Primer

Over your first few years of life, you learned how to do a lot of things: how to speak, how to think, how to walk, how to grasp and manipulate objects, etc. But you learned most of these things implicitly—that is, without having words for what you were doing and how. For example, you learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). Here’s another example: Many of you have probably never thought much about how to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into component parts and this will have given you more control over the way you walk. Likewise, when athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer grained control over their movements. It is possible to gain greater control of your thinking in the same way, by learning to analyzing the complex activity of thinking into the various mental acts that make it up. In this primer we’re going to focus on a part of our mental activity that looms large in our daily lives, in the sciences, and in philosophy: the activity of arguing. We will learn what an argument is, how to analyze an argument into its parts, and how to use this analysis to methodically assess an argument. In §1, I provide an overview of the whole process, and §2–5 deal in greater detail with different aspects of the process.

Propositions

Before we discuss arguments in earnest, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are composed. A proposition is the sort of thought that is capable of being true or false, believed or disbelieved, and asserted or denied. Such thoughts are asserted by declarative sentences. Here are some examples:

1. Healthy grass is green.

2. O. J. Simpson killed Nicole Brown.

3. Twice two is four.

4. Twice two is five.

5. Many diseases are caused by bacteria.

6. Stalin was evil.

7. Joe Biden is the 46th President of the United States.

8. Either a Republican or a Democrat will win the 2024 Presidential election.

9. The Senate should have convicted Donald Trump in both of his impeachment trials.

10. Hillary Clinton would have been an awful president.

The proposition is not the same thing as the sentence asserting it because the same thought can be asserted by different sentences. For example, here are several different ways of asserting Proposition 3 from the list above:

3a. Twice two is four.

3b. Two times two is four.

3c. 2 x 2 = 4

3d. Deux fois deux c'est quatre.

3e. 兩次兩次是四次。

Sentences 3a and 3b are two different ways of asserting the same proposition in English. 3c is a way of asserting it in mathematical notation, 3d is a way of asserting it in French, and 3e is a way of asserting it in Chinese.

Another reason why a proposition is not the same thing as a sentence, is that propositions can be asserted as parts of more complex sentences that include multiple propositions. For example, here’s a sentence that asserts both Propositions 9 and 10 from the list above: "Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials."

Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will all agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false.

Some of you may think that some of the propositions we may disagree over aren’t really the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people believe or disbelieve each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or falce. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.

The Anatomy of an Argument

As the term is used in philosophy, an argument is a set of related propositions (called premises) that is given as a reason for believing a further proposition (called the conclusion). Consider, for example, the following, simple argument:

Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that make its structure clearer. One popular way is called standard form. Here’s what the argument we have been discussing looks like in standard form:

1. Whoever murdered Carl had access to his rose garden at midnight. 2. Only Natalie had access to Carl’s rose garden at midnight.

3. Natalie murdered Carl.

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the inference—the mental act of moving in thought from the premises to the conclusion.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

Map 1:

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1 Template:Reflist

Both of these ways of representing the argument are meant to make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. The argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

Uses of Argument

If you were trying to convince someone, perhaps a jury, of Natalie’s guilt, you might present them with the argument we discussed in the last section. Or, you might formulate this argument silently to yourself in the course of trying to figure out who killed Carl. In either case, we would say that you inferred that Natalie was Carl’s murderer from the premises that the murderer had access to the rose garden at midnight and that only Natalie had such access.

We tend to think of making arguments in situations where people disagree and are trying to convince the other (or to convince some third party). This is the case when people argue in court or around a dinner table; but this is not the only use of arguments, nor is it their fundamental use. Much of what we know is based on other knowledge and inference is the process by which we reach new knowledge from old. It is only because of arguments that we know many of the things we do, and it is only by further arguments that we can come to know many of the things we would like to learn.

Let’s survey some of the areas in which much of our knowledge is due to inference. Arguments like the one concerning Carl and Natalie enable us to know who committed crimes for which there were no eyewitnesses. In the natural sciences, almost everything we know beyond the basic data (consisting in observations and measurements) is reached by inference.2(***CITATION TBA***) So is much of our knowledge in higher mathematics. Our knowledge of the future is inferred from what we know about the past and present. And our knowledge of the distant past (beyond the scope of our memories) is also based on argument. Here, in some cases, we have firsthand accounts from people who claim to have observed or taken part in various historical events, but there are questions about the honesty and accuracy of these reports (especially when some contradict others), so we need arguments to determine which accounts we can rely on.

Inferring is a crucial part of how you as an individual come to know the world. It’s a process that’s fallible, and sometimes it results in errors—beliefs that aren’t really knowledge. When two people argue with one another—if they’re arguing honestly—they are sharing with some of the reasons they each have for believing the things they do. Each is trying to teach the other some of what he thinks he knows, and each can help the other identify errors in his own thinking.

Of course, people also often argue with one another dishonestly. Think of a conman who sells a bogus medicine and gives arguments to trick sick people into believing that his medicine will cure their illnesses. The conman knows that the conclusion he’s trying to convince them of is false—or, at least, he doesn’t really care if it is true. His goal is not to help them to tell what’s true, but to get them to believe a conclusion that he wants them to believe, regardless of whether it is true. It is possible to be dishonest with oneself in this same way. You may not be able to work to convince yourself of something you self-consciously know is a lie, but people often make arguments to convince themselves of things that they want to believe—or that they think they are supposed to believe—regardless of whether the things are really true. For example, someone who suspects her husband of having cheated may not want to believe it because she finds the idea too painful, or she may feel guilty for believing it because she thinks she is supposed to trust him. In either case, she may fish around for arguments to convince her that he is faithful.

