral motivations. For Aristotle and many of his ancient successors, the two are closely linked, in that someone not brought up into virtuous motivations will not see things correctly. For instance, cowards will overestimate dangers, the rash will underestimate them, and the virtuous will perceive them correctly ( Eudemian Ethics 1229b23–27). By the Stoics, too, having the right motivations was regarded as intimately tied to perceiving the world correctly; but whereas Aristotle saw the emotions as allies to enlist in support of sound moral discernment, the Stoics saw them as inimical to clear perception of the truth (cf. Nussbaum 2001).

That one discerns features and qualities of some situation that are relevant to sizing it up morally does not yet imply that one explicitly or even implicitly employs any general claims in describing it. Perhaps all that one perceives are particularly embedded features and qualities, without saliently perceiving them as instantiations of any types. Sartre’s student may be focused on his mother and on the particular plights of several of his fellow Frenchmen under Nazi occupation, rather than on any purported requirements of filial duty or patriotism. Having become aware of some moral issue in such relatively particular terms, he might proceed directly to sorting out the conflict between them. Another possibility, however, and one that we frequently seem to exploit, is to formulate the issue in general terms: “An only child should stick by an otherwise isolated parent,” for instance, or “one should help those in dire need if one can do so without significant personal sacrifice.” Such general statements would be examples of “moral principles,” in a broad sense. (We do not here distinguish between principles and rules. Those who do include Dworkin 1978 and Gert 1998.)

We must be careful, here, to distinguish the issue of whether principles commonly play an implicit or explicit role in moral reasoning, including well-conducted moral reasoning, from the issue of whether principles necessarily figure as part of the basis of moral truth. The latter issue is best understood as a metaphysical question about the nature and basis of moral facts. What is currently known as moral particularism is the view that there are no defensible moral principles and that moral reasons, or well-grounded moral facts, can exist independently of any basis in a general principle. A contrary view holds that moral reasons are necessarily general, whether because the sources of their justification are all general or because a moral claim is ill-formed if it contains particularities. But whether principles play a useful role in moral reasoning is certainly a different question from whether principles play a necessary role in accounting for the ultimate truth-conditions of moral statements. Moral particularism, as just defined, denies their latter role. Some moral particularists seem also to believe that moral particularism implies that moral principles cannot soundly play a useful role in reasoning. This claim is disputable, as it seems a contingent matter whether the relevant particular facts arrange themselves in ways susceptible to general summary and whether our cognitive apparatus can cope with them at all without employing general principles. Although the metaphysical controversy about moral particularism lies largely outside our topic, we will revisit it in section 2.5 , in connection with the weighing of conflicting reasons.

With regard to moral reasoning, while there are some self-styled “anti-theorists” who deny that abstract structures of linked generalities are important to moral reasoning (Clarke, et al. 1989), it is more common to find philosophers who recognize both some role for particular judgment and some role for moral principles. Thus, neo-Aristotelians like Nussbaum who emphasize the importance of “finely tuned and richly aware” particular discernment also regard that discernment as being guided by a set of generally describable virtues whose general descriptions will come into play in at least some kinds of cases (Nussbaum 1990). “Situation ethicists” of an earlier generation (e.g. Fletcher 1997) emphasized the importance of taking into account a wide range of circumstantial differentiae, but against the background of some general principles whose application the differentiae help sort out. Feminist ethicists influenced by Carol Gilligan’s path breaking work on moral development have stressed the moral centrality of the kind of care and discernment that are salient and well-developed by people immersed in particular relationships (Held 1995); but this emphasis is consistent with such general principles as “one ought to be sensitive to the wishes of one’s friends”(see the entry on feminist moral psychology ). Again, if we distinguish the question of whether principles are useful in responsibly-conducted moral thinking from the question of whether moral reasons ultimately all derive from general principles, and concentrate our attention solely on the former, we will see that some of the opposition to general moral principles melts away.

It should be noted that we have been using a weak notion of generality, here. It is contrasted only with the kind of strict particularity that comes with indexicals and proper names. General statements or claims – ones that contain no such particular references – are not necessarily universal generalizations, making an assertion about all cases of the mentioned type. Thus, “one should normally help those in dire need” is a general principle, in this weak sense. Possibly, such logically loose principles would be obfuscatory in the context of an attempt to reconstruct the ultimate truth-conditions of moral statements. Such logically loose principles would clearly be useless in any attempt to generate a deductively tight “practical syllogism.” In our day-to-day, non-deductive reasoning, however, such logically loose principles appear to be quite useful. (Recall that we are understanding “reasoning” quite broadly, as responsibly conducted thinking: nothing in this understanding of reasoning suggests any uniquely privileged place for deductive inference: cf. Harman 1986. For more on defeasible or “default” principles, see section 2.5 .)

In this terminology, establishing that general principles are essential to moral reasoning leaves open the further question whether logically tight, or exceptionless, principles are also essential to moral reasoning. Certainly, much of our actual moral reasoning seems to be driven by attempts to recast or reinterpret principles so that they can be taken to be exceptionless. Adherents and inheritors of the natural-law tradition in ethics (e.g. Donagan 1977) are particularly supple defenders of exceptionless moral principles, as they are able to avail themselves not only of a refined tradition of casuistry but also of a wide array of subtle – some would say overly subtle – distinctions, such as those mentioned above between doing and allowing and between intending as a means and accepting as a byproduct.

A related role for a strong form of generality in moral reasoning comes from the Kantian thought that one’s moral reasoning must counter one’s tendency to make exceptions for oneself. Accordingly, Kant holds, as we have noted, that we must ask whether the maxims of our actions can serve as universal laws. As most contemporary readers understand this demand, it requires that we engage in a kind of hypothetical generalization across agents, and ask about the implications of everybody acting that way in those circumstances. The grounds for developing Kant’s thought in this direction have been well explored (e.g., Nell 1975, Korsgaard 1996, Engstrom 2009). The importance and the difficulties of such a hypothetical generalization test in ethics were discussed the influential works Gibbard 1965 and Goldman 1974.

Whether or not moral considerations need the backing of general principles, we must expect situations of action to present us with multiple moral considerations. In addition, of course, these situations will also present us with a lot of information that is not morally relevant. On any realistic account, a central task of moral reasoning is to sort out relevant considerations from irrelevant ones, as well as to determine which are especially relevant and which only slightly so. That a certain woman is Sartre’s student’s mother seems arguably to be a morally relevant fact; what about the fact (supposing it is one) that she has no other children to take care of her? Addressing the task of sorting what is morally relevant from what is not, some philosophers have offered general accounts of moral relevant features. Others have given accounts of how we sort out which of the relevant features are most relevant, a process of thinking that sometimes goes by the name of “casuistry.”

Before we look at ways of sorting out which features are morally relevant or most morally relevant, it may be useful to note a prior step taken by some casuists, which was to attempt to set out a schema that would capture all of the features of an action or proposed action. The Roman Catholic casuists of the middle ages did so by drawing on Aristotle’s categories. Accordingly, they asked, where, when, why, how, by what means, to whom, or by whom the action in question is to be done or avoided (see Jonsen and Toulmin 1988). The idea was that complete answers to these questions would contain all of the features of the action, of which the morally relevant ones would be a subset. Although metaphysically uninteresting, the idea of attempting to list all of an action’s features in this way represents a distinctive – and extreme – heuristic for moral reasoning.

Turning to the morally relevant features, one of the most developed accounts is Bernard Gert’s. He develops a list of features relevant to whether the violation of a moral rule should be generally allowed. Given the designed function of Gert’s list, it is natural that most of his morally relevant features make reference to the set of moral rules he defended. Accordingly, some of Gert’s distinctions between dimensions of relevant features reflect controversial stances in moral theory. For example, one of the dimensions is whether “the violation [is] done intentionally or only knowingly” (Gert 1998, 234) – a distinction that those who reject the doctrine of double effect would not find relevant.

In deliberating about what we ought, morally, to do, we also often attempt to figure out which considerations are most relevant. To take an issue mentioned above: Are surrogate motherhood contracts more akin to agreements with babysitters (clearly acceptable) or to agreements with prostitutes (not clearly so)? That is, which feature of surrogate motherhood is more relevant: that it involves a contract for child-care services or that it involves payment for the intimate use of the body? Both in such relatively novel cases and in more familiar ones, reasoning by analogy plays a large role in ordinary moral thinking. When this reasoning by analogy starts to become systematic – a social achievement that requires some historical stability and reflectiveness about what are taken to be moral norms – it begins to exploit comparison to cases that are “paradigmatic,” in the sense of being taken as settled. Within such a stable background, a system of casuistry can develop that lends some order to the appeal to analogous cases. To use an analogy: the availability of a widely accepted and systematic set of analogies and the availability of what are taken to be moral norms may stand to one another as chicken does to egg: each may be an indispensable moment in the genesis of the other.

Casuistry, thus understood, is an indispensable aid to moral reasoning. At least, that it is would follow from conjoining two features of the human moral situation mentioned above: the multifariousness of moral considerations that arise in particular cases and the need and possibility for employing moral principles in sound moral reasoning. We require moral judgment, not simply a deductive application of principles or a particularist bottom-line intuition about what we should do. This judgment must be responsible to moral principles yet cannot be straightforwardly derived from them. Accordingly, our moral judgment is greatly aided if it is able to rest on the sort of heuristic support that casuistry offers. Thinking through which of two analogous cases provides a better key to understanding the case at hand is a useful way of organizing our moral reasoning, and one on which we must continue to depend. If we lack the kind of broad consensus on a set of paradigm cases on which the Renaissance Catholic or Talmudic casuists could draw, our casuistic efforts will necessarily be more controversial and tentative than theirs; but we are not wholly without settled cases from which to work. Indeed, as Jonsen and Toulmin suggest at the outset of their thorough explanation and defense of casuistry, the depth of disagreement about moral theories that characterizes a pluralist society may leave us having to rest comparatively more weight on the cases about which we can find agreement than did the classic casuists (Jonsen and Toulmin 1988).

Despite the long history of casuistry, there is little that can usefully be said about how one ought to reason about competing analogies. In the law, where previous cases have precedential importance, more can be said. As Sunstein notes (Sunstein 1996, chap. 3), the law deals with particular cases, which are always “potentially distinguishable” (72); yet the law also imposes “a requirement of practical consistency” (67). This combination of features makes reasoning by analogy particularly influential in the law, for one must decide whether a given case is more like one set of precedents or more like another. Since the law must proceed even within a pluralist society such as ours, Sunstein argues, we see that analogical reasoning can go forward on the basis of “incompletely theorized judgments” or of what Rawls calls an “overlapping consensus” (Rawls 1996). That is, although a robust use of analogous cases depends, as we have noted, on some shared background agreement, this agreement need not extend to all matters or all levels of individuals’ moral thinking. Accordingly, although in a pluralist society we may lack the kind of comprehensive normative agreement that made the high casuistry of Renaissance Christianity possible, the path of the law suggests that normatively forceful, case-based, analogical reasoning can still go on. A modern, competing approach to case-based or precedent-respecting reasoning has been developed by John F. Horty (2016). On Horty’s approach, which builds on the default logic developed in (Horty 2012), the body of precedent systematically shifts the weights of the reasons arising in a new case.

Reasoning by appeal to cases is also a favorite mode of some recent moral philosophers. Since our focus here is not on the methods of moral theory, we do not need to go into any detail in comparing different ways in which philosophers wield cases for and against alternative moral theories. There is, however, an important and broadly applicable point worth making about ordinary reasoning by reference to cases that emerges most clearly from the philosophical use of such reasoning. Philosophers often feel free to imagine cases, often quite unlikely ones, in order to attempt to isolate relevant differences. An infamous example is a pair of cases offered by James Rachels to cast doubt on the moral significance of the distinction between killing and letting die, here slightly redescribed. In both cases, there is at the outset a boy in a bathtub and a greedy older cousin downstairs who will inherit the family manse if and only if the boy predeceases him (Rachels 1975). In Case A, the cousin hears a thump, runs up to find the boy unconscious in the bath, and reaches out to turn on the tap so that the water will rise up to drown the boy. In Case B, the cousin hears a thump, runs up to find the boy unconscious in the bath with the water running, and decides to sit back and do nothing until the boy drowns. Since there is surely no moral difference between these cases, Rachels argued, the general distinction between killing and letting die is undercut. “Not so fast!” is the well-justified reaction (cf. Beauchamp 1979). Just because a factor is morally relevant in a certain way in comparing one pair of cases does not mean that it either is or must be relevant in the same way or to the same degree when comparing other cases. Shelly Kagan has dubbed the failure to take account of this fact of contextual interaction when wielding comparison cases the “additive fallacy” (1988). Kagan concludes from this that the reasoning of moral theorists must depend upon some theory that helps us anticipate and account for ways in which factors will interact in various contexts. A parallel lesson, reinforcing what we have already observed in connection with casuistry proper, would apply for moral reasoning in general: reasoning from cases must at least implicitly rely upon a set of organizing judgments or beliefs, of a kind that would, on some understandings, count as a moral “theory.” If this is correct, it provides another kind of reason to think that moral considerations could be crystallized into principles that make manifest the organizing structure involved.

We are concerned here with moral reasoning as a species of practical reasoning – reasoning directed to deciding what to do and, if successful, issuing in an intention. But how can such practical reasoning succeed? How can moral reasoning hook up with motivationally effective psychological states so as to have this kind of causal effect? “Moral psychology” – the traditional name for the philosophical study of intention and action – has a lot to say to such questions, both in its traditional, a priori form and its newly popular empirical form. In addition, the conclusions of moral psychology can have substantive moral implications, for it may be reasonable to assume that if there are deep reasons that a given type of moral reasoning cannot be practical, then any principles that demand such reasoning are unsound. In this spirit, Samuel Scheffler has explored “the importance for moral philosophy of some tolerably realistic understanding of human motivational psychology” (Scheffler 1992, 8) and Peter Railton has developed the idea that certain moral principles might generate a kind of “alienation” (Railton 1984). In short, we may be interested in what makes practical reasoning of a certain sort psychologically possible both for its own sake and as a way of working out some of the content of moral theory.

The issue of psychological possibility is an important one for all kinds of practical reasoning (cf. Audi 1989). In morality, it is especially pressing, as morality often asks individuals to depart from satisfying their own interests. As a result, it may appear that moral reasoning’s practical effect could not be explained by a simple appeal to the initial motivations that shape or constitute someone’s interests, in combination with a requirement, like that mentioned above, to will the necessary means to one’s ends. Morality, it may seem, instead requires individuals to act on ends that may not be part of their “motivational set,” in the terminology of Williams 1981. How can moral reasoning lead people to do that? The question is a traditional one. Plato’s Republic answered that the appearances are deceiving, and that acting morally is, in fact, in the enlightened self-interest of the agent. Kant, in stark contrast, held that our transcendent capacity to act on our conception of a practical law enables us to set ends and to follow morality even when doing so sharply conflicts with our interests. Many other answers have been given. In recent times, philosophers have defended what has been called “internalism” about morality, which claims that there is a necessary conceptual link between agents’ moral judgment and their motivation. Michael Smith, for instance, puts the claim as follows (Smith 1994, 61):

If an agent judges that it is right for her to Φ in circumstances C , then either she is motivated to Φ in C or she is practically irrational.

Even this defeasible version of moral judgment internalism may be too strong; but instead of pursuing this issue further, let us turn to a question more internal to moral reasoning. (For more on the issue of moral judgment internalism, see moral motivation .)

The traditional question we were just glancing at picks up when moral reasoning is done. Supposing that we have some moral conclusion, it asks how agents can be motivated to go along with it. A different question about the intersection of moral reasoning and moral psychology, one more immanent to the former, concerns how motivational elements shape the reasoning process itself.

A powerful philosophical picture of human psychology, stemming from Hume, insists that beliefs and desires are distinct existences (Hume 2000, Book II, part iii, sect. iii; cf. Smith 1994, 7). This means that there is always a potential problem about how reasoning, which seems to work by concatenating beliefs, links up to the motivations that desire provides. The paradigmatic link is that of instrumental action: the desire to Ψ links with the belief that by Φing in circumstances C one will Ψ. Accordingly, philosophers who have examined moral reasoning within an essentially Humean, belief-desire psychology have sometimes accepted a constrained account of moral reasoning. Hume’s own account exemplifies the sort of constraint that is involved. As Hume has it, the calm passions support the dual correction of perspective constitutive of morality, alluded to above. Since these calm passions are seen as competing with our other passions in essentially the same motivational coinage, as it were, our passions limit the reach of moral reasoning.

