Supposing for the Sake of Argument

James Cargile

It is very common for elementary texts to explain the idea of validity as follows: "An argument is valid, if supposing the premises to be true, the conclusion must necessarily be true also." Or again, "On the assumption that the premises are true, the conclusion must necessarily be true also." Or again, "On the assumption that the premises are true, it is impossible for the conclusion to be false."

I have asked large classes, confronted with such definitions this question: "What if we are asking whether an argument is valid and we neglect to suppose or assume that the premises are true?" The result is always general confusion. A substantial number (10%) will say that in that case the argument isn't valid. A sharper and larger number (half or more) will say that in that case we can't determine whether the argument is valid. This group will be ready for the further question "What if some of us make the assumption and some don't?" Those who do can proceed, those who don't can't.

My view is that the proper antidote for this confusion is the warning that 'supposing' or 'assuming' for the sake of argument is not a kind of 'supposing.' It adds nothing as to validity to the enquiry beyond warning against mistaking the enquiry for a case which includes 'supposing' or 'assuming' that the premises are true. That the effect of "suppose for the sake of argument, that p-then it is impossible that it be false that q" should be that the student thinks a kind of supposition is involved is a reason for avoiding the locution-or else introducing it in the style advocated here.

Supposing or assuming are types of belief, of a kind held uncritically, whether appropriately or not. This I concede for the sake of argument. Such a concession is made to keep an argument moving. Concessions for the sake of argument need not involve belief at all. In order to keep political negotiations going, you may concede terrority, actually giving up sovereignty over some region, to keep others engaged in bargaining. Conceding, or granting, for the sake of argument, are kinds of conceding or granting. You give up, at least for a time, your right to argue against p when you grant it for the sake of argument. Though this acceptance of p does not require believing that p, it is acceptance. Formally accepting someone's claim in a discussion, for the sake of discussion, is a kind of accepting, even without belief.

By contrast, supposing or assuming for the sake of argument are not kinds of supposing or assuming. A remark such as "He is in a blue suit and a matching blue mood" involves a sort of word play. The same sort occurs in "What a rational man would barely be willing to suppose for the sake of argument, Sam will just cheerfully suppose." That reads better with "assume" but the point is the same-the same word is marking quite distinct things.

What then, is the propositional attitude, of supposing that p for the sake of argument? It is a relation between parties to a discussion or argument and a proposition that p, when they are going to enquire as to what follows from p, without thereby undertaking any commitment on the question whether it is the case that p. That is, to agree that p is supposed or assumed for the sake of argument is to guard against the possibility of misunderstanding arising from a mutual enquiry as to the consequences of p. Such enquiry may give the impression that it is being supposed or assumed that p. The qualifier "for the sake of argument" makes clear that the enquiry is no indication at all that p is supposed or assumed by any of the parties. Perhaps some of them do suppose it. But the enquiry is not based on any such assumption. It is merely the enquiry as to what follows from p, which requires no departure from neutrality or disbelief with respect to p

It is possible to suppose, in a belief form, for the sake of argument. That is, to keep the argument going, you may make the concession of trying to belief-suppose that p, and perhaps succeed in supposing in this way, and for the sake of argument.

This is just one reason why it would be incorrect to claim that "supposing for the sake of argument" never implies anything more than a mutual recognition of non-assertion, and preparation for enquiry about the consequences of a proposition. The point argued here is not a general claim about the phrase, but about one central use of it

Another question could be raised about the mutuality. Supposing for the sake of argument is a conversational mode of non-commital proposition introduction which does not seem natural for thinking to oneself. But it is easy enough to say to oneself "Suppose, for the sake of argument..." It might seem that the point of doing this could not be to remind yourself that you aren't really supposing (believing). It is not important to the present point to determine what point the private recital of the words might have. It is enough to observe that there is the function of considering a proposition while warning it is not being advanced, whether or not this can be of use privately.

The most serious problem for my view concerns the unasserted proposition. For the conceptualists, a proposition is essentially something proposed, either to oneself in a mental operation, or to others, where the criterion of sincerity is that the proposal represents the making public of a private mental operation of judging. For these thinkers, to consider an unasserted proposition is not, strictly speaking, possible. What is considered in that case is a supposition. Supposing is a way of introducing a thing which can also be introduced in a different way by proposing. The proposition is an assertion, and an "unasserted assertion" is a confused terminology for a "supposition."

When I speak of "considering the proposition that p to determine what are its consequences," the phrase "The proposition" is important. To say "consider that p" suggests rather "consider the fact that p." It seems that we have three things (to consider?): that p (the fact), the proposition that p, and the supposition that p. The first is what determines the truth of the position that p. The second is a taking of that position, and the third a considering of that position. On this line, to consider the unasserted position that p requires the supposition, even if only for the sake of argument, or discussion. The assertion comes into existence with the act of assertion, and the proposition, which is the same, with the act of propounding or proposing. And the supposition begins with the act of supposing.

As a platonist, I hold that the proposition is eternal, does not come into being, and is independent of our minds. (The topic of God's mind will not be discussed here.) That two and two makes four was always true, before any person asserted or proposed or supposed it. (That the same goes for the proposition that I just felt a twinge in my left shin will not be universally accepted, but that cannot be discussed here.) The linguistic term "proposition" has no doubt an etymology that is at odds with this picture, but we should transcend our roots.

An opponent might suggest that the ontological question could be avoided here and the focus be simply on whether in considering a proposition one is not thereby supposing it, if only for the sakeof argument.

This is a generous "proposition" which might leave us with nothing but a verbal dispute. I hold that someone may recognize that the proposition that q follows from the proposition that p, without having to reflect on the matter. It may just occur to someone that there is that entailment. But if it is said that when one has to consider the matter, that consideration of the proposition just is supposing it (for the sake of argument), then how could I object to that? It could be added that this sort of supposing is not belief-supposing.

If it is merely a matter of using the word "suppose" in place of some uses of "consider" then my claim that supposing for the sake of argument is not a kind of supposing would seem to translate into the claim that it is not a kind of considering. But my positive account is that supposing that p for the sake of argument is considering the proposition that p to see what follows from it, while stressing that no one need be committed to the proposition. Thus my account conflicts with this generous proposal to be casual about the rules for "suppose."

"Suppose that Smith is guilty" and "Consider that Smith is guilty" differ in meaning. The latter standardly asks that you pay attention to the fact that Smith is guilty while the former does not. "Consider the proposition that Smith is guilty" differs from "Suppose the proposition that Smith is guilty" in that the latter doesn't have a good standard interpretation. The former could also be ambiguous between "Consider so-and-so's proposition and "Consider proposing that."

Thus, supposing that p (for sake of argument or not) is not considering that p. However, if you wish to say it is considering the proposition that p (while stressing, etc.) then I will give up, whether or not I should, for the sake of discussion. But this concession is made in the hope that you will consider adopting the view that this considering or supposing does not bring together an object of thought or discussion in the way that proper supposing or proposing has been supposed by some to do. Recognizing that the proposition that p has the consequence that q may require some reflection, or considering. But this is not a specific kind of mental activity.

One last candidate for a specific mode of introduction is imagining. Imagining that p may indeed be helpful in determining what follows from it. And some philosophers have taken imagining as a basis of judging or inner assertion. But one can unproblematically consider figures which cannot be imagined by any person, as counter-examples to some thesis. One cannot unproblematically imagine such figures. To consider them, or suppose them for the sake of argument need not involve such a specific activity as imagining. Such supposing is merely non-committal introduction into a discussion, and what is introduced is not constituted or held together by being introduced.