What’s the point in arguing?

Automatic gainsaying
Automatic gainsaying

by Jeremy W Bowman

1. Argument as Persuasion

In a well-known Monty Python sketch, Michael Palin walks into the office of John Cleese, who sits behind his desk like a bank manager. He has come for an “argument” — apparently, an argument of the sort prized by logicians and philosophers. But instead of giving him “a collected series of statements to establish a definite proposition”, Cleese simply contradicts everything he says. And so it goes for a few minutes.

But then suddenly, Cleese’s mindless disagreement stops. Palin’s time is up. He pays more money, and once again Cleese reverts to “automatically gainsaying” everything Palin says — starting off by denying the fact that he has paid more money.

One of the funny things about the sketch is that that sort of argument can hardly be of any use to anyone — only a weirdo like Palin would part with money to get one. What about the other sort of argument — the celebrated “series of statements to establish a definite proposition”? Philosophy tutors are always urging their students to “come up with” arguments, and those who succeed in doing so are rewarded with higher marks. Why? What’s an argument for? I think the standard answer to this question tells only half the story. In this article, I try to give a more complete answer, one that I think can help to clear up some philosophical confusion. To see why, let’s briefly examine what logicians and philosophers mean when they talk about arguments.

In logic (rather than a Python sketch, or a tiff with the wife) an argument is a set of sentences, one of which (the conclusion) follows from some others (the premises). In a valid argument, the conclusion follows from the premises in a very strict way: if the premises were true, then the conclusion would have to be true as well. So there is a “special relationship” between the premises and conclusion in a valid argument. This special logical connection can be expressed in various ways. We might put it like this: the conclusion follows from the premises of necessity. Or, to say the same thing a slightly different way: the truth of the premises is sufficient for the truth of the conclusion. Or, to say the same thing yet another way: if the conclusion is false, then one or more of the premises must be false as well.

Here’s an example of a valid argument:

1. In any species of bird, if the plumage of one sex is drabber than the other, then the drabber sex incubates the eggs.

2. Male phalaropes have drabber plumage than female phalaropes.

Therefore, male phalaropes incubate the eggs.

This argument has two premises, numbered 1 and 2 (an argument can have any number of them). And by the way, I don’t know whether they are true. But I do know that if they are true, then the conclusion must be true as well, because I know that the argument is valid. If I could get an assurance, somehow, that both 1 and 2 are true, I would thereby be assured that the conclusion is true. In that sense, the premises “guarantee” the conclusion.

Obviously, that could be useful. Suppose I have good reasons for thinking that the premises of an argument are true, but for some reason don’t yet believe the conclusion (maybe it hasn’t even occurred to me yet). Then the argument gives me a warrant for believing the conclusion. That is, the argument is valuable because it gives me a good reason for thinking the conclusion is true. Conceivably, that might spare me a trip to the Outer Hebrides, one of the few places where phalaropes breed.

In this example, the “point” of the valid argument is primarily to persuade: it provides a warrant for believing the conclusion. Arguments are often put to this purpose. For example, each of the various branches of mathematics (such as geometry) has the following structure. We start off with some axioms or definitions — i.e. some very obvious or “self-evident” claims that are not open to question. From these, we derive theorems. The theorems are much less obvious than the axioms, and we can accept them as being true, because they can be proved by valid arguments like the one above. Theorems probably first occur to mathematicians when they think creatively, and try to imagine what might be the case. But a theorem can only be formally incorporated into the “edifice” of mathematics when it is established that it necessarily follows from the axioms. In other words, a theorem is not accepted as true until it is proved. Once it is proved, we have an assurance that whatever it says must be the case. The axioms (or definitions) guarantee the theorems in the same way as the premises guarantee the conclusion of the more modest example of an argument given above.

In his Brief Lives, seventeenth-century biographer John Aubrey described Hobbes’s incredulous reaction on meeting an unlikely-sounding theorem in Euclid’s book of geometry: “By G--, sayd he (he would now and then sweare an emphaticall Oath by way of emphasis) this is impossible!” After reading through the Euclid’s “demonstration” (i.e. a series of valid arguments whose eventual conclusion was the unlikely-sounding theorem) Hobbes had to accept it as true. According to Aubrey, “This made him in love with Geometry.” And it may even have changed the course of history: Hobbes’s influential political theory was modelled on the definitions-and-theorems structure of mathematics.


2. Argument as Explication

In the above examples, the “object of the game” was to persuade. For an argument to succeed at this, the person we wish to persuade must already believe the premises of the argument, and understand how the conclusion follows from the premises. But persuasion is not the only thing a valid argument is good for. As I mentioned above, one of the many ways of explaining the concept of validity is to say that in a valid argument, the truth of the premises is sufficient for the truth of its conclusion. They express “all you need to know” to be convinced of it. That important fact can be used to bring otherwise hidden assumptions “out into the open” . How?

