2 CHAPTER 2

Reconstructing and Analyzing Arguments

In chapter 1, we looked the structure of arguments. We learned how to determine what the premises are and how they lead to a conclusion. We also discussed the important concepts of validity and soundness and considered various tests that we can apply to arguments to make initial evaluations.

In this chapter, we are going to build on our initial discussion by considering additional steps that we can take to make sure our evaluation is correct. In “real life,” people frequently build arguments that are incomplete by building arguments on unspoken assumptions. If we do not evaluate the assumptions, we can frequently be led to accept conclusions that are not warranted. In the “real world,” people also present arguments that are not explicit. It is important to learn how to “interpret” fuzzy arguments into clearer premises and conclusions so that we can evaluate them properly.

2.1 Arguments With Missing Premises

Quite often, an argument will not explicitly state a premise that we can see is needed in order for the argument to be valid. In such a case, we can supply the premise(s) needed in order so make the argument valid. Making missing premises explicit is a central part of reconstructing arguments in standard form. We have already dealt in part with this in the section on paraphrasing, but now that we have introduced the concept of validity, we have a useful tool for knowing when to supply missing premises in our reconstruction of an argument. In some cases, the missing premise will be fairly obvious, as in the following:

Gary is a convicted sex-offender, so Gary is not allowed to work with children.

The premise and conclusion of this argument are straightforward:

Gary is a convicted sex-offender

Therefore, Gary is not allowed to work with children (from 1)

However, as stated, the argument is invalid. (Before reading on, see if you can provide a counterexample for this argument. That is, come up with an imaginary scenario in which the premise is true and yet the conclusion is false.) Here is just one counterexample (there could be many): Gary is a convicted sex-offender but the country in which he lives does not restrict convicted sex-offenders from working with children. I do not know whether there are any such countries, although I suspect there are (and it does not matter for the purpose of validity whether there are or are not). In any case, it seems clear that this argument is relying upon a premise that is not explicitly stated. We can and should state that premise explicitly in our reconstruction of the standard form argument. But what is the argument’s missing premise? The obvious one is that no sex-offenders are allowed to work with children, but we could also use a more carefully statement like this one:

Where Gary lives, no convicted sex-offenders are allowed to work with children.

It should be obvious why this is a more “careful” statement. It is more careful because it is not so universal in scope, which means that it is easier for the statement to be made true. By relativizing the statement that sex-offenders are not allowed to work with children to the place where Gary lives, we leave open the possibility that other places in the world do not have this same restriction. So even if there are other places in the world where convicted sex-offenders are allowed to work with children, our statements could still be true since in this place (the place where Gary lives) they are not. (For more on strong and weak statements, see section 1.10). So here is the argument in standard form:

Gary is a convicted sex-offender.

Where Gary lives, no convicted sex-offenders are allowed to work with children.

Therefore, Gary is not allowed to work with children. (from 1-2)

This argument is now valid: there is no way for the conclusion to be false, assuming the truth of the premises. This was a fairly simple example where the missing premise needed to make the argument valid was relatively easy to see. As we can see from this example, a missing premise is a premise that the argument needs in order to be as strong as possible. Typically, this means supplying the statement(s) that are needed to make the argument valid. But in addition to making the argument valid, we want to make the argument plausible. This is called “the principle of charity.” The principle of charity states that when reconstructing an argument, you should try to make that argument (whether inductive or deductive) as strong as possible. When it comes to supplying missing premises, this means supplying the most plausible premises needed in order to make the argument either valid (for deductive arguments) or inductively strong (for inductive arguments).

Normative statements can be contrasted with descriptive statements, which are simply factual claims about what is true. For example, “Russia does not allow gay couples to raise children” is a descriptive statement. That is, it is simply a claim about what is in fact the case in Russia today. In contrast, “Russia should not allow gay couples to raise children” is a normative statement since it is not a claim about what is true, but what ought to be true, relative to some standard of evaluation (for example, a moral or legal standard). An important idea within philosophy, which is often traced back to the Scottish philosopher David Hume (1711-1776), is that statements about what ought to be the case (i.e., normative statements) can never be derived from statements about what is the case (i.e., descriptive statements). This is known within philosophy as the is-ought gap. The problem with the above argument is that it attempts to infer a normative statement from a purely descriptive statement, violating the is-ought gap. We can see the problem by constructing a counterexample. Suppose that in society x it is true that children raised by gay couples have psychological problems. However, suppose that in that society people do not accept that the state should do what it can to decrease harm to children. In this case, the conclusion, that the state should discourage gay couples from raising children, does not follow. Thus, we can see that the argument depends on a missing or assumed premise that is not explicitly stated. That missing premise must be a normative statement, in order that we can infer the conclusion, which is also a normative statement. There is an important general lesson here: Many times, an argument with a normative conclusion will depend on a normative premise which is not explicitly stated. The missing normative premise of this particular argument seems to be something like this:

The state should always do what it can to decrease harm to children.