An important step away from a narrow understanding of Humean moral psychology is taken if one recognizes the existence of what Rawls has called “principle-dependent desires” (Rawls 1996, 82–83; Rawls 2000, 46–47). These are desires whose objects cannot be characterized without reference to some rational or moral principle. An important special case of these is that of “conception-dependent desires,” in which the principle-dependent desire in question is seen by the agent as belonging to a broader conception, and as important on that account (Rawls 1996, 83–84; Rawls 2000, 148–152). For instance, conceiving of oneself as a citizen, one may desire to bear one’s fair share of society’s burdens. Although it may look like any content, including this, may substitute for Ψ in the Humean conception of desire, and although Hume set out to show how moral sentiments such as pride could be explained in terms of simple psychological mechanisms, his influential empiricism actually tends to restrict the possible content of desires. Introducing principle-dependent desires thus seems to mark a departure from a Humean psychology. As Rawls remarks, if “we may find ourselves drawn to the conceptions and ideals that both the right and the good express … , [h]ow is one to fix limits on what people might be moved by in thought and deliberation and hence may act from?” (1996, 85). While Rawls developed this point by contrasting Hume’s moral psychology with Kant’s, the same basic point is also made by neo-Aristotelians (e.g., McDowell 1998).

The introduction of principle-dependent desires bursts any would-be naturalist limit on their content; nonetheless, some philosophers hold that this notion remains too beholden to an essentially Humean picture to be able to capture the idea of a moral commitment. Desires, it may seem, remain motivational items that compete on the basis of strength. Saying that one’s desire to be just may be outweighed by one’s desire for advancement may seem to fail to capture the thought that one has a commitment – even a non-absolute one – to justice. Sartre designed his example of the student torn between staying with his mother and going to fight with the Free French so as to make it seem implausible that he ought to decide simply by determining which he more strongly wanted to do.

One way to get at the idea of commitment is to emphasize our capacity to reflect about what we want. By this route, one might distinguish, in the fashion of Harry Frankfurt, between the strength of our desires and “the importance of what we care about” (Frankfurt 1988). Although this idea is evocative, it provides relatively little insight into how it is that we thus reflect. Another way to model commitment is to take it that our intentions operate at a level distinct from our desires, structuring what we are willing to reconsider at any point in our deliberations (e.g. Bratman 1999). While this two-level approach offers some advantages, it is limited by its concession of a kind of normative primacy to the unreconstructed desires at the unreflective level. A more integrated approach might model the psychology of commitment in a way that reconceives the nature of desire from the ground up. One attractive possibility is to return to the Aristotelian conception of desire as being for the sake of some good or apparent good (cf. Richardson 2004). On this conception, the end for the sake of which an action is done plays an important regulating role, indicating, in part, what one will not do (Richardson 2018, §§8.3–8.4). Reasoning about final ends accordingly has a distinctive character (see Richardson 1994, Schmidtz 1995). Whatever the best philosophical account of the notion of a commitment – for another alternative, see (Tiberius 2000) – much of our moral reasoning does seem to involve expressions of and challenges to our commitments (Anderson and Pildes 2000).

Recent experimental work, employing both survey instruments and brain imaging technologies, has allowed philosophers to approach questions about the psychological basis of moral reasoning from novel angles. The initial brain data seems to show that individuals with damage to the pre-frontal lobes tend to reason in more straightforwardly consequentialist fashion than those without such damage (Koenigs et al. 2007). Some theorists take this finding as tending to confirm that fully competent human moral reasoning goes beyond a simple weighing of pros and cons to include assessment of moral constraints (e.g., Wellman & Miller 2008, Young & Saxe 2008). Others, however, have argued that the emotional responses of the prefrontal lobes interfere with the more sober and sound, consequentialist-style reasoning of the other parts of the brain (e.g. Greene 2014). The survey data reveals or confirms, among other things, interesting, normatively loaded asymmetries in our attribution of such concepts as responsibility and causality (Knobe 2006). It also reveals that many of moral theory’s most subtle distinctions, such as the distinction between an intended means and a foreseen side-effect, are deeply built into our psychologies, being present cross-culturally and in young children, in a way that suggests to some the possibility of an innate “moral grammar” (Mikhail 2011).

A final question about the connection between moral motivation and moral reasoning is whether someone without the right motivational commitments can reason well, morally. On Hume’s official, narrow conception of reasoning, which essentially limits it to tracing empirical and logical connections, the answer would be yes. The vicious person could trace the causal and logical implications of acting in a certain way just as a virtuous person could. The only difference would be practical, not rational: the two would not act in the same way. Note, however, that the Humean’s affirmative answer depends on departing from the working definition of “moral reasoning” used in this article, which casts it as a species of practical reasoning. Interestingly, Kant can answer “yes” while still casting moral reasoning as practical. On his view in the Groundwork and the Critique of Practical Reason , reasoning well, morally, does not depend on any prior motivational commitment, yet remains practical reasoning. That is because he thinks the moral law can itself generate motivation. (Kant’s Metaphysics of Morals and Religion offer a more complex psychology.) For Aristotle, by contrast, an agent whose motivations are not virtuously constituted will systematically misperceive what is good and what is bad, and hence will be unable to reason excellently. The best reasoning that a vicious person is capable of, according to Aristotle, is a defective simulacrum of practical wisdom that he calls “cleverness” ( Nicomachean Ethics 1144a25).

Moral considerations often conflict with one another. So do moral principles and moral commitments. Assuming that filial loyalty and patriotism are moral considerations, then Sartre’s student faces a moral conflict. Recall that it is one thing to model the metaphysics of morality or the truth conditions of moral statements and another to give an account of moral reasoning. In now looking at conflicting considerations, our interest here remains with the latter and not the former. Our principal interest is in ways that we need to structure or think about conflicting considerations in order to negotiate well our reasoning involving them.

One influential building-block for thinking about moral conflicts is W. D. Ross’s notion of a “ prima facie duty”. Although this term misleadingly suggests mere appearance – the way things seem at first glance – it has stuck. Some moral philosophers prefer the term “ pro tanto duty” (e.g., Hurley 1989). Ross explained that his term provides “a brief way of referring to the characteristic (quite distinct from that of being a duty proper) which an act has, in virtue of being of a certain kind (e.g., the keeping of a promise), of being an act which would be a duty proper if it were not at the same time of another kind which is morally significant.” Illustrating the point, he noted that a prima facie duty to keep a promise can be overridden by a prima facie duty to avert a serious accident, resulting in a proper, or unqualified, duty to do the latter (Ross 1988, 18–19). Ross described each prima facie duty as a “parti-resultant” attribute, grounded or explained by one aspect of an act, whereas “being one’s [actual] duty” is a “toti-resultant” attribute resulting from all such aspects of an act, taken together (28; see Pietroski 1993). This suggests that in each case there is, in principle, some function that generally maps from the partial contributions of each prima facie duty to some actual duty. What might that function be? To Ross’s credit, he writes that “for the estimation of the comparative stringency of these prima facie obligations no general rules can, so far as I can see, be laid down” (41). Accordingly, a second strand in Ross simply emphasizes, following Aristotle, the need for practical judgment by those who have been brought up into virtue (42).

How might considerations of the sort constituted by prima facie duties enter our moral reasoning? They might do so explicitly, or only implicitly. There is also a third, still weaker possibility (Scheffler 1992, 32): it might simply be the case that if the agent had recognized a prima facie duty, he would have acted on it unless he considered it to be overridden. This is a fact about how he would have reasoned.

Despite Ross’s denial that there is any general method for estimating the comparative stringency of prima facie duties, there is a further strand in his exposition that many find irresistible and that tends to undercut this denial. In the very same paragraph in which he states that he sees no general rules for dealing with conflicts, he speaks in terms of “the greatest balance of prima facie rightness.” This language, together with the idea of “comparative stringency,” ineluctably suggests the idea that the mapping function might be the same in each case of conflict and that it might be a quantitative one. On this conception, if there is a conflict between two prima facie duties, the one that is strongest in the circumstances should be taken to win. Duly cautioned about the additive fallacy (see section 2.3 ), we might recognize that the strength of a moral consideration in one set of circumstances cannot be inferred from its strength in other circumstances. Hence, this approach will need still to rely on intuitive judgments in many cases. But this intuitive judgment will be about which prima facie consideration is stronger in the circumstances, not simply about what ought to be done.

The thought that our moral reasoning either requires or is benefited by a virtual quantitative crutch of this kind has a long pedigree. Can we really reason well morally in a way that boils down to assessing the weights of the competing considerations? Addressing this question will require an excursus on the nature of moral reasons. Philosophical support for this possibility involves an idea of practical commensurability. We need to distinguish, here, two kinds of practical commensurability or incommensurability, one defined in metaphysical terms and one in deliberative terms. Each of these forms might be stated evaluatively or deontically. The first, metaphysical sort of value incommensurability is defined directly in terms of what is the case. Thus, to state an evaluative version: two values are metaphysically incommensurable just in case neither is better than the other nor are they equally good (see Chang 1998). Now, the metaphysical incommensurability of values, or its absence, is only loosely linked to how it would be reasonable to deliberate. If all values or moral considerations are metaphysically (that is, in fact) commensurable, still it might well be the case that our access to the ultimate commensurating function is so limited that we would fare ill by proceeding in our deliberations to try to think about which outcomes are “better” or which considerations are “stronger.” We might have no clue about how to measure the relevant “strength.” Conversely, even if metaphysical value incommensurability is common, we might do well, deliberatively, to proceed as if this were not the case, just as we proceed in thermodynamics as if the gas laws obtained in their idealized form. Hence, in thinking about the deliberative implications of incommensurable values , we would do well to think in terms of a definition tailored to the deliberative context. Start with a local, pairwise form. We may say that two options, A and B, are deliberatively commensurable just in case there is some one dimension of value in terms of which, prior to – or logically independently of – choosing between them, it is possible adequately to represent the force of the considerations bearing on the choice.

Philosophers as diverse as Immanuel Kant and John Stuart Mill have argued that unless two options are deliberatively commensurable, in this sense, it is impossible to choose rationally between them. Interestingly, Kant limited this claim to the domain of prudential considerations, recognizing moral reasoning as invoking considerations incommensurable with those of prudence. For Mill, this claim formed an important part of his argument that there must be some one, ultimate “umpire” principle – namely, on his view, the principle of utility. Henry Sidgwick elaborated Mill’s argument and helpfully made explicit its crucial assumption, which he called the “principle of superior validity” (Sidgwick 1981; cf. Schneewind 1977). This is the principle that conflict between distinct moral or practical considerations can be rationally resolved only on the basis of some third principle or consideration that is both more general and more firmly warranted than the two initial competitors. From this assumption, one can readily build an argument for the rational necessity not merely of local deliberative commensurability, but of a global deliberative commensurability that, like Mill and Sidgwick, accepts just one ultimate umpire principle (cf. Richardson 1994, chap. 6).

Sidgwick’s explicitness, here, is valuable also in helping one see how to resist the demand for deliberative commensurability. Deliberative commensurability is not necessary for proceeding rationally if conflicting considerations can be rationally dealt with in a holistic way that does not involve the appeal to a principle of “superior validity.” That our moral reasoning can proceed holistically is strongly affirmed by Rawls. Rawls’s characterizations of the influential ideal of reflective equilibrium and his related ideas about the nature of justification imply that we can deal with conflicting considerations in less hierarchical ways than imagined by Mill or Sidgwick. Instead of proceeding up a ladder of appeal to some highest court or supreme umpire, Rawls suggests, when we face conflicting considerations “we work from both ends” (Rawls 1999, 18). Sometimes indeed we revise our more particular judgments in light of some general principle to which we adhere; but we are also free to revise more general principles in light of some relatively concrete considered judgment. On this picture, there is no necessary correlation between degree of generality and strength of authority or warrant. That this holistic way of proceeding (whether in building moral theory or in deliberating: cf. Hurley 1989) can be rational is confirmed by the possibility of a form of justification that is similarly holistic: “justification is a matter of the mutual support of many considerations, of everything fitting together into one coherent view” (Rawls 1999, 19, 507). (Note that this statement, which expresses a necessary aspect of moral or practical justification, should not be taken as a definition or analysis thereof.) So there is an alternative to depending, deliberatively, on finding a dimension in terms of which considerations can be ranked as “stronger” or “better” or “more stringent”: one can instead “prune and adjust” with an eye to building more mutual support among the considerations that one endorses on due reflection. If even the desideratum of practical coherence is subject to such re-specification, then this holistic possibility really does represent an alternative to commensuration, as the deliberator, and not some coherence standard, retains reflective sovereignty (Richardson 1994, sec. 26). The result can be one in which the originally competing considerations are not so much compared as transformed (Richardson 2018, chap. 1)

Suppose that we start with a set of first-order moral considerations that are all commensurable as a matter of ultimate, metaphysical fact, but that our grasp of the actual strength of these considerations is quite poor and subject to systematic distortions. Perhaps some people are much better placed than others to appreciate certain considerations, and perhaps our strategic interactions would cause us to reach suboptimal outcomes if we each pursued our own unfettered judgment of how the overall set of considerations plays out. In such circumstances, there is a strong case for departing from maximizing reasoning without swinging all the way to the holist alternative. This case has been influentially articulated by Joseph Raz, who develops the notion of an “exclusionary reason” to occupy this middle position (Raz 1990).

“An exclusionary reason,” in Raz’s terminology, “is a second order reason to refrain from acting for some reason” (39). A simple example is that of Ann, who is tired after a long and stressful day, and hence has reason not to act on her best assessment of the reasons bearing on a particularly important investment decision that she immediately faces (37). This notion of an exclusionary reason allowed Raz to capture many of the complexities of our moral reasoning, especially as it involves principled commitments, while conceding that, at the first order, all practical reasons might be commensurable. Raz’s early strategy for reconciling commensurability with complexity of structure was to limit the claim that reasons are comparable with regard to strength to reasons of a given order. First-order reasons compete on the basis of strength; but conflicts between first- and second-order reasons “are resolved not by the strength of the competing reasons but by a general principle of practical reasoning which determines that exclusionary reasons always prevail” (40).

If we take for granted this “general principle of practical reasoning,” why should we recognize the existence of any exclusionary reasons, which by definition prevail independently of any contest of strength? Raz’s principal answer to this question shifts from the metaphysical domain of the strengths that various reasons “have” to the epistemically limited viewpoint of the deliberator. As in Ann’s case, we can see in certain contexts that a deliberator is likely to get things wrong if he or she acts on his or her perception of the first-order reasons. Second-order reasons indicate, with respect to a certain range of first-order reasons, that the agent “must not act for those reasons” (185). The broader justification of an exclusionary reason, then, can consistently be put in terms of the commensurable first-order reasons. Such a justification can have the following form: “Given this agent’s deliberative limitations, the balance of first-order reasons will likely be better conformed with if he or she refrains from acting for certain of those reasons.”

Raz’s account of exclusionary reasons might be used to reconcile ultimate commensurability with the structured complexity of our moral reasoning. Whether such an attempt could succeed would depend, in part, on the extent to which we have an actual grasp of first-order reasons, conflict among which can be settled solely on the basis of their comparative strength. Our consideration, above, of casuistry, the additive fallacy, and deliberative incommensurability may combine to make it seem that only in rare pockets of our practice do we have a good grasp of first-order reasons, if these are defined, à la Raz, as competing only in terms of strength. If that is right, then we will almost always have good exclusionary reasons to reason on some other basis than in terms of the relative strength of first-order reasons. Under those assumptions, the middle way that Raz’s idea of exclusionary reasons seems to open up would more closely approach the holist’s.

The notion of a moral consideration’s “strength,” whether put forward as part of a metaphysical picture of how first-order considerations interact in fact or as a suggestion about how to go about resolving a moral conflict, should not be confused with the bottom-line determination of whether one consideration, and specifically one duty, overrides another. In Ross’s example of conflicting prima facie duties, someone must choose between averting a serious accident and keeping a promise to meet someone. (Ross chose the case to illustrate that an “imperfect” duty, or a duty of commission, can override a strict, prohibitive duty.) Ross’s assumption is that all well brought-up people would agree, in this case, that the duty to avert serious harm to someone overrides the duty to keep such a promise. We may take it, if we like, that this judgment implies that we consider the duty to save a life, here, to be stronger than the duty to keep the promise; but in fact this claim about relative strength adds nothing to our understanding of the situation. Yet we do not reach our practical conclusion in this case by determining that the duty to save the boy’s life is stronger. The statement that this duty is here stronger is simply a way to embellish the conclusion that of the two prima facie duties that here conflict, it is the one that states the all-things-considered duty. To be “overridden” is just to be a prima facie duty that fails to generate an actual duty because another prima facie duty that conflicts with it – or several of them that do – does generate an actual duty. Hence, the judgment that some duties override others can be understood just in terms of their deontic upshots and without reference to considerations of strength. To confirm this, note that we can say, “As a matter of fidelity, we ought to keep the promise; as a matter of beneficence, we ought to save the life; we cannot do both; and both categories considered we ought to save the life.”