In real life, most arguments are incomplete. It is not unusual to find a single sentence offered in support of another sentence — yet if we try to understand the first sentence as the “premise” and the second sentence as the “conclusion” of an argument, we find it is distinctly less than explicitly valid. To turn an incomplete train of thought like that into a valid argument, we have to make it complete by adding a few other sentences, understood as further premises. Usually, these extra premises are truisms that go without saying. For example, suppose I want to convince you that at this moment clouds are in the sky. I might say, “It’s raining”, as if that’s all you need to hear. Strictly speaking, I haven’t presented you with a valid argument unless I add the further premise “If it’s raining then it’s cloudy” — but I don’t bother saying it, because everyone accepts that already. (And strictly speaking I should also add the word ‘therefore’ before the conclusion “It’s cloudy”, to indicate that it follows from the premises in the strict way we’ve been discussing.)

Occasionally, what is needed to complete an argument is not a truism that everyone accepts already, but instead a vital point of disagreement. And in those situations, the demand for a complete valid argument is really a demand for explicitness.

For example, suppose two people get into a discussion about the cause of the well-known fact that comparatively few women seem to get top management jobs.

The first person might argue like this:

1. If male candidates for management jobs were given preference over female candidates, then there would be more males than females in management jobs.

2. Male candidates for management jobs are given preference over female candidates.

Therefore, there are more males than females in management jobs.

The second person might argue like this:

1. If men strove to succeed in business more than women, then there would be more men than women in management jobs.

2. Men do strive to succeed in business more than women.

Therefore, there are more men than women in management jobs.

Here, two people agree about the conclusion of their arguments (there is merely a slight difference in terminology). The shared conclusion expresses an undisputed fact. They disagree over its cause. Unlike the first example above (about phalaropes) the “point” of these arguments is not primarily to persuade (i.e. to provide a warrant for believing an argument’s conclusion). Rather, their purpose is to make premises explicit. The premises are these individuals’ respective reasons for a belief they happen to share.

Of course, one or other of these disputants might have the eventual aim of persuading the other person of their particular reasons. But even then, it won’t be the conclusion of either argument that will eventually call for justification — it’s one or other set of premises. These premises work a bit like rival scientific hypotheses — according to one of them, there’s a “glass ceiling” that keeps women down; according to the other, men and women tend to have different goals in life.

So the main purpose of these arguments is to make reasons (i.e. hypotheses) explicit, and justification doesn’t really come into it at all. If there is a question of justification, it is “further business”, something to be attended to after the primary business of making reasons explicit has been completed. And furthermore, the justification we are thinking of here doesn’t follow the pattern we saw in our first example of argument as persuasion. A hypothesis is not normally given support by featuring as the conclusion of an argument to persuade. Instead, we evaluate hypotheses by comparing them to their rivals. To be persuaded that a hypothesis is true, we usually expect it to exhibit various “virtues” that shine less brightly in its rivals (its relative simplicity, its meshing smoothly with what we already believe, and so on).

I hope these examples illustrate that an argument can serve at least two separate purposes: it can be used to persuade someone of the truth of its conclusion, or it can be used to make a person’s reasons for belief explicit. I think the second purpose of argument is often neglected.

Suppose, then, that we resolve not to lose sight of the fact the “point” in arguing is often explication rather than persuasion. How can that help us to solve problems in philosophy? To answer that question, let’s take a problem in philosophy and solve it.


3. Mistakes in Reasoning

A valid argument whose premises are true (and therefore, whose conclusion is true as well) is called a sound argument. Sound arguments exemplify correct ways of thinking, because when we “think through” them, our minds move from true beliefs to further true beliefs. But human beings make mistakes. Sometimes, the beliefs we start out with are false, which is often just a matter of bad luck. But when the pattern of our reasoning itself is faulty, we commit an error called a fallacy. Some fallacies are the result of wrongly taking an argument as valid when in fact it is invalid. That sort of mistake is called a “formal” fallacy, because it involves an argument whose shape or “form” is wrong.

For example, many arguments have the following form:

1. If P then Q

2. P

Therefore, Q

This valid argument form is so common it has its own Latin name: modus ponens. (Don’t ask me what it means!) We can be sure that an argument is valid if it exemplifies this valid argument form. (We have already met a couple of examples above.) But now consider the following argument form:

1. If P then Q

2. Q

Therefore, P

This is not a valid argument form, because it is possible for the premises (1 and 2) to be true, yet for the conclusion to be false. Here is an example (for added effect, utter the following words on a Sunday):

1. If today is Saturday, then this is the weekend.

2. This is the weekend.

Therefore, today is Saturday.

This sort of formal fallacy is so common that it too has its own technical name: “affirming the consequent” . (The phase that appears after the word ‘then’ in premise 1 is called the “consequent” , and premise 2 “affirms” it.)