Notice that this is a normative statement, which is indicated by the use of the word “should.” There are many other words that can be used to capture normative statements such as: good, bad, and ought. Thus, we can reconstruct the argument, filling in the missing normative premise like this:

Children who are raised by gay couples often have psychological and emotional problems.

The state should always do what it can to decrease harm to children.

Therefore, the state should discourage gay couples from raising children. (from 1-2)

However, although the argument is now in better shape, it is still invalid because it is still possible for the premises to be true and yet the conclusion false. In order to show this, we just have to imagine a scenario in which both the premises are true and yet the conclusion is false. Here is one counterexample to the argument (there are many). Suppose that while it is true that children of gay couples often have psychological and emotional problems, the rate of psychological problems in children raised by gay couples is actually lower than in children raised by heterosexual couples. In this case, even if it were true that the state should always do what it can to decrease harm to children, it does not follow that the state should discourage gay couples from raising children. In fact, in the scenario I have described, just the opposite would seem to follow: the state should discourage heterosexual couples from raising children.

But even if we suppose that the rate of psychological problems in children of gay couples is higher than in children of heterosexual couples, the conclusion still does not seem to follow. For example, it could be that the reason that children of gay couples have higher rates of psychological problems is that in a society that is not yet accepting of gay couples, children of gay couples will face more teasing, bullying and general lack of acceptance than children of heterosexual couples. If this were true, then the harm to these children is not so much due to the fact that their parents are gay as it is to the fact that their community does not accept them. In that case, the state should not necessarily discourage gay couples from raising children. Here is an analogy: At one point in our country’s history (if not still today) it is plausible that the children of black Americans suffered more psychologically and emotionally than the children of white Americans. But for the government to discourage black Americans from raising children would have been unjust, since it is likely that if there was a higher incidence of psychological and emotional problems in black Americans, then it was due to unjust and unequal conditions, not to the black parents, per se. So, to return to our example, the state should only discourage gay couples from raising children if they know that the higher incidence of psychological problems in children of gay couples is not the result of any kind of injustice but is due to the simple fact that the parents are gay.

Thus, one way of making the argument (at least closer to) valid would be to add the following two missing premises:

The rate of psychological problems in children of gay couples is higher than in children of heterosexual couples.

The higher incidence of psychological problems in children of gay couples is not due to any kind of injustice in society, but to the fact that the parents are gay.

So, the reconstructed standard form argument would look like this:

Children who are raised by gay couples often have psychological and emotional problems.

The rate of psychological problems in children of gay couples is higher than in children of heterosexual couples.

The higher incidence of psychological problems in children of gay couples is not due to any kind of injustice in society, but to the fact that the parents are gay.

The state should always do what it can to decrease harm to children.

Therefore, the state should discourage gay couples from raising children. (from 1-4)

In this argument, premises 2-4 are the missing or assumed premises. Their addition makes the argument much stronger but making them explicit enables us to clearly see what assumptions the argument relies on in order for the argument to be valid. This is useful since we can now clearly see which premises of the argument we may challenge as false. Arguably, premise 4 is false since the state should not always do what it can to decrease harm to children. Rather, it should only do so as long as such an action did not violate other rights that the state has to protect or create larger harms elsewhere.

The important lesson from this example is that supplying the missing premises of an argument is not always a simple matter. In the example above, I have used the principle of charity to supply missing premises. Mastering this skill is truly an art (rather than a science) since there is never just one correct way of doing it and because it requires a lot of skilled practice.

2.2 Assuring, Guarding And Discounting

As we have seen, arguments often have complex structures including subarguments (recall that a subargument is an argument for one of the premises of the main argument). But in practice people do not always give further reasons or argument in support of every statement they make. Sometimes they use certain rhetorical devices to cut the argument short, or to hint at a further argument without actually stating it. There are three common strategies for doing this:

Assuring: informing someone that there are further reasons although one is not giving them now

Guarding: weakening one’s claims so that it is harder to show that the claims are false

Discounting: anticipating objections that might be raised to one’s claim or argument as a way of dismissing those objections.

We will discuss these in order, starting with assuring. Why would we want to assure our audience?