Understanding the notion of one duty overriding another in this way puts us in a position to take up the topic of moral dilemmas . Since this topic is covered in a separate article, here we may simply take up one attractive definition of a moral dilemma. Sinnott-Armstrong (1988) suggested that a moral dilemma is a situation in which the following are true of a single agent:

• He ought to do A .
• He ought to do B .
• He cannot do both A and B .
• (1) does not override (2) and (2) does not override (1).

This way of defining moral dilemmas distinguishes them from the kind of moral conflict, such as Ross’s promise-keeping/accident-prevention case, in which one of the duties is overridden by the other. Arguably, Sartre’s student faces a moral dilemma. Making sense of a situation in which neither of two duties overrides the other is easier if deliberative commensurability is denied. Whether moral dilemmas are possible will depend crucially on whether “ought” implies “can” and whether any pair of duties such as those comprised by (1) and (2) implies a single, “agglomerated” duty that the agent do both A and B . If either of these purported principles of the logic of duties is false, then moral dilemmas are possible.

Jonathan Dancy has well highlighted a kind of contextual variability in moral reasons that has come to be known as “reasons holism”: “a feature that is a reason in one case may be no reason at all, or an opposite reason, in another” (Dancy 2004). To adapt one of his examples: while there is often moral reason not to lie, when playing liar’s poker one generally ought to lie; otherwise, one will spoil the game (cf. Dancy 1993, 61). Dancy argues that reasons holism supports moral particularism of the kind discussed in section 2.2 , according to which there are no defensible moral principles. Taking this conclusion seriously would radically affect how we conducted our moral reasoning. The argument’s premise of holism has been challenged (e.g., Audi 2004, McKeever & Ridge 2006). Philosophers have also challenged the inference from reasons holism to particularism in various ways. Mark Lance and Margaret Olivia Little (2007) have done so by exhibiting how defeasible generalizations, in ethics and elsewhere, depend systematically on context. We can work with them, they suggest, by utilizing a skill that is similar to the skill of discerning morally salient considerations, namely the skill of discerning relevant similarities among possible worlds. More generally, John F. Horty has developed a logical and semantic account according to which reasons are defaults and so behave holistically, but there are nonetheless general principles that explain how they behave (Horty 2012). And Mark Schroeder has argued that our holistic views about reasons are actually better explained by supposing that there are general principles (Schroeder 2011).

This excursus on moral reasons suggests that there are a number of good reasons why reasoning about moral matters might not simply reduce to assessing the weights of competing considerations.

If we have any moral knowledge, whether concerning general moral principles or concrete moral conclusions, it is surely very imperfect. What moral knowledge we are capable of will depend, in part, on what sorts of moral reasoning we are capable of. Although some moral learning may result from the theoretical work of moral philosophers and theorists, much of what we learn with regard to morality surely arises in the practical context of deliberation about new and difficult cases. This deliberation might be merely instrumental, concerned only with settling on means to moral ends, or it might be concerned with settling those ends. There is no special problem about learning what conduces to morally obligatory ends: that is an ordinary matter of empirical learning. But by what sorts of process can we learn which ends are morally obligatory, or which norms morally required? And, more specifically, is strictly moral learning possible via moral reasoning?

Much of what was said above with regard to moral uptake applies again in this context, with approximately the same degree of dubiousness or persuasiveness. If there is a role for moral perception or for emotions in agents’ becoming aware of moral considerations, these may function also to guide agents to new conclusions. For instance, it is conceivable that our capacity for outrage is a relatively reliable detector of wrong actions, even novel ones, or that our capacity for pleasure is a reliable detector of actions worth doing, even novel ones. (For a thorough defense of the latter possibility, which intriguingly interprets pleasure as a judgment of value, see Millgram 1997.) Perhaps these capacities for emotional judgment enable strictly moral learning in roughly the same way that chess-players’ trained sensibilities enable them to recognize the threat in a previously unencountered situation on the chessboard (Lance and Tanesini 2004). That is to say, perhaps our moral emotions play a crucial role in the exercise of a skill whereby we come to be able to articulate moral insights that we have never before attained. Perhaps competing moral considerations interact in contextually specific and complex ways much as competing chess considerations do. If so, it would make sense to rely on our emotionally-guided capacities of judgment to cope with complexities that we cannot model explicitly, but also to hope that, once having been so guided, we might in retrospect be able to articulate something about the lesson of a well-navigated situation.

A different model of strictly moral learning puts the emphasis on our after-the-fact reactions rather than on any prior, tacit emotional or judgmental guidance: the model of “experiments in living,” to use John Stuart Mill’s phrase (see Anderson 1991). Here, the basic thought is that we can try something and see if “it works.” For this to be an alternative to empirical learning about what causally conduces to what, it must be the case that we remain open as to what we mean by things “working.” In Mill’s terminology, for instance, we need to remain open as to what are the important “parts” of happiness. If we are, then perhaps we can learn by experience what some of them are – that is, what are some of the constitutive means of happiness. These paired thoughts, that our practical life is experimental and that we have no firmly fixed conception of what it is for something to “work,” come to the fore in Dewey’s pragmatist ethics (see esp. Dewey 1967 [1922]). This experimentalist conception of strictly moral learning is brought to bear on moral reasoning in Dewey’s eloquent characterizations of “practical intelligence” as involving a creative and flexible approach to figuring out “what works” in a way that is thoroughly open to rethinking our ultimate aims.

Once we recognize that moral learning is a possibility for us, we can recognize a broader range of ways of coping with moral conflicts than was canvassed in the last section. There, moral conflicts were described in a way that assumed that the set of moral considerations, among which conflicts were arising, was to be taken as fixed. If we can learn, morally, however, then we probably can and should revise the set of moral considerations that we recognize. Often, we do this by re-interpreting some moral principle that we had started with, whether by making it more specific, making it more abstract, or in some other way (cf. Richardson 2000 and 2018).

So far, we have mainly been discussing moral reasoning as if it were a solitary endeavor. This is, at best, a convenient simplification. At worst, it is, as Jürgen Habermas has long argued, deeply distorting of reasoning’s essentially dialogical or conversational character (e.g., Habermas 1984; cf. Laden 2012). In any case, it is clear that we often do need to reason morally with one another.

Here, we are interested in how people may actually reason with one another – not in how imagined participants in an original position or ideal speech situation may be said to reason with one another, which is a concern for moral theory, proper. There are two salient and distinct ways of thinking about people morally reasoning with one another: as members of an organized or corporate body that is capable of reaching practical decisions of its own; and as autonomous individuals working outside any such structure to figure out with each other what they ought, morally, to do.

The nature and possibility of collective reasoning within an organized collective body has recently been the subject of some discussion. Collectives can reason if they are structured as an agent. This structure might or might not be institutionalized. In line with the gloss of reasoning offered above, which presupposes being guided by an assessment of one’s reasons, it is plausible to hold that a group agent “counts as reasoning, not just rational, only if it is able to form not only beliefs in propositions – that is, object-language beliefs – but also belief about propositions” (List and Pettit 2011, 63). As List and Pettit have shown (2011, 109–113), participants in a collective agent will unavoidably have incentives to misrepresent their own preferences in conditions involving ideologically structured disagreements where the contending parties are oriented to achieving or avoiding certain outcomes – as is sometimes the case where serious moral disagreements arise. In contexts where what ultimately matters is how well the relevant group or collective ends up faring, “team reasoning” that takes advantage of orientation towards the collective flourishing of the group can help it reach a collectively optimal outcome (Sugden 1993, Bacharach 2006; see entry on collective intentionality ). Where the group in question is smaller than the set of persons, however, such a collectively prudential focus is distinct from a moral focus and seems at odds with the kind of impartiality typically thought distinctive of the moral point of view. Thinking about what a “team-orientation” to the set all persons might look like might bring us back to thoughts of Kantian universalizability; but recall that here we are focused on actual reasoning, not hypothetical reasoning. With regard to actual reasoning, even if individuals can take up such an orientation towards the “team” of all persons, there is serious reason, highlighted by another strand of the Kantian tradition, for doubting that any individual can aptly surrender their moral judgment to any group’s verdict (Wolff 1998).

This does not mean that people cannot reason together, morally. It suggests, however, that such joint reasoning is best pursued as a matter of working out together, as independent moral agents, what they ought to do with regard to an issue on which they have some need to cooperate. Even if deferring to another agent’s verdict as to how one morally ought to act is off the cards, it is still possible that one may licitly take account of the moral testimony of others (for differing views, see McGrath 2009, Enoch 2014).

In the case of independent individuals reasoning morally with one another, we may expect that moral disagreement provides the occasion rather than an obstacle. To be sure, if individuals’ moral disagreement is very deep, they may not be able to get this reasoning off the ground; but as Kant’s example of Charles V and his brother each wanting Milan reminds us, intractable disagreement can arise also from disagreements that, while conceptually shallow, are circumstantially sharp. If it were true that clear-headed justification of one’s moral beliefs required seeing them as being ultimately grounded in a priori principles, as G.A. Cohen argued (Cohen 2008, chap. 6), then room for individuals to work out their moral disagreements by reasoning with one another would seem to be relatively restricted; but whether the nature of (clearheaded) moral grounding is really so restricted is seriously doubtful (Richardson 2018, §9.2). In contrast to what such a picture suggests, individuals’ moral commitments seem sufficiently open to being re-thought that people seem able to engage in principled – that is, not simply loss-minimizing – compromise (Richardson 2018, §8.5).

What about the possibility that the moral community as a whole – roughly, the community of all persons – can reason? This possibility does not raise the kind of threat to impartiality that is raised by the team reasoning of a smaller group of people; but it is hard to see it working in a way that does not run afoul of the concern about whether any person can aptly defer, in a strong sense, to the moral judgments of another agent. Even so, a residual possibility remains, which is that the moral community can reason in just one way, namely by accepting or ratifying a moral conclusion that has already become shared in a sufficiently inclusive and broad way (Richardson 2018, chap. 7).

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agency: shared | intentionality: collective | moral dilemmas | moral particularism | moral particularism: and moral generalism | moral relativism | moral skepticism | practical reason | prisoner’s dilemma | reflective equilibrium | value: incommensurable

Acknowledgments

The author is grateful for help received from Gopal Sreenivasan and the students in a seminar on moral reasoning taught jointly with him, to the students in a more recent seminar in moral reasoning, and, for criticisms received, to David Brink, Margaret Olivia Little and Mark Murphy. He welcomes further criticisms and suggestions for improvement.

Copyright © 2018 by Henry S. Richardson < richardh @ georgetown . edu >

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6 CHAPTER 6

A fallacy is simply a mistake in reasoning. Some fallacies are formal, and some are informal. We will discuss formal fallacies in this chapter and information fallacies in the next. From a practical standpoint, these are probably the most practical of the chapters in the course. Learning how to recognize fallacies can be an extremely valuable “shield” against false arguments.

6.1. Formal Fallacies

In previous chapters, we have discovered what we can determine whether an argument was valid or invalid without even having to know or understand what the argument was about. We saw that we could define certain valid rules of inference, such as modus ponens and modus tollens. These inference patterns are valid in virtue of their form, not their content. That is, any argument that has the same form as modus ponens or modus tollens will automatically be valid.

This helps us understand what philosophers mean when they talk about formal fallacies. A formal fallacy is an argument whose form is invalid. Thus, any argument that has an invalid form will automatically be invalid, regardless of the meaning of the sentences. Two formal fallacies that are similar to, but should never be confused with, modus ponens and modus tollens are denying the antecedent and affirming the consequent . Here are the forms of those invalid inferences:

Denying the antecedent

Affirming the consequent

Any argument that has either of these forms is an invalid argument. For example:

If Kant was a deontologist, then he was a non-consequentialist.

Kant was not a deontologist.

Therefore, Kant was a not a non-consequentialist.

The form of this argument is:

As you can see, this argument has the form of the fallacy, denying the antecedent. Thus, we know that this argument is invalid even if we do not know what “Kant” or “deontologist” or “non-consequentialist” means. (“Kant” was a famous German philosopher from the early 1800s, whereas “deontology” and “non-consequentialist” are terms that come from ethical theory.) It is mark of a formal fallacy that we can identify it even if we do not really understand the meanings of the sentences in the argument. Recall our Jabberwocky argument from chapter 2. Here is an argument which uses silly, made-up words from Lewis Carrol’s “Jabberwocky.” See if you can determine whether the argument’s form is valid or invalid:

If toves are brillig then toves are slithy.

Toves are slithy

Therefore, toves are brillig.

You should be able to see that this argument has the form of affirming the consequent:

As such, we know that the argument is invalid, even though we haven’t got a clue what “toves” are or what “slithy” or “brillig” means. The point is that we can identify formal fallacies without having to know what they mean.

6.2 Informal Fallacies

In contrast to formal fallacies which focus on the structure of an argument, informal fallacies are those which cannot be identified without understanding the concepts involved in the argument. In this section, we will discuss some of the most important informal fallacies to be on guard against!

Composition Fallacy

A paradigm example of an informal fallacy is the fallacy of composition. Consider the following argument:

Each member on the gymnastics team weighs less than 110 lbs. Therefore, the whole gymnastics team weighs less than 110 lbs.

This argument commits the composition fallacy. In the composition fallacy one argues that since each part of the whole has a certain feature, it follows that the whole has that same feature. However, you cannot generally identify any argument that moves from statements about parts to statements about wholes as committing the composition fallacy because whether or not there is a fallacy depends on what feature we are attributing to the parts and wholes. Here is an example of an argument that moves from claims about the parts possessing a feature to a claim about the whole possessing that same feature, but does not commit the composition fallacy:

Every part of the car is made of plastic. Therefore, the whole car is made of plastic.

This conclusion does follow from the premises; there is no fallacy here. The difference between this argument and the preceding argument (about the gymnastics team) is not their form. In fact, both arguments have the same form:

Every part of X has the feature f. Therefore, the whole X has the feature f.

And yet one of the arguments is clearly fallacious, while the other is not. The difference between the two arguments is not their form, but their content. That is, the difference is what feature is being attributed to the parts and wholes. Some features (like weighing a certain amount ) are such that if they belong to each part, then it does not follow that they belong to the whole. Other features (such as being made of plastic ) are such that if they belong to each part, it follows that they belong to the whole.

Here is another example:

Every member of the team has been to Paris. Therefore, the team has been to Paris.

The conclusion of this argument does not follow. Just because each member of the team has been to Paris, it does not follow that the whole team has been to Paris, since it may not have been the case that each individual was there at the same time and was there in their capacity as a member of the team. Thus, even though it is plausible to say that the team is composed of every member of the team, it does not follow that since every member of the team has been to Paris, the whole team has been to Paris. Contrast that example with this one:

Every member of the team was on the plane. Therefore, the whole team was on the plane.

This argument, in contrast to the last one, contains no fallacy. It is true that if every member is on the plane, then the whole team is on the plane. And yet these two arguments have almost exactly the same form. The only difference is that the first argument is talking about the property, having been to Paris , whereas the second argument is talking about the property, being on the plane . The only reason we are able to identify the first argument as committing the composition fallacy and the second argument as not committing a fallacy is that we understand the relationship between the concepts involved. In the first case, we understand that it is possible that every member could have been to Paris without the team ever having been; in the second case we understand that as long as every member of the team is on the plane, it has to be true that the whole team is on the plane. The take home point here is that in order to identify whether an argument has committed the composition fallacy, one must understand the concepts involved in the argument. This is the mark of an informal fallacy: we have to rely on our understanding of the meanings of the words or concepts involved, rather than simply being able to identify the fallacy from its form.