Every invalid argument form has its corresponding formal fallacy, so such mistakes fall into an indefinitely large (and mostly unremarkable) collection. But not all fallacies are “formal”. That is, not all of them are committed by taking an invalid argument to be valid. There is also a motley collection of informal fallacies, which tend to be more interesting philosophically. One or two of them are fascinatingly insidious. The most problematic sort of informal fallacy is called “begging the question”.


4. Begging the Question

Most television interviewers don’t know it yet, but “begging the question” is not the same thing as saying something that calls for further probing. To logicians and philosophers, it’s the mistake of “assuming what you are setting out to prove” , or in other words, “arguing in a circle” . If a circular argument is fully written out in detail, the conclusion appears (often in cleverly disguised form) as one of the premises.

For example, consider the following argument:

1. The Bible says that God exists.

2. The Bible is the word of God, so what it says must be true.

Therefore, God exists.

Like most real-life arguments, this one isn’t quite complete. To understand it as anything like a valid argument, we must take premise 2 as having a rather special meaning. In particular, what could it mean to say that “The Bible is the word of God”? The argument would be silly (and entirely unconvincing) unless it meant something like “God’s (genuine) authority underwrites whatever the Bible says (because He exists)”.

The trouble is, once premise 2 is spelled out like this, we see that it asserts (among other things) the very thing we are supposed to arrive at when we reach the conclusion. But then it wasn’t the validity of the argument that “did the work” here, so much as a clever “sneaking in” of the conclusion into one of the premises. The rest of the argument seems entirely superfluous.

The historical origins of this expression are obscure, but here’s a way of remembering that this clever sort of “sneaking in” is called “begging the question”: one of the premises borrows (or “begs”) an assumption it isn’t entitled to (i.e. the very “question” at issue).


5. What’s Wrong with Begging the Question?

One of the more remarkable things about the fallacy of “begging the question” is that everyone seems to think there’s something wrong with it, yet everyone seems to find it rather hard to say exactly what’s wrong with it. Consider the following example:

1. Today is Tuesday.

Therefore, today is Tuesday.

This is a valid argument, because if the premise were true, then the conclusion would have to be true as well. But it’s very hard to resist the feeling that it’s not doing something it’s supposed to do. What is it failing to do?

The most obvious answer is that a question-begging argument fails to provide a reason for believing the conclusion. But this can mean more than one thing, depending on whether we take the purpose of the argument to be persuasion or explication. Suppose we assume that the “point” of such an argument is to persuade someone of the conclusion. That can only work if the person we are trying to persuade already believes the premise(s). In the case of a question-begging argument, the premises include the conclusion. So a question-begging argument could only persuade a person of something he already believes. So it’s pointless.

This is the standard answer to the question why begging the question is a mistake: it’s pointless or redundant. But it seems to me that this standard answer is unsatisfactory. All we’ve done so far is describe a personal failing on the part of the person proposing the argument, rather than a real shortcoming in the argument itself. The person offering the argument doesn’t seem to see that the argument is redundant. In other words, what’s wrong is not the argument itself, but rather his understanding of the discursive situation. Suppose the other person does believe that today is Tuesday. What better reason could he possibly have for thinking that today is Tuesday than that he already believes it? To already believe something is not a bad reason for believing it — on the contrary, it’s the very best reason a person can possibly have!

The standard answer depends on the assumption that the purpose of an argument is to persuade someone of its conclusion. But now suppose, instead, that the purpose of this argument is explication. Then, I think, we suddenly see what is wrong with the question-begging argument above. It fails to provide a further reason for believing the conclusion, beyond merely re-stating the conclusion. In other words, it fails to come up with premises that are any more explicit than the conclusion itself.

Up to the last paragraph, nothing I have said is controversial. But this is philosophy, so I want to stick my neck out. I would like to claim that there is nothing wrong with begging the question as long as the purpose of the argument is persuasion. But when the purpose of an argument is explication, every question-begging argument is a failure. Only in the context of explication should we regard begging the question as a genuine fallacy, in other words, as a mistake in reasoning.

If there really is nothing wrong with begging the question in certain contexts, I should be able to provide a few examples of situations in which begging the question is innocuous. Here goes.

Suppose you are trying to persuade someone of something he believes “on and off” because he has a very bad memory. He has written down something he believes on a piece of paper, but he has forgotten that he believes it. You persuade him by simply reminding him of what he already believes. You go through the argument as follows. As you utter the premise, you hold up the piece of paper in his handwriting (which he recognises). Then you utter the (identical) conclusion, this time nodding suggestively to make him realise that he is supposed to agree with it. We might think of this simple reminder as the trivial case of argument. Trivial though it may be, it is perfectly valid.