Presumably when we make a claim that is not obvious, and that the audience may not be inclined to believe. For example, if I am trying to convince you that the United States is one of the leading producers of CO₂ emissions, then I might cite certain authorities such as the Intergovernmental Panel on Climate Change (IPCC) as saying so. This is one way of assuring our audience: by citing authorities. There are many ways to cite authorities, some examples of which are these:

Dentists agree that…

Recent studies have shown…

It has been established that…

Another way of assuring is to comment on the strength of one’s own convictions. The rhetorical effect is that by commenting on how sure you are that something is true, you imply, without saying, that there must be very strong reasons for what you believe—assuming that the audience believes you are a reasonable person, of course. Here are some ways of commenting on the strength of one’s beliefs

I am certain that…

I am sure that…

I can assure you that…

Over the years, I have become convinced that…

I would bet a million dollars that…

Yet another way of assuring one’s audience is to make an audience member feel that it would be stupid, odd, or strange to deny the claim one is making. One common way to do this is by implying that every sensible person would agree with the claim. Here are some examples:

Everyone with any sense agrees that…

Of course, no one will deny that…

There is no question that…

No one with any sense would deny that…

Another common way of doing this is by implying that no sensible person would agree with a claim that we are trying to establish as false:

It is no longer held that…

No intelligent person would ever maintain that…

You would have to live under a rock to think that…

Assurances are not necessarily illegitimate, since the person may be right and may in fact have good arguments to back up the claims, but the assurances are not themselves arguments and a critical thinker will always regard them as somewhat suspect. This is especially so when the claim is not obviously true.

Next, we will turn to guarding. Guarding involves weakening a claim so that it is easier to make that claim true. Here is a simple contrast that will make the point. Consider the following claims:

All U.S. Presidents were monogamous

Almost all U.S. Presidents were monogamous

Most U.S. Presidents were monogamous

Many U.S. Presidents were monogamous

Some U.S. Presidents were monogamous

The weakest of these claims is E, whereas the strongest is A and each claim descending from A-E is increasingly weaker. It does not take very much for E to be true: there just has to be at least one U.S. President who was monogamous. In contrast, A is much less likely than E to be true because it requires every U.S. President to have been monogamous. One way of thinking about this is that any time A is true, it is also true that B-E is true, but B-E could be true without A being true. That is what it means for a claim to be stronger or weaker. A weak claim is more likely to be true whereas a strong claim is less likely to be true. E is much more likely to be true than A. Likewise, D is somewhat more likely to be true than C, and so on.

So, guarding involves taking a stronger claim and making it weaker so there is less room to object to the claim. We can also guard a claim by introducing a probability clause such as, “it is possible that…” and “it is arguable that…” or by reducing our level of commitment to the claim, such as moving from “I know that x” to “I believe that x.” One common use of guarding is in reconstructing arguments with missing premises using the principle of charity (section 1.9). For example, if an argument is that “Tom works for Merrill Lynch, so Tom has a college degree,” the most charitable reconstruction of this argument would fill in the missing premise with “most people who work for Merrill Lynch have college degrees” rather than “everyone who works for Merrill Lynch has a college degree.” Here we have created a more charitable (plausible) premise by weakening the claim from “all” to “most,” which as we have seen is a kind of guarding.

Finally, we will consider discounting. Discounting involves acknowledging an objection to the claim or argument that one is making, while dismissing that same objection. The rhetorical force of discounting is to make it seem as though the argument has taken account of the objections—especially the ones that might be salient in a person’s mind. The simplest and most common way of discounting is by using the “A but B” locution. Contrast the following two claims:

The worker was inefficient, but honest.

The worker was honest, but inefficient.

Although each statement asserts the same facts, A seems to be recommending the worker, whereas B does not. We can imagine A continuing: “And so the manager decided to keep her on the team.” We can imagine B continuing: “Which is why the manager decided to let her go.” This is what we can call the “A but B” locution. The “A but B” locution is a form of discounting that introduces what will be dismissed or overridden first and then follows it by what is supposed to be the more important consideration. By introducing the claim to be dismissed, we are discounting that claim. There are many other words that can be used as discounting words instead of using “but.” The table below gives a partial list of words and phrases that commonly function as discounting terms.

2.3 Evaluative Language

Yet another rhetorical technique that is commonly encountered in argumentation is the use of evaluative language to influence one’s audience to accept the conclusion one is arguing for. Evaluative language can be contrasted with descriptive language. Whereas descriptive language simply describes a state of affairs, without passing judgment (positive or negative) on that state of affairs, evaluative language (also called normative language) is used to pass some sort of judgment, positive or negative, on something. Contrast the following two statements:

Bob is tall.

Bob is good.