Division fallacy

The division fallacy is like the composition fallacy and they are easy to confuse. The difference is that the division fallacy argues that since the whole has some feature, each part must also have that feature. The composition fallacy, as we have just seen, goes in the opposite direction: since each part has some feature, the whole must have that same feature. Here is an example of a division fallacy:

The house costs 1 million dollars. Therefore, each part of the house costs 1 million dollars.

This is clearly a fallacy. Just because the whole house costs 1 million dollars, it does not follow that each part of the house costs 1 million dollars. However, here is an argument that has the same form, but that does not commit the division fallacy:

The whole team died in the plane crash. Therefore, each individual on the team died in the plane crash.

In this example, since we seem to be referring to one plane crash in which all the members of the team died (“the” plane crash), it follows that if the whole team died in the crash, then every individual on the team died in the crash. So, this argument does not commit the division fallacy. In contrast, the following argument has exactly the same form, but does commit the division fallacy:

The team played its worst game ever tonight. Therefore, each individual on the team played their worst game ever tonight.

It can be true that the whole team played its worst game ever even if it is true that no individual on the team played their worst game ever. Thus, this argument does commit the fallacy of division even though it has the same form as the previous argument, which does not commit the fallacy of division. This shows (again) that in order to identify informal fallacies (like composition and division), we must rely on our understanding of the concepts involved in the argument. Some concepts (like “team” and “dying in a plane crash”) are such that if they apply to the whole, they also apply to all the parts. Other concepts (like “team” and “worst game played”) are such that they can apply to the whole even if they do not apply to all the parts.

Begging the Question Fallacy

Consider the following argument:

Capital punishment is justified for crimes such as rape and murder because it is quite legitimate and appropriate for the state to put to death someone who has committed such heinous and inhuman acts.

The premise indicator, “because” denotes the premise and (derivatively) the conclusion of this argument. In standard form, the argument is this:

It is legitimate and appropriate for the state to put to death someone who commits rape or murder.

Therefore, capital punishment is justified for crimes such as rape and murder.

You should notice something peculiar about this argument: the premise is essentially the same claim as the conclusion. The only difference is that the premise spells out what capital punishment means (the state putting criminals to death) whereas the conclusion just refers to capital punishment by name, and the premise uses terms like “legitimate” and “appropriate” whereas the conclusion uses the related term, “justified.” But these differences do not add up to any real differences in meaning. Thus, the premise is essentially saying the same thing as the conclusion. This is a problem: we want our premise to provide a reason for accepting the conclusion. But if the premise is the same claim as the conclusion, then it cannot possibly provide a reason for accepting the conclusion! Begging the question occurs when one (either explicitly or implicitly) assumes the truth of the conclusion in one or more of the premises. Begging the question is thus a kind of circular reasoning.

One interesting feature of this fallacy is that formally there is nothing wrong with arguments of this form. Here is what I mean. Consider an argument that explicitly commits the fallacy of begging the question. For example,

Capital punishment is morally permissible

Therefore, capital punishment is morally permissible

Now, apply any method of assessing validity to this argument and you will see that it is valid by any method. If we use the informal test (by trying to imagine that the premises are true while the conclusion is false), then the argument passes the test, since any time the premise is true, the conclusion will have to be true as well (since it is the exact same statement). Likewise, the argument is valid by our formal test of validity, truth tables. But while this argument is technically valid, it is still a really bad argument. Why? Because the point of giving an argument in the first place is to provide some reason for thinking the conclusion is true for those who do not already accept the conclusion . But if one does not already accept the conclusion, then simply restating the conclusion in a different way is not going to convince them. Rather, a good argument will provide some reason for accepting the conclusion that is sufficiently independent of that conclusion itself. Begging the question utterly fails to do this and this is why it counts as an informal fallacy. What is interesting about begging the question is that there is absolutely nothing wrong with the argument formally.

Whether or not an argument begs the question is not always an easy matter to sort out. As with all informal fallacies, detecting it requires a careful understanding of the meaning of the statements involved in the argument. Here is an example of an argument where it is not as clear whether there is a fallacy of begging the question:

Christian belief is warranted because according to Christianity there exists a being called “the Holy Spirit” which reliably guides Christians towards the truth regarding the central claims of Christianity.

One might think that there is a kind of circularity (or begging the question) involved in this argument since the argument appears to assume the truth of Christianity in justifying the claim that Christianity is true. But whether or not this argument really does beg the question is something on which there is much debate within the sub-field of philosophy called epistemology (“study of knowledge”). The philosopher Alvin Plantinga argues persuasively that the argument does not beg the question, but being able to assess that argument takes patient years of study in the field of epistemology (not to mention a careful engagement with Plantinga’s work). As this example illustrates, the issue of whether an argument begs the question requires us to draw on our general knowledge of the world. This is the mark of an informal, rather than formal, fallacy.

False Dichotomy Fallacy

Suppose I argued as follows:

Raising taxes on the wealthy will either hurt the economy or it will help it. But it will not help the economy. Therefore, it will hurt the economy.

The standard form of this argument is:

Either raising taxes on the wealthy will hurt the economy or it will help it.

Raising taxes on the wealthy will not help the economy.

Therefore, raising taxes on the wealthy will hurt the economy.

This argument contains a fallacy called a “false dichotomy.” A false dichotomy is simply a disjunction that does not exhaust all of the possible options. In this case, the problematic disjunction is the first premise: either raising the taxes on the wealthy will hurt the economy or it will help it. But these are not the only options. Another option is that raising taxes on the wealthy will have no effect on the economy. Notice that the argument above has the form of a disjunctive syllogism:

However, since the first premise presents two options as if they were the only two options, when in fact they are not, the first premise is false, and the argument fails. Notice that the form of the argument is perfectly good—the argument is valid. The problem is that this argument is not sound because the first premise of the argument commits the false dichotomy fallacy. False dichotomies are commonly encountered in the context of a disjunctive syllogism or constructive dilemma (see chapter 2).

In a speech made on April 5, 2004, President Bush made the following remarks about the causes of the Iraq war:

Saddam Hussein once again defied the demands of the world. And so I had a choice: Do I take the word of a madman, do I trust a person who had used weapons of mass destruction on his own people, plus people in the neighborhood, or do I take the steps necessary to defend the country? Given that choice, I will defend America every time.

The false dichotomy here is the claim that:

Either I trust the word of a madman or I defend America (by going to war against Saddam Hussein’s regime).

The problem is that these are not the only options. Other options include ongoing diplomacy and economic sanctions. Thus, even if it true that Bush should not have trusted the word of Hussein, it does not follow that the only other option is going to war against Hussein’s regime. (Furthermore, it is not clear in what sense this was needed to defend America .) That is a false dichotomy.

As with all the previous informal fallacies we have considered, the false dichotomy fallacy requires an understanding of the concepts involved. Thus, we have to use our understanding of world in order to assess whether a false dichotomy fallacy is being committed or not.

Equivocation Fallacy

Children are a headache. Aspirin will make headaches go away. Therefore, aspirin will make children go away.

This is a silly argument, but it illustrates the fallacy of equivocation. The problem is that the word “headache” is used equivocally—that is, in two different senses. In the first premise, “headache” is used figuratively, whereas in the second premise “headache” is used literally. The argument is only successful if the meaning of “headache” is the same in both premises. But it is not and this is what makes this argument an instance of the fallacy of equivocation.

Taking a logic class helps you learn how to argue. But there is already too much hostility in the world today, and the fewer arguments the better. Therefore, you should not take a logic class.

In this example, the word “argue” and “argument” are used equivocally. Hopefully, at this point in the text, you recognize the difference. (If not, go back and reread section 1.1.)

The fallacy of equivocation is not always so easy to spot. Here is a trickier example:

The existence of laws depends on the existence of intelligent beings like humans who create the laws. However, some laws existed before there were any humans (e.g., laws of physics). Therefore, there must be some non-human, intelligent being that created these laws of nature.

The term “law” is used equivocally here. In the first premise it is used to refer to societal laws, such as criminal law; in the second premise it is used to refer to laws of nature. Although we use the term “law” to apply to both cases, they are importantly different. Societal laws, such as the criminal law of a society, are enforced by people and there are punishments for breaking the laws. Natural laws, such as laws of physics, cannot be broken and thus there are no punishments for breaking them. (Does it make sense to scold the electron for not doing what the law says it will do?)

As with every informal fallacy we have examined in this section, equivocation can only be identified by understanding the meanings of the words involved. In fact, the definition of the fallacy of equivocation refers to this very fact: the same word is being used in two different senses (i.e., with two different meanings). So, unlike formal fallacies, identifying the fallacy of equivocation requires that we draw on our understanding of the meaning of words and of our understanding of the world, generally.

Slippery Slope Fallacies

Slippery slope fallacies depend on the concept of vagueness . When a concept or claim is vague, it means that we do not know precisely what claim is being made, or what the boundaries of the concept are. The classic example used to illustrate vagueness is the “ sorites paradox .” The term “sorites” is the Greek term for “heap” and the paradox comes from ancient Greek philosophy. Here is the paradox. I will give you two claims that each sound very plausible, but in fact lead to a paradox. Here are the two claims:

One grain of sand is not a heap of sand.

If I start with something that is not a heap of sand, then adding one grain of sand to that will not create a heap of sand.

For example, two grains of sand are not a heap, thus (by the second claim) neither are three grains of sand.

But since three grains of sand is not a heap then (by the second claim again) neither is four grains of sand. You can probably see where this is going. By continuing to add one grain of sand over and over, I will eventually end up with something that is clearly a heap of sand, but that will not be counted as a heap of sand if we accept both claims 1 and 2 above.

Philosophers continue to argue and debate about how to resolve the sorites paradox, but the point for us is just to illustrate the concept of vagueness. The concept “heap” is a vague concept in this example. But so are so many other concepts, such a color concepts (red, yellow, green, etc.), moral concepts (right, wrong, good, bad), and just about any other concept you can think of. The one domain that seems to be unaffected by vagueness is mathematical and logical concepts. There are two fallacies related to vagueness: the causal slippery slope and the conceptual slippery slope. We will cover the conceptual slippery slope first since it relates most closely to the concept of vagueness I have explained above.

It may be true that there is no essential difference between 499 grains of sand and 500 grains of sand. But even if that is so, it does not follow that there is no difference between 1 grain of sand and 5 billion grains of sand. In general, just because we cannot draw a distinction between A and B, and we cannot draw a distinction between B and C, it does not mean we cannot draw a distinction between A and C. Here is an example of a conceptual slippery slope fallacy .

It is illegal for anyone under 21 to drink alcohol. But there is no difference between someone who is 21 and someone who is 20 years 11 months old. So, there is nothing wrong with someone who is 20 years and 11 months old drinking. But since there is no real distinction between being one month older and one month younger, there should not be anything wrong with drinking at any age. Therefore, there is nothing wrong with allowing a 10-year-old to drink alcohol.

Imagine the life of an individual in stages of 1-month intervals. Even if it is true that there is no distinction in kind between any one of those stages, it does not follow that there is not a distinction to be drawn at the extremes of either end. Clearly there is a difference between a 5-year-old and a 25-year-old—a distinction in kind that is relevant to whether they should be allowed to drink alcohol. The conceptual slippery slope fallacy assumes that because we cannot draw a distinction between adjacent stages, we cannot draw a distinction at all between any stages. One clear way of illustrating this is with color. Think of a color spectrum from purple to red to orange to yellow to green to blue. Each color grades into the next without there being any distinguishable boundaries between the colors—a continuous spectrum. Even if it is true that for any two adjacent hues on the color wheel, we cannot distinguish between the two, it does not follow from this that there is no distinction to be drawn between any two portions of the color wheel, because then we would be committed to saying that there is no distinguishable difference between purple and yellow! The example of the color spectrum illustrates the general point that just because the boundaries between very similar things on a spectrum are vague, it does not follow that there are no differences between any two things on that spectrum.

Whether or not one will identify an argument as committing a conceptual slippery slope fallacy, depends on the other things one believes about the world. Thus, whether or not a conceptual slippery slope fallacy has been committed will often be a matter of some debate. It will itself be vague. Here is a good example that illustrates this point.

People are found not guilty by reason of insanity when they cannot avoid breaking the law. But people who are brought up in certain deprived social circumstances are not much more able than the legally insane to avoid breaking the law. So, we should not find such individuals guilty any more than those who are legally insane.

Whether there is conceptual slippery slope fallacy here depends on what you think about a host of other things, including individual responsibility, free will, the psychological and social effects of deprived social circumstances such as poverty, lack of opportunity, abuse, etc. Some people may think that there are big differences between those who are legally insane and those who grow up in deprived social circumstances. Others may not think the differences are so great. The issues here are subtle, sensitive, and complex, which is why it is difficult to determine whether there is any fallacy here or not. If the differences between those who are insane and those who are the product of deprived social circumstances turn out to be like the differences between one shade of yellow and an adjacent shade of yellow, then there is no fallacy here. But if the differences turn out to be analogous to those between yellow and green (i.e., with many distinguishable stages of difference between) then there would indeed be a conceptual slippery slope fallacy here. The difficulty of distinguishing instances of the conceptual slippery slope fallacy, and the fact that distinguishing it requires us to draw on our knowledge about the world, shows that the conceptual slippery slope fallacy is an informal fallacy.

The causal slippery slope fallacy is committed when one event is said to lead to some other (usually disastrous) event via a chain of intermediary events. If you have ever seen Direct TV’s “get rid of cable” commercials, you will know exactly what I am talking about. (If you do not know what I am talking about you should Google it right now and find out. They are quite funny.) Here is an example of a causal slippery slope fallacy (it is adapted from one of the Direct TV commercials):

If you use cable, your cable will probably go on the fritz. If your cable is on the fritz, you will probably get frustrated. When you get frustrated you will probably hit the table. When you hit the table, your young daughter will probably imitate you. When your daughter imitates you, she will probably get thrown out of school. When she gets thrown out of school, she will probably meet undesirables. When she meets undesirables, she will probably marry undesirables. When she marries undesirables, you will probably have a grandson with a dog collar. Therefore, if you use cable, you will probably have a grandson with dog collar.

This example is silly and absurd, yes. But it illustrates the causal slippery slope fallacy. Slippery slope fallacies are always made up of a series of conjunctions of probabilistic conditional statements that link the first event to the last event. A causal slippery slope fallacy is committed when one assumes that just because each individual conditional statement is probable, the conditional that links the first event to the last event is also probable. Even if we grant that each “link” in the chain is individually probable, it does not follow that the whole chain (or the conditional that links the first event to the last event) is probable. Suppose, for the sake of the argument, we assign probabilities to each “link” or conditional statement, like this. (I have italicized the consequents of the conditionals and assigned high conditional probabilities to them. The high probability is for the sake of the argument; I do not actually think these things are as probable as I have assumed here.)

If you use cable, then your cable will probably go on the fritz (.9)

If your cable is on the fritz, then you will probably get angry (.9)

If you get angry, then you will probably hit the table (.9)

If you hit the table, your daughter will probably imitate you (.8)

If your daughter imitates you, she will probably be kicked out of school (.8)

If she is kicked out of school, she will probably meet undesirables (.9)

If she meets undesirables, she will probably marry undesirables (.8)

If she marries undesirables, you will probably have a grandson with a dog collar (.8)

However, even if we grant the probabilities of each link in the chain is high (80-90% probable), the conclusion does not even reach a probability higher than chance. Recall that in order to figure the probability of a conjunction, we must multiply the probability of each conjunct:

(.9) × (.9) × (.9) × (.8) × (.8) × (.9) × (.8) × (.8) = .27

That means the probability of the conclusion (i.e., that if you use cable, you will have a grandson with a dog collar) is only 27%, despite the fact that each conditional has a relatively high probability! The causal slippery slope fallacy is actually a formal probabilistic fallacy and so could have been discussed in chapter 3 with the other formal probabilistic fallacies. What makes it a formal rather than informal fallacy is that we can identify it without even having to know what the sentences of the argument mean. I could just have easily written out a nonsense argument comprised of series of probabilistic conditional statements. But I would still have been able to identify the causal slippery slope fallacy because I would have seen that there was a series of probabilistic conditional statements leading to a claim that the conclusion of the series was also probable. That is enough to tell me that there is a causal slippery slope fallacy, even if I do not really understand the meanings of the conditional statements.