The example of begging the question I have just given you is rather unusual in that it’s so obvious. Most cases of begging the question are much less obvious because the conclusion occurs as a premise in somewhat disguised form. For example:

1. Males predominate over females in management jobs.

Therefore, there are more men than women in management jobs.

The conclusion and premise use different words, but if all we mean by ‘males’ here is “men” , and by ‘females’ “women” , then the conclusion just re-states the premise. That’s all the earlier “today is Tuesday” example did, of course, but this is a slightly less clear example of begging the question. You can see where we’re headed: keep this up, and we’ll eventually reach very sneaky, disguised versions of the conclusion hiding in premises that use very different words. According to the standard answer to the question what’s wrong with begging the question, what’s wrong with all of them is that they’re redundant. But I would say the fault lies with the person who presents such an argument, rather than the argument itself. If he disguises his conclusion and hides it away somewhere in the premises, he’s being sneaky. An honest arguer should be upfront and open. He should be explicit about the reasons he has for believing the conclusion. There’s nothing logically wrong with the argument he presents, but there is something rhetorically wrong with it, if the person who hears it is looking for more explicit reasons for believing the conclusion than the reasons he already has.


[Note: Re-reading this a few years after putting it online, the final few paragraophs struck me as incoherent. I have re-written a couple of paragraphs in the section below. – Jeremy, 2012]


6. Radical Skepticism

Let’s apply this idea to an old problem in philosophy: that of radical skepticism. Philosophers have found it remarkably difficult to come up with reasons for thinking that the familiar world that lies “outside” our heads is as we all naturally assume it is, that is, as containing tables, chairs, other animals, plants, etc. The apparent absence of such reasons gives rise to a weird philosophical sort of “worry”: does the outside world exist at all? Or is it all just my very coherent dream? Of course, no philosopher really thinks that the outside world doesn’t exist. It’s just rather surprising that no one seems to be able to come up with a good, easy-to-understand reason for thinking that it does.

Descartes gave this idea vivid expression in his Meditations. In this hugely influential work, Descartes finds himself apparently sitting by the fire in his dressing gown. Is he actually sitting by the fire, or is he merely dreaming it? He seems to be having all of the experiences we normally associate with sitting by the fire, but since he would have the same experiences if he were merely dreaming it, there doesn’t seem to be any way of telling one way or the other.

In the middle of the twentieth century, the American philosopher WVO Quine suggested a rather curious approach to this problem. It goes like this. Radical skeptical doubts (i.e. the extreme sort of doubt we have just been considering) are only possible if we assume quite a lot about the outside world. These assumptions are then used to show, apparently, that we haven’t the faintest reason to think the outside world exists. This form of argument starts off by assuming something, then it arrives at something absurd, and it ends up going back to reject the initial assumption that led to the absurdity. In general, there’s nothing wrong with that form of argument, although the specific details of any such argument might be mistaken. This method is called reductio ad absurdum, and as a general strategy it is accepted by everyone. (Although any particular example of it might contain errors.)

Quine’s rejection of radical skepticism goes like this: if the skeptic is allowed to assume quite a lot about the outside world to reach his conclusion, then so too are the rest of us. At the very least, we may assume that outside world exists.

Against Quine, the skeptic is now inclined to say that while he (the skeptic) is using those assumptions as part of a reductio ad absurdum, the non-skeptic is using it as part of a question-begging argument, which is therefore fallacious.

This is where we can step in with our newly-acquired knowledge of “what’s wrong with begging the question”. It seems to me that we would only beg the question in a malign or unacceptable way if we were trying to make our reasons for thinking the outside world exists more explicit, and failing to do anything more than simply re-asserting our assumption that it exists by using it as a premise in a deductive argument whose conclusion is the same assumption. But a decent response to the skeptic goes much further than that: it makes explicit the mistaken epistemological theory that gives rise to radical skepticism. It rejects that theory and presents a better alternative. It involves weighing rival hypotheses rather than presenting a valid deductive argument.

The usual accusation of begging the question is prompted by the thought that it is unacceptable to use a single claim both as a premise and as the conclusion of an argument. But I think there’s nothing malign about that sort of begging the question. If our hearer already has a reason, our work here is done.

We do not need to persuade anyone of the existence of the outside world. Why? Because they believe it already, unless they are mad. Radical skepticism is a sort of “academic” madness in which a particular theory of knowledge is given more credence than common sense. That theory of knowledge is “foundationalism” , and it says that everything we know about the outside world is based on (i.e. inferred from) the nature of our conscious experiences and logic. These experiences form a sort of “foundation” upon which all of our knowledge of the outside world rests. It is a long story for another day, but this theory is profoundly mistaken. None of us can successfully call all of our knowledge of the world into doubt at the same time. The skeptic may think he is doing that, but in fact he is fooling himself. So we may as well tell him to get lost. Perhaps in getting lost he might gain his bearings anew.