“Tall” is a descriptive term since being tall is, in itself, neither a good nor bad thing. Rather, it is a purely descriptive term that does not pass any sort of judgment, positive or negative, on the fact that Bob is tall. In contrast, “good” is a purely evaluative term, which means that the only thing the word does is make an evaluation (in this case, a positive evaluation) and does not carry any descriptive content. “Good,” “bad,” “right,” and “wrong” are examples of purely evaluative terms. A more interesting kind of term is one that is partly descriptive and partly evaluative. For example:

Bob is nosy.

“Nosy” is a negatively evaluative term since to call someone nosy is to make a negative evaluation of them— or at least of that aspect of them. But it also implies a descriptive content, such as that Bob is curious about other people’s affairs. We could re-describe Bob’s nosiness using purely descriptive language:

Bob is very curious about other people’s affairs.

Notice that while the phrase “very curious about other people’s affairs” does capture the descriptive sense of “nosy,” it does not capture the evaluative sense of nosy, since it does not carry with it the negative connotation that “nosy” does.

Evaluative language is rife in our society, perhaps especially so in political discourse. This is not surprising since by using evaluative language to describe certain persons, actions, or events we can influence how people understand and interpret the world. If you can get a person to think of someone or some state of affairs in terms of a positively or negatively evaluative term, chances are you will be able to influence their evaluation of that person or state of affairs. That is one of the rhetorical uses of evaluative language. Compare, for example,

Bob is a rebel.

Bob is a freedom fighter.

Whereas “rebel” tends to be a negatively evaluative term, “freedom fighter,” at least for many Americans, tends to be a positively evaluative term. Both words, however, have the same descriptive content, namely, that Bob is someone who has risen in armed resistance to an existing government. The difference is that whereas “rebel” makes a negative evaluation, “freedom fighter” makes a positive evaluation. The Table below gives a small sampling of some evaluative terms.

English contains an interesting mechanism for turning positively evaluative terms into negative evaluative ones. All you have to do is put the word “too” before a positively evaluative terms and it will all of a sudden take on a negative connotation. Compare the following:

John is honest.

John is too honest.

Whereas “honest” is a positive evaluative term, “too honest” is a negative evaluative term. When someone describes John as “too honest,” we can easily imagine that person going on to describe how John’s honesty is actually a liability or negative trait. Not so when he is simply described as honest. Since the word “too” indicates an excess, and to say that something is an excess is to make a criticism, we can see why the word “too” changes the valence of an evaluation from positive to negative.

Like assuring and discounting, using evaluative language to try to influence one’s audience is a rhetorical technique. As such, it is more concerned with non-rational persuasion than it is with giving reasons. Non-rational persuasion is ubiquitous in our society today, not the least of which because advertising is ubiquitous, and advertising today almost always uses non-rational persuasion. Think of the last time you saw some commercial present evidence for why you should buy their product (i.e., never) and you will realize how pervasive this kind of rhetoric is. Philosophy has a complicated relationship with rhetoric—a relationship that stretches back to Ancient Greece. Socrates disliked those, such as the Sophists, who promised to teach people how to effectively persuade someone of something, regardless of whether that thing was true. Although some people might claim that there is no essential difference between giving reasons for accepting a conclusion and trying to persuade by any means, most philosophers, including the author of this text, think otherwise. If we define rhetoric as the art of persuasion, then although argumentation is a kind of rhetoric (since it is a way of persuading), not all rhetoric is argumentation. The essential difference, as already hinted at, is that argumentation attempts to persuade by giving reasons whereas rhetoric attempts to persuade by any means, including non-rational means. If I tell you over and over again (in creative and subliminal ways) to drink Beer x because Beer x is the best beer, then I may very well make you think that Beer x is the best beer, but I have not thereby given you an argument that Beer x is the best beer. Thinking of it rationally, the mere fact that I have told you lots of times that Beer x is the best beer gives you no good reason for believing that Beer x is in fact the best beer.

The rhetorical devices surveyed in the last two sections—especially assuring, discounting and the use of evaluative language—may be effective ways of persuading people, but they are not the same thing as offering an argument. And if we attempt to see them as arguments, they turn out to be typically pretty poor arguments. One of the many things that psychologists study is how we are persuaded to believe or do things. As an empirical science, psychology attempts to describe and explain the way things are, in this case, the processes that lead us to believe or act as we do. Logic, in contrast, is not an empirical science. Logic is not trying to tell us how we do think, but what good thinking is and, thus, how we ought to think. The study of logic is the study of the nature of arguments and, importantly, of what distinguishes a good argument from a bad one. “Good” and “bad” are what philosophers call normative concepts because they involve standards of evaluation. Since logic concerns what makes something a good argument, logic is sometimes referred to as a normative science. They key standard of evaluation of arguments that we have seen so far is that of validity.