It is helpful to contrast the causal slippery slope fallacy with the valid form of inference, hypothetical syllogism. Recall that a hypothetical syllogism has the following kind of form:

The only difference between this and the causal slippery slope fallacy is that whereas in the hypothetical syllogism, the link between each component is certain , in a causal slippery slope fallacy, the link between each event is probabilistic . It is the fact that each link is probabilistic that accounts for the fallacy. One way of putting this is point is that probability is not transitive . Just because A makes B probable and B makes C probable and C makes X probable, it does not follow that A makes X probable. In contrast, when the links are certain rather than probable, then if A always leads to B and B always leads to C and C always leads to X, then it has to be the case that A always leads to X.

Fallacies of Relevance

What all fallacies of relevance have in common is that they make an argument or response to an argument that is irrelevant to that argument. Fallacies of relevance can be psychologically compelling, but it is important to distinguish between rhetorical techniques that are psychologically compelling, on the one hand, and rationally compelling arguments, on the other. What makes something a fallacy is that it fails to be rationally compelling once we have carefully considered it. That said, arguments that fail to be rationally compelling may still be psychologically or emotionally compelling. The first fallacy of relevance that we will consider, the ad hominem fallacy, is an excellent example of a fallacy that can be psychologically compelling.

“Ad hominem” is a Latin phrase that can be translated into English as the phrase, “against the man.” In an ad hominem fallacy, instead of responding to (or attacking) the argument a person has made, one attacks the person him or herself. In short, one attacks the person making the argument rather than the argument itself. Here is an anecdote that reveals an ad hominem fallacy (and that has actually occurred in my ethics class before).

A philosopher named Peter Singer had made an argument that it is morally wrong to spend money on luxuries for oneself rather than give all of your money that you do not strictly need away to charity. The argument is actually an argument from analogy (whose details I discussed in section 3.3), but the essence of the argument is that there are every day in this world children who die preventable deaths, and there are charities who could save the lives of these children if they are funded by individuals from wealthy countries like our own. Since there are things that we all regularly buy that we do not need (e.g., Starbuck’s lattes, beer, movie tickets, or extra clothes or shoes we do not really need), if we continue to purchase those things rather than using that money to save the lives of children, then we are essentially contributing to the deaths of those children if we choose to continue to live our lifestyle of buying things we do not need, rather than donating the money to a charity that will save lives of children in need. In response to Singer’s argument, one student in the class asked: “Does Peter Singer give his money to charity? Does he do what he says we are all morally required to do?”

The implication of this student’s question (which I confirmed by following up with her) was that if Peter Singer himself does not donate all his extra money to charities, then his argument is not any good and can be dismissed. But that would be to commit an ad hominem fallacy. Instead of responding to the argument that Singer had made, this student attacked Singer himself . That is, they wanted to know how Singer lived and whether he was a hypocrite or not. Was he the kind of person who would tell us all that we had to live a certain way but fail to live that way himself? But all of this is irrelevant to assessing Singer’s argument . Suppose that Singer did not donate his excess money to charity and instead spent it on luxurious things for himself. Still, the argument that Singer has given can be assessed on its own merits. Even if it were true that Peter Singer was a total hypocrite, his argument may nevertheless be rationally compelling. And it is the quality of the argument that we are interested in, not Peter Singer’s personal life and whether or not he is hypocritical. Whether Singer is or is not a hypocrite, is irrelevant to whether the argument he has put forward is strong or weak, valid, or invalid. The argument stands on its own and it is that argument rather than Peter Singer himself that we need to assess.

Nonetheless, there is something psychologically compelling about the question: Does Peter Singer practice what he preaches? I think what makes this question seem compelling is that humans are very interested in finding “cheaters” or hypocrites—those who say one thing and then do another. Evolutionarily, our concern with cheaters makes sense because cheaters cannot be trusted, and it is essential for us (as a group) to be able to pick out those who cannot be trusted. That said, whether or not a person giving an argument is a hypocrite is irrelevant to whether that person’s argument is good or bad. So, there may be psychological reasons why humans are prone to find certain kinds of ad hominem fallacies psychologically compelling , even though ad hominem fallacies are not rationally compelling .

Not every instance in which someone attacks a person’s character is an ad hominem fallacy. Suppose a witness is on the stand testifying against a defendant in a court of law. When the witness is cross examined by the defense lawyer, the defense lawyer tries to go for the witness’s credibility, perhaps by digging up things about the witness’s past. For example, the defense lawyer may find out that the witness cheated on her taxes five years ago or that the witness failed to pay her parking tickets. The reason this is not an ad hominem fallacy is that in this case the lawyer is trying to establish whether what the witness is saying is true or false and in order to determine that we have to know whether the witness is trustworthy. These facts about the witness’s past may be relevant to determining whether we can trust the witness’s word. In this case, the witness is making claims that are either true or false rather than giving an argument. In contrast, when we are assessing someone’s argument, the argument stands on its own in a way the witness’s testimony does not. In assessing an argument, we want to know whether the argument is strong or weak and we can evaluate the argument using the logical techniques surveyed in this text. In contrast, when a witness is giving testimony, they are not trying to argue anything. Rather, they are simply making a claim about what did or did not happen. So, although it may seem that a lawyer is committing an ad hominem fallacy in bringing up things about the witness’s past, these things are actually relevant to establishing the witness’s credibility. In contrast, when considering an argument that has been given, we do not have to establish the arguer’s credibility because we can assess the argument they have given on its own merits. The arguer’s personal life is irrelevant.

Suppose that my opponent has argued for a position, call it position A, and in response to his argument, I give a rationally compelling argument against position B, which is related to position A, but is much less plausible (and thus much easier to refute). What I have just done is attacked a straw man—a position that “looks like” the target position but is actually not that position. When one attacks a straw man, one commits the straw man fallacy. The straw man fallacy misrepresents one’s opponent’s argument and is thus a kind of irrelevance. Here is an example.

Two candidates for political office in Colorado, Tom and Fred, are having an exchange in a debate in which Tom has laid out his plan for putting more money into health care and education and Fred has laid out his plan which includes earmarking more state money for building more prisons which will create more jobs and, thus, strengthen Colorado’s economy. Fred responds to Tom’s argument that we need to increase funding to health care and education as follows: “I am surprised, Tom, that you are willing to put our state’s economic future at risk by sinking money into these programs that do not help to create jobs. You see, folks, Tom’s plan will risk sending our economy into a tailspin, risking harm to thousands of Coloradans. On the other hand, my plan supports a healthy and strong Colorado and would never bet our state’s economic security on idealistic notions that simply do not work when the rubber meets the road.”

Fred has committed the straw man fallacy. Just because Tom wants to increase funding to health care and education does not mean he does not want to help the economy. Furthermore, increasing funding to health care and education does not entail that fewer jobs will be created. Fred has attacked a position that is not the position that Tom holds, but is in fact a much less plausible, easier to refute position. However, it would be silly for any political candidate to run on a platform that included “harming the economy.” Presumably, no political candidate would run on such a platform. Nonetheless, this exact kind of straw man is ubiquitous in political discourse in our country.

Here is another example.

Nancy has just argued that we should provide middle schoolers with sex education classes, including how to use contraceptives so that they can practice safe sex should they end up in the situation where they are having sex. Fran responds: “proponents of sex education try to encourage our children to a sex-with-no-strings-attached mentality, which is harmful to our children and to our society.”

Fran has committed the straw man (or straw woman) fallacy by misrepresenting Nancy’s position. Nancy’s position is not that we should encourage children to have sex, but that we should make sure that they are fully informed about sex so that if they do have sex, they go into it at least a little less blindly and are able to make better decision regarding sex.

As with other fallacies of relevance, straw man fallacies can be compelling on some level, even though they are irrelevant. It may be that part of the reason we are taken in by straw man fallacies is that humans are prone to “demonize” the “other”—including those who hold a moral or political position different from our own. It is easy to think bad things about those with whom we do not regularly interact. And it is easy to forget that people who are different than us are still people just like us in all the important respects. Many years ago, atheists were commonly thought of as highly immoral people and stories about the horrible things that atheists did in secret circulated widely. People believed that these strange “others” were capable of the most horrible savagery. After all, they may have reasoned, if you do not believe there is a God holding us accountable, why be moral? The Jewish philosopher, Baruch Spinoza, was an atheist who lived in the Netherlands in the 17 th century. He was accused of all sorts of things that were commonly believed about atheists. But he was in fact as upstanding and moral as any person you could imagine. The people who knew Spinoza knew better, but how could so many people be so wrong about Spinoza? I suspect that part of the reason is that since at that time there were very few atheists (or at least very few people actually admitted to it), very few people ever knowingly encountered an atheist. Because of this, the stories about atheists could proliferate without being put in check by the facts. I suspect the same kind of phenomenon explains why certain kinds of straw man fallacies proliferate. If you are a conservative and mostly only interact with other conservatives, you might be prone to holding lots of false beliefs about liberals. And so maybe you are less prone to notice straw man fallacies targeted at liberals because the false beliefs you hold about them incline you to see the straw man fallacies as true.

Tu quoque (Appeal to Hypocrisy)

“ Tu quoque ” is a Latin phrase that can be translated into English as “you too” or “you, also.” The tu quoque fallacy is a way of avoiding answering a criticism by bringing up a criticism of your opponent rather than answer the criticism. For example, suppose that two political candidates, A and B, are discussing their policies and A brings up a criticism of B’s policy. In response, B brings up her own criticism of A’s policy rather than respond to A’s criticism of her policy. B has here committed the tu quoque fallacy. The fallacy is best understood as a way of avoiding having to answer a tough criticism that one may not have a good answer to. This kind of thing happens all the time in political discourse. Tu quoque , as I have presented it, is fallacious when the criticism one raises is simply in order to avoid having to answer a difficult objection to one’s argument or view. However, there are circumstances in which a tu quoque kind of response is not fallacious. If the criticism that A brings toward B is a criticism that equally applies not only to A’s position but to any position, then B is right to point this fact out. For example, suppose that A criticizes B for taking money from special interest groups. In this case, B would be totally right (and there would be no tu quoque fallacy committed) to respond that not only does A take money from special interest groups, but every political candidate running for office does. That is just a fact of life in American politics today. So, A really has no criticism at all to B since everyone does what B is doing and it is in many ways unavoidable. Thus, B could (and should) respond with a “you too” rebuttal and in this case that rebuttal is not a tu quoque fallacy.

Genetic fallacy

The genetic fallacy occurs when one argues (or, more commonly, implies) that the origin of something (e.g., a theory, idea, policy, etc.) is a reason for rejecting (or accepting) it. For example, suppose that Jack is arguing that we should allow physician assisted suicide and Jill responds that that idea first was used in Nazi Germany. Jill has just committed a genetic fallacy because she is implying that because the idea is associated with Nazi Germany, there must be something wrong with the idea itself. What she should have done instead is explain what, exactly, is wrong with the idea rather than simply assuming that there must be something wrong with it since it has a negative origin. The origin of an idea has nothing inherently to do with its truth or plausibility. Suppose that Hitler constructed a mathematical proof in his early adulthood (he did not, but just suppose). The validity of that mathematical proof stands on its own; the fact that Hitler was a horrible person has nothing to do with whether the proof is good. Likewise, with any other idea: ideas must be assessed on their own merits and the origin of an idea is neither a merit nor demerit of the idea.

Although genetic fallacies are most often committed when one associates an idea with a negative origin, it can also go the other way: one can imply that because the idea has a positive origin, the idea must be true or more plausible. For example, suppose that Jill argues that the Golden Rule is a good way to live one’s life because the Golden Rule originated with Jesus in the Sermon on the Mount (it did not, actually, even though Jesus does state a version of the Golden Rule). Jill has committed the genetic fallacy in assuming that the (presumed) fact that Jesus is the origin of the Golden Rule has anything to do with whether the Golden Rule is a good idea.

Appeal to Consequences

The appeal to consequences fallacy is like the reverse of the genetic fallacy: whereas the genetic fallacy consists in the mistake of trying to assess the truth or reasonableness of an idea based on the origin of the idea, the appeal to consequences fallacy consists in the mistake of trying to assess the truth or reasonableness of an idea based on the (typically negative) consequences of accepting that idea. For example, suppose that the results of a study revealed that there are IQ differences between different races (this is a fictitious example, there is no such study that I know of). In debating the results of this study, one researcher claims that if we were to accept these results, it would lead to increased racism in our society, which is not tolerable. Therefore, these results must not be right since if they were accepted, it would lead to increased racism. The researcher who responded in this way has committed the appeal to consequences fallacy. Again, we must assess the study on its own merits. If there is something wrong with the study, some flaw in its design, for example, then that would be a relevant criticism of the study. However, the fact that the results of the study, if widely circulated, would have a negative effect on society is not a reason for rejecting these results as false. The consequences of some idea (good or bad) are irrelevant to the truth or reasonableness of that idea. Notice that the researchers, being convinced of the negative consequences of the study on society, might rationally choose not to publish the study (for fear of the negative consequences). This is totally fine and is not a fallacy. The fallacy consists not in choosing not to publish something that could have adverse consequences, but in claiming that the results themselves are undermined by the negative consequences they could have. The fact is, sometimes truth can have negative consequences and falsehoods can have positive consequences. This just goes to show that the consequences of an idea are irrelevant to the truth or reasonableness of an idea.

Appeal to Authority (Ad Verecundiam )

In a society like ours, we have to rely on authorities to get on in life. For example, the things I believe about electrons are not things that I have ever verified for myself. Rather, I have to rely on the testimony and authority of physicists to tell me what electrons are like. Likewise, when there is something wrong with my car, I have to rely on a mechanic (since I lack that expertise) to tell me what is wrong with it. Such is modern life. So there is nothing wrong with needing to rely on authority figures in certain fields (people with the relevant expertise in that field)—it is inescapable. The problem comes when we invoke someone whose expertise is not relevant to the issue for which we are invoking it. For example, suppose that a group of doctors sign a petition to prohibit abortions, claiming that abortions are morally wrong. If Bob cites that fact that these doctors are against abortion, therefore abortion must be morally wrong, then Bob has committed the appeal to authority fallacy. The problem is that doctors are not authorities on what is morally right or wrong. Even if they are authorities on how the body works and how to perform certain procedures (such as abortion), it does not follow that they are authorities on whether or not these procedures should be performed —the ethical status of these procedures. It would be just as much an appeal to consequences fallacy if Melissa were to argue that since some other group of doctors supported abortion, that shows that it must be morally acceptable. In either case, since doctors are not authorities on moral issues, their opinions on a moral issue like abortion is irrelevant. In general, an appeal to authority fallacy occurs when someone takes what an individual says as evidence for some claim, when that individual has no particular expertise in the relevant domain (even if they do have expertise in some other, unrelated, domain).

6.3 Formal Fallacies of Probability

In this and the remaining sections of this chapter, we will consider some formal fallacies of probability. These fallacies are easy to spot once you see them, but they can be difficult to detect because of the way our minds mislead us—analogous to the way our minds can be misled when watching a magic trick. In addition to introducing the fallacies, I will suggest some psychological explanations for why these fallacies are so common, despite how easy they are to see once we have spotted them.

The conjunction fallacy is best introduced with an example.

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Given this information about Linda, which of the following is more probable?

Linda is a bank teller.

Linda is a bank teller and is active in the feminist movement.

If you are like most people who answer this question, you will answer “b.” But that cannot be correct because it violates the basic rules of probability. In particular, notice that option b contains option a (i.e., Linda is a bank teller). But option b also contains more information—that Linda is also active in the feminist movement. The problem is that a conjunction can never be more probable than either one of its conjuncts . Suppose we say it is very probable that Linda a bank teller (how boring, given the description of Linda which makes her sound interesting!). Let usset the probability low, say .4. Then what is the probability of her being active in the feminist movement? Let usset that high, say .9. However, the probability that she is both a bank teller and active in the feminist movement must be computed as the probability of a conjunction, like this:

.4 × .9 = .36

So, given these probability assignments (which I have just made up but seem fairly plausible), the probability of Linda being both a bank teller and active in the feminist movement is .36. But .36 is a lower probability than .4, which was the probability that she is bank teller. So, option b cannot be more probable than option a. Notice that even if we say it is absolutely certain that Linda is active in the feminist movement (i.e., we set the probability of her being active in the feminist movement at 1), option b is still only equal to the probability of option a, since (.4)(1) = .4.

Sometimes it is easy to spot conjunction fallacies. Here is an example that illustrates that we can in fact easily see that a conjunction is not more probable than either of its conjuncts.

Mark is drawing cards from a shuffled deck of cards. Which is more probable?