This brings me to an important point of clarification. Earlier I said that an argument is meant to give us a “reason to believe” its conclusion. When we speak of the reasons we have for performing an action, we usually have in mind either some goal that we hope to achieve by performing the action, or some obligation that we think we have for taking it. These are called pragmatic or practical reasons. By contrast, we can call the reasons that arguments give epistemic reasons. They are the sort of reasons that help one to tell that a conclusion is true and thereby to put one in a position to know it.

The primary use of arguments is to tell what’s true. A secondary use is to persuade oneself or others that something is true. We can distinguish two forms of persuasion, which we might call "honest" and "dishonest." In Honest persuasion, you articulate your own actual reasons for thinking the conclusion is true, in order to persuade someone else of it or to make clearer in your own mind. In dishonest persuasion you come up with reasons to convince someone of something without regard for whether that thing is really true. Thus a dishonest lawyer or salesman, might try to persuade someone of innocence of his client or the quality of his wares by appealing to premises that he knows are false (or has no reason to think are true), but that he thinks his audience is likely to believe, or he may use arguments that seem strong at first glance, but don't stand up to scrutiny. Not all sorts of dishonest persuasion stem from trying to make money or advance one's career (as these two cases do). People also argue dishonestly to impress others or to feel important themselves.

It is possible to engage in dishonest persuasion with themselves as well as with others. This often happens when someone wants to believe something (or thinks that he is supposed to believe it). Thus someone in an unhappy marriage might try to convince himself that he and his spouse are happy together, despite the growing evidence that they are not, or someone who has grown up in a family that professes certain beliefs and feels that he's supposed to believe them, might try to convince himself that they're true. We can call this dishonest reasoning with oneself, rationalizing, or BSing oneself. It is often hard to tell whether someone is being honest or dishonest in his use of arguments, and it can sometimes even be difficult to tell in one's own case. However, the essential difference between the two ways of arguing is clear: Is one using argument in an attempt to tell what's true (and to share this with others) or is one using them to defend a position that one is committed to defending regardless of its actual merits? Genuine reasoning is the attempt to tell what's true, and dishonest uses of arguments are just attempts to fake (to oneself or others) that one is engaged in this process. It is for the sake of genuine reasoning that we really need arguments, so we will focus on honest reasoning in this primer.

Mapping Relations Between Arguments

Our thinking isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.

Map 1

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts we can look at and discuss more complex maps that show relations between arguments.

Arguments that share a conclusion

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:

Map 2:

Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument, and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. You will see that in order for Proposition 1 to convince you that Natalie murdered Carl, you would need to also know Proposition 2, but that you wouldn’t need to know Propositions 4, 5, or 6. Likewise, in order for Proposition 5 to convince you, you’d need to also know Propositions 4 and 6, but not Propositions 1 or 2.

Chains of Argument

A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that:

Map 3:

Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a premise for a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)

Complex Maps

Now let’s consider a larger map that includes all the arguments we’ve looked at plus three others.

Map 4:

Argument E is a third argument for Proposition 3. I expect you’ll agree that it a bad argument. The map shows two objections to this argument, each symbolized by a red octagon. Objections are (in effect) arguments that something is wrong with the argument they're objecting too.

Objection H objects to Proposition 11, which is a premise of Argument E. When someone objects to a premise, he is arguing that it is not a suitable premise. This could be because the premise us false (as is the case with Proposition 11), but there are other reasons why a premise might not be suitable. For example, we might not be in a position to tell whether it's true, which would make it useless as a premise. Or we might only have reason to think that it's true if we already believe the conclusion, in which case it would be a case of circular reasoning. In addition to objections to premises, there are objections to inferences. These are arguments that the inference is faulty.

Objection I objects to Inference E. To object to an inference is to argue that it's not a good inference—that, even we knew the premises to be true, the inference wouldn't give us a reason to believe the conclusion. We'll discuss the factors that make for a good or bad inferences later.

Inference F is represented by a red inference symbol instead of the usual green one because it represents a counterargument. Counterarguments are an arguments against conclusions, rather than for them. Counterargument F gives us a reason to think that its conclusion, Proposition 3 is false. If we wanted to treat F as a regular argument (represented by a green symbol), then it's conclusion would be that “Natalie did not murder Carl.” We could write this conclusion out as a distinct proposition, in its own box, but since it is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate F to Proposition 3 on the map, so that we could see a glance that F is arguing against the very same conclusion that Arguments A, B, and E are arguing for. This is the purpose of the red counterargument symbol.

Argument G supports Proposition 14, which is a premise for Counterargument F.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be an error somewhere. In this map, Objections H and I, indicate what's wrong with Argument E. But even if we eliminate Argument E, we have two other arguments for Proposition 3, and we have a counterargument against this same proposition. Proposition 3 cannot be both true and false, so something must be wrong either with Arguments A and B or with Counterargument F. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.

How to Assess Arguments

(Or maybe this should be it's own overview article.) (There should definitely be separate articles (linked here) on Epistemic Status of Propositions, and on Assessing Different Types of Inference.)