Mark draws a spade

Mark draws a spade that is a 7

In this case, it is clear which of the options is more probable. Clearly a is more probable since it requires less to be true. Option a would be true even if option b is true. But option a could also be true even if option b were false (i.e., Mark could have drawn any other card from the spades suit). The chances of drawing a spade of any suit is ¼ (or .25) whereas the chances of drawing a 7 of spades is computed using the probability of the conjunction:

P(drawing a spade) = .25

P(drawing a 7) = 4/52 (since there are four 7s in the deck of 52) = .077

Thus, the probability of being both a spade and a 7 = (.25)(.077) = .019

Since .25 > .019, option a is more probable (not that you had to do all the calculations to see this).

Thus, there are cases where we can easily avoid committing the conjunction fallacy. So, what is the difference between this case and the Linda case? The Nobel Prize-winning psychologist, Daniel Kahneman (and his long-time collaborator, Amos Tversky), has for many years suggested a psychological explanation for this difference. The explanation is complex, but I can give you the gist of it quite simply. Kahneman suggests that our minds are wired to find patterns and many of these patterns we find are based on what he calls “representativeness.” In the Linda case, the idea of Linda being active in the feminist movement fits better with the description of Linda as a philosophy major, as being active in social justice movements, and, perhaps, as being single. We build up a picture of Linda and then we try to match the descriptions to her. “Bank teller” does not really match anything in the description of Linda. That is, the description of Linda is not representative of a bank teller. However, for many people, it is representative of a feminist. Thus, our minds more or less automatically see the match between representativeness of the description of Linda and option b, which mentions she is a feminist. Kahneman thinks that in cases like these, our minds substitute a question of representativeness for the question of probability, thus answering the probability question incorrectly. We are distracted from the probability question by seeking representativeness, which our minds more automatically look for and think about than probability. For Kahneman, the psychological explanation is needed to explain why even trained mathematicians and those who deal regularly with probability still commit the conjunction fallacy. The psychological explanation that our brains are wired to look for representativeness, and that we unwittingly substitute the question of representativeness for the question of probability, explains why even experts make these kinds of mistakes.

The Base Rate Fallacy

Consider the following scenario. You go in for some testing for some health problems you have been having and after a number of tests, you test positive for colon cancer. What are the chances that you really do have colon cancer? Let us suppose that the test is not perfect, but it is 95% accurate. That is, in the case of those who really do have colon cancer, the test will detect the cancer 95% of the time (and thus miss it 5% of the time). (The test will also misdiagnose those who do not actually have colon cancer 5% of the time.) Many people would be inclined to say that, given the test and its accuracy, there is a 95% chance that you have colon cancer. However, if you are like most people and are inclined to answer this way, you are wrong. In fact, you have committed the fallacy of ignoring the base rate (i.e., the base rate fallacy).

The base rate in this example is the rate of those who have colon cancer in a population. There is very small percentage of the population that actually has colon cancer (Let us suppose it is .005 or .5%), so the probability that you have it must take into account the very low probability that you are one of the few that have it. That is, prior to the test (and not taking into account any other details about you), there was a very low probability that you have it—that is, a half of one percent chance (.5%). The test is 95% accurate but given the very low prior probability that you have colon cancer, we cannot simply now say that there is a 95% chance that you have it. Rather, we must temper that figure with the very low base rate. Here is how we do it. Let us suppose that our population is 100,000 people. If we were to apply the test to that whole population, it would deliver 5000 false positives. A false positive occurs when a test registers that some feature is present, when the feature is not really present. In this case, the false positive is when the test for colon cancer (which will give false positives in 5% of the cases) says that someone has it when they really do not. The number of people who actually have colon cancer (based on the stated base rate) is 500, and the test will accurately identify 95 percent of those (or 475 people). So, what you need to know is the probability that you are one who tested positive and actually has colon cancer rather than one of the false positives. And what is the probability of that? It is simply the number of people who actually have colon cancer (500) divided by the number that the test would identify as having colon cancer. This latter number includes those the test would misidentify (5000) as well as the number it would accurately identify (475)—thus the total number the test would identify as having colon cancer would be 5475. So, the probability that you have it, given the positive test = 500/5475 = .091 or 9.1%. So, the probability that you have cancer, given the evidence of the positive test is 9.1%. Thus, contrary to our initial reasoning that there was a 95% chance that you have colon cancer, the chance is only a tenth of that—it is less than 10%! In thinking that the probability that you have cancer is closer to 95% you would be ignoring the base rate of the probability of having the disease in the first place (which, as we have seen, is quite low). This is the signature of any base rate fallacy. Before closing this section, Let us look at one more example of a base rate fallacy.

Suppose that the government has developed a machine that is able to detect terrorist intent with an accuracy of 90%. During a joint meeting of congress, a highly trustworthy source says that there is a terrorist in the building. (Let us suppose, for the sake of simplifying this example, that there is in fact a terrorist in the building.) In order to determine who the terrorist is, the building security seals all the exits, rounds up all 3000 people in the building and uses the machine to test each person. The first 30 people pass without triggering a positive identification from the machine, but on the very next person, the machine triggers a positive identification of terrorist intent. The question is: what are the chances that the person who set off the machine really is a terrorist? Consider the following three possibilities:

• 90%, b) 10%, or c) .3%.

If you answered 90%, then you committed the base rate fallacy again. The actual answer is “c”—less than 1%! Here is the relevant reasoning. The base rate here is that it is exceedingly unlikely that any individual is a terrorist, given that there is only one terrorist in the building and there are 3000 people in the building. That means the probability of any one person being a terrorist, before any results of the test, is exceedingly low: 1/3000. Since the test is 90% accurate, that means that out of the 3000 people, it will misidentify 10% of them as terrorists = 300 false positives. Assuming the machine does not misidentify the one actual terrorist, the machine will identify a total of 301 individuals as those “possessing terrorist intent.” The probability that any one of them actually possesses terrorist intent is 1/301 = .3%. So, the probability is drastically lower than 90%. It is not even close. This is another good illustration of how far off probabilities can be when the base rate is ignored.

The small numbers fallacy

Suppose a study showed that of the 3,141 counties of the United States, the incidence of kidney cancer was lowest in those counties which are mostly rural, sparsely populated, and located in traditionally Republican states. In fact, this is true. What accounts for this interesting finding? Most people would be tempted to look for a causal explanation—to look for features of the rural environment that account for the lower incidence of cancer. However, they would be wrong (in this case) to do so. It is easy to see why once we consider the counties that have the highest incidence of kidney cancer: they are counties that are mostly rural, sparsely populated, and located in traditionally Republican states! So whatever it was you thought might account for the lower cancer rates in rural counties cannot be the right explanation, since these counties also have the highest rates of cancer. It is important to understand that it is not the same counties that have the highest and lowest rates—for example, county X does not have both a high and a low cancer rate (relative to other U.S. counties). That would be a contradiction (and so cannot possibly be true). Rather, what is the case is that counties that have the highest kidney cancer rates are “mostly rural, sparsely populated, and located in traditionally Republican states” but also counties that have the lowest kidney cancer rates are “mostly rural, sparsely populated, and located in traditionally Republican states.” How could this be? Before giving you the explanation, I’ll give you a simpler example and see if you can figure it out from that example.

Suppose that a jar contains equal amounts of red and white marbles. Jack and Jill are taking turns drawing marbles from the jar. However, they draw marbles at different rates. Jill draws 5 marbles at a time while Jack draws 2 marbles at a time. Who is more likely to draw either all red or all white marbles more often: Jack or Jill?

The answer here should be obvious: Jack is more likely to draw marbles of all the same color more often since Jack is only drawing 2 marbles at a time. Since Jill is drawing 5 marbles at a time, it will be less likely that her draws will yield marbles of all the same color. This is simply a fact of sampling and is related to the sampling errors discussed in section 3.1. A sample that is too small will tend not to be representative of the population. In the marbles case, if we view Jack’s draws as samples, then his samples, when they yield marbles of all the same color, will be far from representative of the ratio of marbles in the jar, since the ratio is 50/50 white to red and his draws sometimes yield 100% red or 100% white. Jill, on the other hand, will tend not to get as unrepresentative a sample. Since Jill is drawing a larger number of marbles, it is less likely that her samples would be drastically off in the way Jack’s could be. The general point to be taken from this example is that smaller samples tend to the extremes—both in terms of overrepresenting some feature and in underrepresenting that same feature.

Can you see how this might apply to the case of kidney cancer rates in rural, sparsely populated counties? There is a national kidney cancer rate which is an average of all the kidney cancer rates of the 3,141 counties in the U.S. Imagine ranking each county in terms of the cancer rates from highest to lowest. The finding is that there is a relatively larger proportion of the sparsely populated counties at the top of this list, but also a relatively larger proportion of the sparsely populated counties at the bottom of the list. But why would it be that the more sparsely populated counties would be overrepresented at both ends of the list? The reason is that these counties have smaller populations, so they will tend to have more extreme results (of either the higher or lower rates). Just as Jack is more likely to get either all white marbles or all red marbles (an extreme result), the less populated counties will tend to have cancer rates that are at the extreme, relative to the national average. And this is a purely statistical fact; it has nothing to do with features of those environments causing the cancer rate to be higher or lower. Just as Jack’s extreme draws have nothing to do with the way he is drawing (but are simply the result of statistical, mathematical facts), the extremes of the smaller counties have nothing to do with features of those counties, but only with the fact that they are smaller and so will tend to have more extreme results (i.e., cancer rates that are either higher or lower than the national average).

The first take home lesson here is that smaller groups will tend towards the extremes in terms of their possession of some feature, relative to larger groups. We can call this the law of small numbers . The second take home message is that our brains are wired to look for causal explanations rather than mathematical explanations, and because of this we are prone to ignore the law of small numbers and look for a causal explanation of phenomena instead. The small numbers fallacy is our tendency to seek a causal explanation for some phenomenon when only the law of small numbers is needed to explain that phenomenon.

We will end this section with a somewhat humorous and incredible example of a small numbers bias that, presumably, wasted billions of dollars. Some time ago, the Gates foundation (which is the charitable foundation of Microsoft founder, Bill Gates) donated 1.7 billion to research a curious finding: smaller schools tend to be more successful than larger schools. That is, if you consider a rank ordering of the most successful schools, the smaller schools will tend to be overrepresented near the top (i.e., there is a higher proportion of them near the top of the list compared to the proportion of larger schools at the top of the list). This is the finding that the Gates Foundation invested 1.7 billion dollars to help understand. In order to do so, they created smaller schools, sometimes splitting larger schools in half. However, none of this was necessary. Had the Gates Foundation (or those advising them) looked that the characteristics of the worst schools, they would have found that those schools also tended to be smaller! The “finding” is merely a result of the law of small numbers: smaller groups tend towards the extremes (on both ends of a spectrum) more so than larger groups. In this case, the fact that smaller schools tend to be both more successful and less successful is explained in the same way as we explain why Jack tends to get either all red or all white marbles more often than Jill.

Regression to the mean fallacy

Humans are prone to see causes even when no such cause is present. For example, if I have just committed some wrong and then immediately after the thunder cracks, I may think that my wrong action caused the lightning (e.g., because the gods were angry with me). The term “snake oil” refers to a product that promises certain (e.g., health) benefits but is actually fraudulent and has no benefits whatsoever. For example, consider a product that is supposed to help you recover from a common cold. You take the medicine and then within a few days, you are all better! No cold! It must have been the medicine. Or maybe you just regressed to the mean. Regression to the mean describes the tendency of things to go back to normal or to return to something close to the relevant statistical average. In the case of a cold, when you have a cold, you are outside of the average in terms of health. But you will naturally return to the state of health, with or without the “medicine.” If anyone were to try to convince you to buy such a medicine, you should not. Because the fact that you got better from your cold more likely has to do with the fact that you will naturally regress to the mean (return to normal) than it has to do with the special medicine.

Another example. Suppose you live in Lansing and it has been over 100 degrees for two weeks straight. Someone says that if you pay tribute and do a special dance to Baal, the temperature will drop. Suppose you do this and the temperature does drop. Was it Baal or just regression to the mean? Probably regression to the mean, unless we have some special reason for thinking it is Baal. The point is, extreme situations tend to regress towards less extreme, more average situations. Since it is very rare for it to ever be over 100 degrees in Lansing, the fact that the temperature drops is to be expected, regardless of one’s prayers to Baal.

Suppose that a professional golfer has been on a hot streak. She has been winning every tournament she enters by ten strokes—She is beating the competition like they were middle school golfers. She is just playing so much better than them. Then something happens. The golfer all of a sudden begins to play like an average player. What explains her fall from greatness? The sports commentators speculate: could it be that she switched her caddy, or that it is warmer now than it was when she was on her streak, or perhaps it was fame that went to her head once she had started winning all those tournaments? Chances are, none of these are the right explanation because no such explanation is needed. Most likely she just regressed to the mean and is now playing like everyone else—still like a pro, just not like a golfer who is out of this world good. Even those who are skilled can get lucky (or unlucky) and when they do, we should expect that eventually that luck will end and they will regress to the mean.

As these examples illustrate, one commits the regression to the mean fallacy when one tries to give a causal explanation of a phenomenon that is merely statistical or probabilistic in nature. The best way to rule out that something is not to be explained as regression to the mean is by doing a study where one compares two groups. For example, suppose we could get our snake oil salesman to agree to a study in which a group of people who had colds took the medicine (experimental group) and another group of people did not take the medicine or took a placebo (control group). In this situation, if we found that the experimental group got better and the control group did not, or if the experimental group got better more quickly than the control group, then perhaps we would have to say that maybe there is something to this snake oil medicine. But without the evidence of a control for comparison, even if lots of people took the snake oil medicine and got better from their colds, it would not prove anything about the efficacy of the medicine.

Gambler’s fallacy

The gambler’s fallacy occurs when one thinks that independent, random events can be influenced by each other. For example, suppose I have a fair coin and I have just flipped 4 heads in a row. Erik, on the other hand, has a fair coin that he has flipped 4 times and gotten tails. We are each taking bets that the next coin flipped is heads. Who should you bet flips the head? If you are inclined to say that you should place the bet with Erik since he has been flipping all tails and since the coin is fair, the flips must even out soon, then you have committed the gambler’s fallacy. The fact is, each flip is independent of the next, so the fact that I have just flipped 4 heads in a row does not increase or decrease my chances of flipping a head. Likewise for Erik. It is true that as long as the coin is fair, then over a large number of flips we should expect that the proportion of heads to tails will be about 50/50. But there is no reason to expect that a particular flip will be more likely to be one or the other. Since the coin is fair, each flip has the same probability of being heads and the same probability of being tails—50%.

An Introduction to Reason and Argument Copyright © by John Mack. All Rights Reserved.

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Is there a better way to have an argument, here are five principles for more constructive and respectful disagreements..

We’re living in an era of deep divisions. Cable television, social media feeds, and fraying personal relationships all reflect the same troubling pattern: Differences of opinion quickly escalate into attacks, mistrust, and civic stalemates.

In this contentious climate, many Americans have retreated from civic life, or have responded to social conflict with calls for civility. But abstaining from civic life only cedes our public dialogue to the most contentious and polarizing voices. And too often “civility” means the mere absence of argument, or politely ignoring our differences.

We believe that American civic life doesn’t need fewer arguments. Instead, it needs better arguments. We believe that argument has the potential to help bridge ideological divides—not by papering over those divides but by teaching Americans how to engage more productively across difference, whether in town meetings or across the dinner table . Indeed, argument has always been a critical aspect of American democracy: Fundamental and perpetual tensions between core values such as liberty and equality, for example, have existed throughout our country’s history. The point of American civic life is not to resolve these tensions. Rather, we need to understand their origins and grow smarter about engaging them. Through the clash of different ideas and points of view, we often emerge with deeper insights and stronger solutions to the problems that affect us all.

However, the arguments in American politics today are inadequate. We believe the more we can equip communities to argue thoughtfully and constructively, the healthier our country will be. We created the Better Arguments Project to make this possible and, by doing so, to help renew civic life.

The Better Arguments Project is a collaboration by the Aspen Institute Citizenship and American Identity Program, Facing History and Ourselves, and the Allstate Corporation. Our efforts began with a deep exploration of the question: What is a better argument? Over the course of a year, our team met with more than 75 advisers from all around the United States. Drawn from more than 25 communities, our advisers were high school students; experts in law, history, politics, communications, and psychology; educators; and former elected and White House officials.

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Free online, starting October 5, 2021: Learn research-based strategies for connecting across divides. Join us to bridge differences in your work, community, and life.

Our advisers helped us to distill five major principles of better arguments. Our team then partnered with communities around the United States to explore what these principles could look like in practice. From rural Arkansas to urban Queens, from Anchorage to Detroit, in large public gatherings and intimate conversations, we tested how to nurture better arguments in the context of real communities divided by real and pressing issues.

Here are our five principles that make arguments better—and what they look like in practice.

1. Pay attention to context

We may be suffering from a general sense of division in the United States, but a Better Argument event must begin in the needs, culture, and context of a specific community.

In our process, local, on-the-ground partners identify issues most relevant to their own community. In Denver, Colorado, we recently explored tensions about housing, jobs, and political power emerging from the region’s major tech boom, in partnership with Anythink Libraries. In Anchorage, Alaska, we considered the human impacts of a changing climate with the Alaska Humanities Forum. All of these arguments expressed the deep American theme of individual rights vs. collective responsibility in a distinct way. 

Attending to context also means intentionally structuring the conversation to create shared knowledge and reflect local culture. In Detroit, Michigan, where a large community event focused on tensions between natives and newcomers in a changing city, a shared sense of the city’s history was an essential precursor to argument. Our local partners at the Urban Consulate invited a prominent local poet to give a dramatic reading that painted a vivid picture of Detroit’s past for all attendees. In Anchorage, where Native Alaskan culture prizes group relationships and cohesion, we invested more time in longer introductions by participants, and facilitators considered a Native “talking circle” as a model for the conversation.

Everywhere we’ve worked, intentional grounding in the local context has been key to a successful encounter.

2. Take winning off the table

Many public arguments surface in contexts where a lot is at stake: persuading the city council to approve or reject a new housing development, or debating a new school districting plan. A Better Argument, however, is not about winning or losing, defeating or converting the “other side.” It’s about presence, and the robust exchange of ideas. Whatever the issue, setting those boundaries fosters a more open and honest discussion.

In Queens, New York, our team worked with a local museum, Socrates Sculpture Park, that wanted to engage the citywide debate about controversial public monuments and memorials. The city government had instituted its own process, with a panel of experts and formally structured public hearings to decide the fate of monuments to Christopher Columbus, Theodore Roosevelt, and others.

Our partners aspired to something different. We suggested inviting a broader public into a shared inquiry framed by open-ended questions that would surface divergent views, like “How should public art reflect the identity, history, and aspirations of our community?”

When we take winning off the table, we preserve a space to both speak and listen, creating relationships that can build connections, support better decision making, and inspire civic involvement.

3. Prioritize relationships and listen passionately

An argument becomes “better” when we start the conversation with human connection and prepare to listen, not just advance our own points of view. The Better Arguments we’ve hosted are crafted to bring together people of diverse viewpoints who may not have engaged with each other before. No matter the setting or the topic for argument, we always ask participants to “be human first.” This means inviting people to share their identities and their stories, not just their opinions.

We set the stage for a “better” argument with conversations that surface personal identity and shared experiences. We began our discussion of the Denver tech boom by asking, “What makes you proud to be a member of your community?” In Detroit, longtimers and newcomers each responded to the question, “Where do you feel at home in this city?”

Any difficult conversation, whether facilitated or informal, can begin with open-ended questions like those to humanize participants as individuals with complex identities, not just representatives of opposing viewpoints.

Active Listening

Connect with a partner through empathy and understanding

We also promote listening with intentional reflection questions. As the conversation evolves into argument, pairs and tables are asked to step back and consider questions like “What is something someone else said that you appreciate? How has others’ thinking connected to, extended, or challenged your own?” Active listening and perspective taking dramatically can enhance arguments, at least as much as evidence and logic do.

4. Embrace vulnerability

Better Arguments are hard work, and there is inherent risk in showing up. A successful Better Argument depends on participants’ willingness to be open, honest, and vulnerable, as both speakers and listeners. We’ve had success with brief “contracting” exercises to establish trust and set norms at the beginning of each event.

In Detroit, the conversation about natives and newcomers was threaded with difficult issues of race, privilege, and painful history. We asked each participant to silently finish the sentence, “When I think about how Detroit is changing, I feel _________ because ________.”  The facilitator asked participants to call out the feeling they wrote down: “Angry.” “Excited.” “Conflicted.” “Invisible.”

“Given this wide range of powerful emotions,” the facilitator asked, “what do we need to feel secure and take risks in today’s conversation?”

Some participants asked for patience; others requested confidentiality. As important as the actual norms is having the opportunity to construct them together. 

5. Be open to transformation

Without a goal of winning or even reaching resolution, the experience of a Better Argument can instead change how we engage with a difficult issue and with one another. Our events end with an invitation to reflect on the shared experience with a simple but powerful prompt: “I came in thinking ________; I’m leaving thinking _______.” In Anchorage, a policymaker said, “I came in thinking I wasn’t sure I wanted to be here, and I’m leaving thinking that this was a different conversation than I’ve ever had about this topic and I want more.”

We also connect reflection to action by asking participants to complete a final statement, “So now I will….” Their responses reveal how engaging consciously in a Better Argument can spark small but powerful changes in individuals and communities. In Detroit, participants said, “I will stay in touch with the five new people I met today”; “I will introduce myself to my neighbors”; “I will plan a tour to introduce my part of town to newcomers”; and even “I will not be so afraid to talk about difficult topics going forward.” Some event organizers have used the “I will…” cards to identify promising ideas and then offered support to those projects. Others have created opportunities for participants to continue to come together to explore the Better Arguments topic.

Every Better Argument we’ve hosted has been distinct, but these five principles were core to each and will be the foundation of our work going forward. As we continue to travel the country and learn from communities, we’re working forward a vision of inspiring and supporting all Americans to have better arguments in the coming years.

Fundamentally, engaging in Better Arguments means showing up for one another as citizens. Painful at times and celebratory at others, Better Arguments are an opportunity to evolve and expand our sense of community. In this sense, arguments don’t have to drive us apart. Better Arguments can bring us together.

About the Authors

Caroline Hopper

Caroline Hopper is the associate director for the Aspen Institute’s Citizenship and American Identity Program, managing initiatives focused on the challenge of sustaining strong citizenship in America and coherent national identity in an age of demographic flux and severe inequality. Caroline joined the Aspen Institute in 2014, and brings experience and passion for advancing human rights and social justice in the United States and around the world.

Laura Tavares

Laura Tavares, M.A. , is program director for organizational learning and thought leadership at Facing History and Ourselves, an education nonprofit whose mission is to engage students of diverse backgrounds in examining racism, prejudice, and anti-semitism in order to promote the development of a more humane and informed citizenry.

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Argument: Claims, Reasons, Evidence

Critical thinking means being able to make good arguments. Arguments are claims backed by reasons that are supported by evidence. Argumentation is a social process of two or more people making arguments, responding to one another--not simply restating the same claims and reasons--and modifying or defending their positions accordingly.

Claims are statements about what is true or good or about what should be done or believed. Claims are potentially arguable. "A liberal arts education prepares students best" is a claim, while "I didn't like the book" is not. The rest of the world can't really dispute whether I liked the book or not, but they can argue about the benefits of liberal arts. "I thought the movie was cool" is not an arguable statement, but "the movie was Paul Newman's best" is, for people can disagree and offer support for their different opinions.

Reasons are statements of support for claims, making those claims something more than mere assertions. Reasons are statements in an argument that pass two tests:

Reasons are answers to the hypothetical challenge to your claim:

• “Why do you say that?”
• “What reason can you give me to believe that?” If a claim about liberal arts education is so challenged, a response with a reason could be: “It teaches students to think independently.”

Reasons can be linked to claims with the word because:

• Liberal arts is best [claim] because it teaches students independent thinking [reason];
• That was Newman's best [claim] because it presented the most difficult role [reason];
• Global warming is real [claim] because the most reputable science points in that direction [reason].
• Everyone should stop wearing seat belts [claim] because it would save lives [reason].

If reasons do not make sense in the hypothetical challenge or the 'because' tests, there is probably something wrong with the logic of the argument. Passing those tests, however, does not insure that arguments are sound and compelling.

Evidence serves as support for the reasons offered and helps compel audiences to accept claims. Evidence comes in different sorts, and it tends to vary from one academic field or subject of argument to another. Scientific arguments about global warming require different kinds of evidence than mealtime arguments about Paul Newman's movies. Evidence answers challenges to the reasons given, and it comes in four main types:

Specific instances include examples, case studies, and narratives. Each can be an effective mode of building support for a reason or claim. In a public speech, they offer audiences a way to see an idea illustrated in a particular case. To be effective, specific instances need to be representative of the broader trend or idea they are supporting. With an example as evidence, someone arguing against seat belt use might say "Last year my cousin crashed her car off a bridge and would have drowned if she were wearing her seatbelt" as evidence (the answer to "Why do you believe that?" question.) An opponent might challenge whether this example was a representative one: surely there are many more car crashes that do not end in water, so this one instance is not a fair gauge of the relative safety of not wearing seat belts.

Statistics include raw numbers (117 million visitors to the Rock and Roll Hall of Fame,), averages ('women's bowling teams drink on average two pitchers less then men's'), statistical probabilities ('crossing North Main during rush hour increases your chances of death 20%'), and statistical trends ('applications have risen 40% over the past three years'). In public speeches, statistics have the advantage of seeming objective, authoritative, and factual, but critical audiences will want to know about the sources and methods for determining your statistical evidence.

Testimony, or appeals to authority, come in two main types, eyewitness and expert. Eyewitness or first-hand testimonies are reports from people who directly experience some phenomenon. If a speaker is arguing about toxic waste dumps, a quotation from someone living next to a dump would fall into this category. First-hand testimony can help give the audience a sense of being there. Experts may also rely on direct experience, but their testimony is also backed by more formal knowledge, methods, and training. Supplementing the neighbor's account with testimony from an environmental scientist, who specializes in toxic waste sites, is an appeal to expertise. When using testimony in arguments, you should always make sure the authority you are appealing to is in fact qualified to speak on the topic being discussed.

There is unequivocal evidence that Earth is warming at an unprecedented rate. Human activity is the principal cause.

• While Earth’s climate has changed throughout its history , the current warming is happening at a rate not seen in the past 10,000 years.
• According to the Intergovernmental Panel on Climate Change ( IPCC ), "Since systematic scientific assessments began in the 1970s, the influence of human activity on the warming of the climate system has evolved from theory to established fact." 1
• Scientific information taken from natural sources (such as ice cores, rocks, and tree rings) and from modern equipment (like satellites and instruments) all show the signs of a changing climate.
• From global temperature rise to melting ice sheets, the evidence of a warming planet abounds.

The rate of change since the mid-20th century is unprecedented over millennia.

Earth's climate has changed throughout history. Just in the last 800,000 years, there have been eight cycles of ice ages and warmer periods, with the end of the last ice age about 11,700 years ago marking the beginning of the modern climate era — and of human civilization. Most of these climate changes are attributed to very small variations in Earth’s orbit that change the amount of solar energy our planet receives.

The current warming trend is different because it is clearly the result of human activities since the mid-1800s, and is proceeding at a rate not seen over many recent millennia. 1 It is undeniable that human activities have produced the atmospheric gases that have trapped more of the Sun’s energy in the Earth system. This extra energy has warmed the atmosphere, ocean, and land, and widespread and rapid changes in the atmosphere, ocean, cryosphere, and biosphere have occurred.

Earth-orbiting satellites and new technologies have helped scientists see the big picture, collecting many different types of information about our planet and its climate all over the world. These data, collected over many years, reveal the signs and patterns of a changing climate.

Scientists demonstrated the heat-trapping nature of carbon dioxide and other gases in the mid-19th century. 2 Many of the science instruments NASA uses to study our climate focus on how these gases affect the movement of infrared radiation through the atmosphere. From the measured impacts of increases in these gases, there is no question that increased greenhouse gas levels warm Earth in response.

Scientific evidence for warming of the climate system is unequivocal.

Intergovernmental Panel on Climate Change

Ice cores drawn from Greenland, Antarctica, and tropical mountain glaciers show that Earth’s climate responds to changes in greenhouse gas levels. Ancient evidence can also be found in tree rings, ocean sediments, coral reefs, and layers of sedimentary rocks. This ancient, or paleoclimate, evidence reveals that current warming is occurring roughly 10 times faster than the average rate of warming after an ice age. Carbon dioxide from human activities is increasing about 250 times faster than it did from natural sources after the last Ice Age. 3

The Evidence for Rapid Climate Change Is Compelling:

Global Temperature Is Rising

The planet's average surface temperature has risen about 2 degrees Fahrenheit (1 degrees Celsius) since the late 19th century, a change driven largely by increased carbon dioxide emissions into the atmosphere and other human activities. 4 Most of the warming occurred in the past 40 years, with the seven most recent years being the warmest. The years 2016 and 2020 are tied for the warmest year on record. 5 Image credit: Ashwin Kumar, Creative Commons Attribution-Share Alike 2.0 Generic.

The Ocean Is Getting Warmer

The ocean has absorbed much of this increased heat, with the top 100 meters (about 328 feet) of ocean showing warming of 0.67 degrees Fahrenheit (0.33 degrees Celsius) since 1969. 6 Earth stores 90% of the extra energy in the ocean. Image credit: Kelsey Roberts/USGS

The Ice Sheets Are Shrinking

The Greenland and Antarctic ice sheets have decreased in mass. Data from NASA's Gravity Recovery and Climate Experiment show Greenland lost an average of 279 billion tons of ice per year between 1993 and 2019, while Antarctica lost about 148 billion tons of ice per year. 7 Image: The Antarctic Peninsula, Credit: NASA

Glaciers Are Retreating

Glaciers are retreating almost everywhere around the world — including in the Alps, Himalayas, Andes, Rockies, Alaska, and Africa. 8 Image: Miles Glacier, Alaska Image credit: NASA

Snow Cover Is Decreasing

Satellite observations reveal that the amount of spring snow cover in the Northern Hemisphere has decreased over the past five decades and the snow is melting earlier. 9 Image credit: NASA/JPL-Caltech

Sea Level Is Rising

Global sea level rose about 8 inches (20 centimeters) in the last century. The rate in the last two decades, however, is nearly double that of the last century and accelerating slightly every year. 10 Image credit: U.S. Army Corps of Engineers Norfolk District

Arctic Sea Ice Is Declining

Both the extent and thickness of Arctic sea ice has declined rapidly over the last several decades. 11 Credit: NASA's Scientific Visualization Studio

Extreme Events Are Increasing in Frequency

The number of record high temperature events in the United States has been increasing, while the number of record low temperature events has been decreasing, since 1950. The U.S. has also witnessed increasing numbers of intense rainfall events. 12 Image credit: Régine Fabri,  CC BY-SA 4.0 , via Wikimedia Commons

Ocean Acidification Is Increasing

Since the beginning of the Industrial Revolution, the acidity of surface ocean waters has increased by about 30%. 13 , 14 This increase is due to humans emitting more carbon dioxide into the atmosphere and hence more being absorbed into the ocean. The ocean has absorbed between 20% and 30% of total anthropogenic carbon dioxide emissions in recent decades (7.2 to 10.8 billion metric tons per year). 1 5 , 16 Image credit: NOAA

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2. In 1824, Joseph Fourier calculated that an Earth-sized planet, at our distance from the Sun, ought to be much colder. He suggested something in the atmosphere must be acting like an insulating blanket. In 1856, Eunice Foote discovered that blanket, showing that carbon dioxide and water vapor in Earth's atmosphere trap escaping infrared (heat) radiation. In the 1860s, physicist John Tyndall recognized Earth's natural greenhouse effect and suggested that slight changes in the atmospheric composition could bring about climatic variations. In 1896, a seminal paper by Swedish scientist Svante Arrhenius first predicted that changes in atmospheric carbon dioxide levels could substantially alter the surface temperature through the greenhouse effect. In 1938, Guy Callendar connected carbon dioxide increases in Earth’s atmosphere to global warming. In 1941, Milutin Milankovic linked ice ages to Earth’s orbital characteristics. Gilbert Plass formulated the Carbon Dioxide Theory of Climate Change in 1956.

3. IPCC Sixth Assessment Report, WG1, Chapter 2 Vostok ice core data; NOAA Mauna Loa CO2 record O. Gaffney, W. Steffen, "The Anthropocene Equation." The Anthropocene Review 4, issue 1 (April 2017): 53-61. https://doi.org/abs/10.1177/2053019616688022.

4. https://www.ncei.noaa.gov/monitoring https://crudata.uea.ac.uk/cru/data/temperature/ http://data.giss.nasa.gov/gistemp

5. https://www.giss.nasa.gov/research/news/20170118/

6. S. Levitus, J. Antonov, T. Boyer, O Baranova, H. Garcia, R. Locarnini, A. Mishonov, J. Reagan, D. Seidov, E. Yarosh, M. Zweng, " NCEI ocean heat content, temperature anomalies, salinity anomalies, thermosteric sea level anomalies, halosteric sea level anomalies, and total steric sea level anomalies from 1955 to present calculated from in situ oceanographic subsurface profile data (NCEI Accession 0164586), Version 4.4. (2017) NOAA National Centers for Environmental Information. https://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/index3.html K. von Schuckmann, L. Cheng, L,. D. Palmer, J. Hansen, C. Tassone, V. Aich, S. Adusumilli, H. Beltrami, H., T. Boyer, F. Cuesta-Valero, D. Desbruyeres, C. Domingues, A. Garcia-Garcia, P. Gentine, J. Gilson, M. Gorfer, L. Haimberger, M. Ishii, M., G. Johnson, R. Killick, B. King, G. Kirchengast, N. Kolodziejczyk, J. Lyman, B. Marzeion, M. Mayer, M. Monier, D. Monselesan, S. Purkey, D. Roemmich, A. Schweiger, S. Seneviratne, A. Shepherd, D. Slater, A. Steiner, F. Straneo, M.L. Timmermans, S. Wijffels. "Heat stored in the Earth system: where does the energy go?" Earth System Science Data 12, Issue 3 (07 September 2020): 2013-2041. https://doi.org/10.5194/essd-12-2013-2020.

7. I. Velicogna, Yara Mohajerani, A. Geruo, F. Landerer, J. Mouginot, B. Noel, E. Rignot, T. Sutterly, M. van den Broeke, M. Wessem, D. Wiese, "Continuity of Ice Sheet Mass Loss in Greenland and Antarctica From the GRACE and GRACE Follow-On Missions." Geophysical Research Letters 47, Issue 8 (28 April 2020): e2020GL087291. https://doi.org/10.1029/2020GL087291.

8. National Snow and Ice Data Center World Glacier Monitoring Service

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The Supreme Court Is Shaming Itself

No good legal reason exists to delay Donald Trump’s January 6 trial any further.

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Donald Trump is determined to avoid accountability before the general election, and, so far, the U.S. Supreme Court is helping him.

Trump has no legal ground whatsoever to delay a ruling in his plea for presidential immunity. The reason Trump has nevertheless sought to slow down the immunity appeals process is obvious: to postpone the trial date, hopefully pushing it into a time when, as president, he would control the Department of Justice and thus could quash the prosecution altogether. The Supreme Court has shamed itself by being a party to this, when the sole issue before the Court is presidential immunity. By contrast, Special Counsel Jack Smith has both law and policy on his side in seeking a prompt determination on immunity and a speedy trial soon thereafter. Yet the Court has ignored all that.

David A. Graham: The cases against Trump–a guide

The Supreme Court’s lollygagging is reflected in its scheduling the immunity case for a leisurely April 25 hearing. It’s too late to do anything about that now, but the Court has an opportunity to correct course following oral argument. The justices should press Trump’s counsel on what possible legitimate reason he has to oppose a speedy resolution of the appeal. And then they should rule with dispatch because there is still time , albeit barely, to vindicate the public’s right to a speedy trial.

Let’s recap how we arrived at the present moment. After Judge Tanya Chutkan ruled against Trump’s claim of presidential immunity on December 1 and Trump appealed that ruling to the D.C. Circuit, Smith asked the Supreme Court to hear the appeal immediately, leapfrogging the delay of the circuit-level argument and decision. Trump opposed that, and the Supreme Court declined Smith’s invitation. The circuit court expedited its appeal and on February 6 issued its decision , again rejecting Trump’s immunity argument in toto. Trump then sought a stay in the Supreme Court, and advocated various measures to slow the Court’s hearing of the case. The Supreme Court then deliberated for a couple of weeks before accepting the case for review, and not scheduling the argument until two months later—on the very last day of oral arguments for this session.

Were he not seeking to avoid any trial in advance of the general election so he could maximize the chances of becoming the next president of the United States, Trump would have an interest in a speedy resolution of the immunity question, in contrast to the foot-dragging positions he has advocated throughout the litigation of this issue. Anyone with a legitimate claim of immunity has every interest in not suffering a single day more under the opprobrium of multiple criminal charges, not to mention being under pretrial bail conditions and a gag order. (Trump’s lawyers have argued against his existing gag order, saying it sweeps so broadly as to undermine their client’s ability to campaign for the presidency.)

The law itself recognizes the need for speed on this issue. With questions of immunity, courts permit an appeal in advance of a trial and forgo the usual rule that appeals are permitted only after a verdict is reached. The hope, in allowing for this, is to relieve someone from the opprobrium and burden of a trial, if the defendant is indeed immune. For the Court to set such a prolonged schedule—antithetical to the appropriate time frame for the only issue actually before the justices—speaks volumes about the role the Court has chosen to play in advancing the interests of the former president over the rule of law.

The government has its own interests in seeking a prompt resolution of the immunity issue and a speedy criminal trial (and it has the same interest as a defendant in not subjecting someone to criminal charges who is immune from prosecution). But before delving into the government’s interests, let’s first dispense with a red herring : Special Counsel Smith is not disputing that Trump should be accorded sufficient time to prepare for trial. An inviolable constitutional safeguard is that all criminal defendants must be able to exercise their procedural rights to prepare. Judge Chutkan already weighed the parties’ competing claims. Her decision on a trial date fell well within the mark for similar cases, and that ruling is not on appeal (despite the Supreme Court’s behaving as if it were).

The district judge’s selected timeline (seven months from the August 1 indictment), in a case whose facts and substantial evidence were already available to the defendant, was longer than deadlines set all around the country. By way of comparison, next door in the more conservative Virginia district, defendants routinely go to trial at great speed, without conservative commentators going to the barricades over alleged violations of the rights of the accused. That Trump is a rich, white, and politically powerful man does not mean he should be accorded more (or fewer) rights than others. And Chutkan has said that when the case returns to her, she will give Trump more time to prepare.

David A. Graham: Judge Chutkan’s impossible choice

With Trump’s rights intact, then, Smith has several legitimate grounds for the immunity appeal to be decided expeditiously and a trial to start as promptly as possible. DOJ internal policy prohibits taking action in a case for “the purpose of” choosing sides in or affecting the outcome of an election. That is unquestionable and not in dispute here. Rather, the point is that well-established neutral criminal-justice principles support a speedy trial. This trial’s outcome, of course, is not known in advance, and it may lead some voters to think better or worse of the defendant and the current presidential administration depending on the evidence and the outcome.

Moreover, the public has a profound interest in a fair and speedy trial. As Justice Samuel Alito wrote for a unanimous Supreme Court, the Speedy Trial Act “was designed not just to benefit defendants but also to serve the public interest.” The refrain that “justice too long delayed is justice denied” has unmistakable resonance in this criminal context. The special counsel’s briefs in the D.C. case are replete with references to this well-settled case law . This means that even when the accused is seeking to delay his day in court, that “does not alter the prosecutor’s obligation to see to it that the case is brought on for trial,” as the Supreme Court has well articulated . Many defendants seek to avoid the day of reckoning—hence Edward Bennett Williams’s famous quip that for the defense, an adjournment is equivalent to an acquittal. The law provides that the public, the prosecution, and most emphatically the courts need not oblige that stratagem.

What’s more, when a defendant seeks to postpone a trial until a point at which he can no longer be prosecuted, the Justice Department may request the trial be held before that deadline. The DOJ’s interest in deterrence and accountability warrants this action. If Trump should win the election, he will become immune as president from criminal trial for at least four years (and perhaps forever by seeking dismissal of the federal case with prejudice or testing the efficacy of granting himself a pardon). The Justice Department can accordingly uphold the public interest in deterrence and accountability by seeking the prompt conviction of the leader of an insurrection. This DOJ need not advance the goals of a future administration led by that very “ oathbreaking insurrectionist .”

Another objective of criminal punishment is “specific deterrence,” ensuring the defendant herself does not commit offenses in the future. Given the grand jury’s determination that Trump committed felonies to try to interfere with the 2020 election, there are strong law-enforcement reasons to obtain a conviction to specifically deter Trump. Indeed, in proposing a trial date to Judge Chutkan, Smith quoted Justice Alito, on behalf of the whole Court, that speedy trials “serve the public interest by … preventing extended pretrial delay from impairing the deterrent effect of punishment.”

Trump’s public denigration of the legal system—the incessant claims that the criminal case is a witch hunt—also gives a nation committed to the rule of law a vital interest in holding a public trial where a jury can assess Trump’s actions. Trials can thus serve to restore faith in the justice system.

It is worth noting that when the government seeks its day in court, it simultaneously affords the defendant his day in court—providing him more process, not less. Indeed, the Department of Justice’s so-called 60-day rule—which generally forbids it from taking overt actions in non-public cases with respect to political candidates and closely related people right before an election—is there to avoid a federal prosecutor hurling untested new allegations against a political candidate precisely because he would not have time to clear his reputation before the election. Here, the government is seeking to provide just that forum for Trump to clear his name before the election—to test the criminal allegations against the highest legal standard we have for adjudicating facts—and yet right-wing critics attack Smith. Trump of course wants to avoid that test, but that is an interest the courts should abjure.

The justices still have time to get back on track. Trump’s claim that presidents have absolute immunity should be an easy issue to resolve given these criminal charges. Whether a president should have criminal immunity in some specific circumstances is an abstract question for another day, because efforts to stay in office and use the levers of the presidency are certainly not those specific circumstances. The appeals have delayed matters long enough at the expense of the right of the American people to a fair and speedy trial. Let them not stand in the way of ever having a trial at all.

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The Supreme Court Got It Wrong: Abortion Is Not Settled Law

By Melissa Murray and Kate Shaw

Ms. Murray is a law professor at New York University. Ms. Shaw is a contributing Opinion writer.

In his majority opinion in the case overturning Roe v. Wade, Justice Samuel Alito insisted that the high court was finally settling the vexed abortion debate by returning the “authority to regulate abortion” to the “people and their elected representatives.”

Despite these assurances, less than two years after Dobbs v. Jackson Women’s Health Organization, abortion is back at the Supreme Court. In the next month, the justices will hear arguments in two high-stakes cases that may shape the future of access to medication abortion and to lifesaving care for pregnancy emergencies. These cases make clear that Dobbs did not settle the question of abortion in America — instead, it generated a new slate of questions. One of those questions involves the interaction of existing legal rules with the concept of fetal personhood — the view, held by many in the anti-abortion movement, that a fetus is a person entitled to the same rights and protections as any other person.

The first case , scheduled for argument on Tuesday, F.D.A. v. Alliance for Hippocratic Medicine, is a challenge to the Food and Drug Administration’s protocols for approving and regulating mifepristone, one of the two drugs used for medication abortions. An anti-abortion physicians’ group argues that the F.D.A. acted unlawfully when it relaxed existing restrictions on the use and distribution of mifepristone in 2016 and 2021. In 2016, the agency implemented changes that allowed the use of mifepristone up to 10 weeks of pregnancy, rather than seven; reduced the number of required in-person visits for dispensing the drug from three to one; and allowed the drug to be prescribed by individuals like nurse practitioners. In 2021, it eliminated the in-person visit requirement, clearing the way for the drug to be dispensed by mail. The physicians’ group has urged the court to throw out those regulations and reinstate the previous, more restrictive regulations surrounding the drug — a ruling that could affect access to the drug in every state, regardless of the state’s abortion politics.

The second case, scheduled for argument on April 24, involves the Emergency Medical Treatment and Labor Act (known by doctors and health policymakers as EMTALA ), which requires federally funded hospitals to provide patients, including pregnant patients, with stabilizing care or transfer to a hospital that can provide such care. At issue is the law’s interaction with state laws that severely restrict abortion, like an Idaho law that bans abortion except in cases of rape or incest and circumstances where abortion is “necessary to prevent the death of the pregnant woman.”

Although the Idaho law limits the provision of abortion care to circumstances where death is imminent, the federal government argues that under EMTALA and basic principles of federal supremacy, pregnant patients experiencing emergencies at federally funded hospitals in Idaho are entitled to abortion care, even if they are not in danger of imminent death.

These cases may be framed in the technical jargon of administrative law and federal pre-emption doctrine, but both cases involve incredibly high-stakes issues for the lives and health of pregnant persons — and offer the court an opportunity to shape the landscape of abortion access in the post-Roe era.

These two cases may also give the court a chance to seed new ground for fetal personhood. Woven throughout both cases are arguments that gesture toward the view that a fetus is a person.

If that is the case, the legal rules that would typically hold sway in these cases might not apply. If these questions must account for the rights and entitlements of the fetus, the entire calculus is upended.

In this new scenario, the issue is not simply whether EMTALA’s protections for pregnant patients pre-empt Idaho’s abortion ban, but rather which set of interests — the patient’s or the fetus’s — should be prioritized in the contest between state and federal law. Likewise, the analysis of F.D.A. regulatory protocols is entirely different if one of the arguments is that the drug to be regulated may be used to end a life.

Neither case presents the justices with a clear opportunity to endorse the notion of fetal personhood — but such claims are lurking beneath the surface. The Idaho abortion ban is called the Defense of Life Act, and in its first bill introduced in 2024, the Idaho Legislature proposed replacing the term “fetus” with “preborn child” in existing Idaho law. In its briefs before the court, Idaho continues to beat the drum of fetal personhood, insisting that EMTALA protects the unborn — rather than pregnant women who need abortions during health emergencies.

According to the state, nothing in EMTALA imposes an obligation to provide stabilizing abortion care for pregnant women. Rather, the law “actually requires stabilizing treatment for the unborn children of pregnant women.” In the mifepristone case, advocates referred to fetuses as “unborn children,” while the district judge in Texas who invalidated F.D.A. approval of the drug described it as one that “starves the unborn human until death.”

Fetal personhood language is in ascent throughout the country. In a recent decision , the Alabama Supreme Court allowed a wrongful-death suit for the destruction of frozen embryos intended for in vitro fertilization, or I.V.F. — embryos that the court characterized as “extrauterine children.”

Less discussed but as worrisome is a recent oral argument at the Florida Supreme Court concerning a proposed ballot initiative intended to enshrine a right to reproductive freedom in the state’s Constitution. In considering the proposed initiative, the chief justice of the state Supreme Court repeatedly peppered Nathan Forrester, the senior deputy solicitor general who was representing the state, with questions about whether the state recognized the fetus as a person under the Florida Constitution. The point was plain: If the fetus was a person, then the proposed ballot initiative, and its protections for reproductive rights, would change the fetus’s rights under the law, raising constitutional questions.

As these cases make clear, the drive toward fetal personhood goes beyond simply recasting abortion as homicide. If the fetus is a person, any act that involves reproduction may implicate fetal rights. Fetal personhood thus has strong potential to raise questions about access to abortion, contraception and various forms of assisted reproductive technology, including I.V.F.

In response to the shifting landscape of reproductive rights, President Biden has pledged to “restore Roe v. Wade as the law of the land.” Roe and its successor, Planned Parenthood v. Casey, were far from perfect; they afforded states significant leeway to impose onerous restrictions on abortion, making meaningful access an empty promise for many women and families of limited means. But the two decisions reflected a constitutional vision that, at least in theory, protected the liberty to make certain intimate choices — including choices surrounding if, when and how to become a parent.

Under the logic of Roe and Casey, the enforceability of EMTALA, the F.D.A.’s power to regulate mifepristone and access to I.V.F. weren’t in question. But in the post-Dobbs landscape, all bets are off. We no longer live in a world in which a shared conception of constitutional liberty makes a ban on I.V.F. or certain forms of contraception beyond the pale.

Melissa Murray, a law professor at New York University and a host of the Supreme Court podcast “ Strict Scrutiny ,” is a co-author of “ The Trump Indictments : The Historic Charging Documents With Commentary.”

Kate Shaw is a contributing Opinion writer, a professor of law at the University of Pennsylvania Carey Law School and a host of the Supreme Court podcast “Strict Scrutiny.” She served as a law clerk to Justice John Paul Stevens and Judge Richard Posner.