The Minimal Principle of Contradiction

A further example to be considered is the Minimal Principle of Contradic- tion.

MPC Not every statement is true.

Thompson (1981), following Putnam (1978), argues that MPC is true and known a priori in virtue of its being a presupposition of thought and expla- nation.

Some truths of logic may be “so basic that the notion of expla- nation collapses when we try to ‘explain’ why they are true.” So suggests Putnam. As an example of such a truth, he mentions “the Minimal Principle of Contradiction (Not every statement is true).” In suggesting that the notion of explanation collapses when we try to explain why this principle is true, he says he does not mean “that there is something ‘unexplainable’ here.” The point is that “there is simply no room for an explanation of what is presupposed by every explanatory activity.” (Thompson, 1981, pp. 458–459)

Insofar as MPC can be said to be a presupposition of thought and expla- nation, it is a principle that we are bound to accept if we are to think or engage in explanatory practices at all.

Thompson invites us to consider a thought experiment: imagine trying to make meaningful utterances in a situation where you have to accept every statement as true. The idea is that such a thought experiment is self-undermining. In order to even imagine such a scenario, one must be adhering to the minimal principle of contradiction. So one can hardly use the thought experiment in a justification of MPC.

[I]n imagining the situation in question, we presuppose the very principle we are supposed to learn from the thought experiment. In order to imagine ourselves in a situation in which we reject the minimal principle of contradiction, we must take it to be true that in this situation we reject the principle and false that we accept it. But then we take for granted at the start that not every statement is true, which is just what the experience is supposed to show. This predicament is unavoidable. (Thompson, 1981, p. 460)

Thompson’s argument here is difficult to tease out. Moreover, there are a number of prima facie problems. E.g., imagination is not closed under logical consequence: just because I imagine myself in a situation where I reject MPC, it does not follow that I imagine that in that situation it is true that I reject MPC and false that I accept it. Moreover, it appears that some kind of assumption against true contradictions is being smuggled in. Even if in this imagined situation it is true that I reject MPC, why shouldn’t it also be true that I accept MPC? We are, after all, in the business of looking for some kind of warrant or justification to believe in MPC, so prejudice against contradictions surely isn’t allowed.

I would like to offer a simpler route into highlighting the curious nature of MPC. Let us recap what we are dealing with, namely, the statement:

Not every statement is true.

Ultimately I want to know if it is possible for thinkers like us to rationally doubt or reject such a principle. So, consider the question: what would it be to rationally doubt this statement? Well, it would be to seriously entertain, or to try to assert, something like the following:

It might not be true that not every statement is true.18

In rationally considering how things might be, it will be natural to consider how things would be if things were indeed that way. So, if it were not true that not every statement is true, how would things be?

If it were not true that not every statement is true, then it would be true that some statement is not true.

18

The ‘might’ here should be read as epistemic possibility. What is up for discussion is doubt, not the thought that MPC is contingent.

From it being true that some statement is not true it follows that Not every statement is true.

Note, I have not claimed here that anything is false. Simply that, in con- sidering how things would be were MPC not to be true, it would turn out that not every statement would be true, and hence that MPC would be true after all.

This is not intended to be an argument for the truth of MPC. Rather, the purpose is to highlight the relationship between MPC and rational doubt. What is it to doubt something? At the very least it will involve entertaining the thought that it might not be true.19 In entertaining that the object of doubt might not be true, one is immediately entertaining MPC. So how can one be expected to doubt MPC, if the very mechanism of doubting brings in the thought that MPC might be true? Taking a step further, to rational rejection, again, what is it to reject something? It is to affirm that it is not true.20 And of course, if something is not true, then MPC is true. So the very mechanism of rejection brings in the thought that MPC is true.

What should we make of this? I want to take this as further evidence for the existence of a genuine phenomenon, whereby there are certain logical principles that we cannot reject in our thinking. It seems that thinkers cannot rationally reject MPC. In engaging in doubt or rejection, one thereby entertains or affirms MPC.

Thompson’s main purpose is to argue that the principle can be classed as a priori, but he also draws some conclusions about thought.

We discover that we presuppose the principle of contradiction in all our thinking only by discovering our inability to think in violation of it regardless of what we are thinking about and of how we express our thought externally. (Thompson, 1981, p. 463)

This highlights an important point. Thompson takes us to be bound to think in accordance with MPC. In contrast, I want to claim that we are bound to take our thought to be right or wrong in light of MPC. I argued above that our ability to think a contradiction shows that we are able to think in violation of logical laws. Thompson claims otherwise.

When we accuse someone of illogical (and not just irrational) thought, what we mean is that the person’s efforts at thought have completely failed. His thoughts cancel each other and he has failed to think anything at all. (Thompson, 1981, p. 471)

19_{Even if more is involved, the thought is at least entertained.} 20

Rejectivists argue that acceptance and rejection are two distinct mental or speech acts, such that rejection of a proposition p is not the same thing as acceptance of its negation ¬p. However, rejection of p and acceptance of ¬p are still logically equivalent, which is all that is presently required. See Smiley (1996).

This still seems wrong. Even in the arguments I have just considered, one can certainly think that every statement is true, but on closer inspection, it will always turn out that that is false. Getting something wrong does not constitute not thinking. Rather, as I argued above, one has been able to make progress and learn something on the basis of considering the statement or thought that every statement is true (i.e. that one cannot rationally sustain a belief in such a statement).

It should be noted that Thompson and I have slightly different notions of “thinking” in mind. I have been working with a minimal notion where merely entertaining a proposition counts as thought. Thompson’s notion might be richer, requiring something more akin to imagining or picturing how things would be according to the proposition. The view that we cannot fully picture a contradictory situation might be easier to defend, however, what then are we to say about entertaining and understanding a contra- dictory proposition? If that doesn’t count as thought, albeit rather simple thought, then the notion of thought in play is too demanding.

Thompson offers a rather obscure argument to the contrary. It might seem wrong to say that with illogical thought one fails to think anything at all. One thinks a contradiction. But we can think a contradiction, think that both p and not-p, only by conforming to the principle of contradiction. Without this con- formity, we would have to think not only both p and not-p but also its negation, neither p nor not-p. With absolute noncon- formity, with strictly illogical thought, we get endless iteration of this process. We do not think merely that both, both p and not-p and neither p nor not-p, but also that neither, neither both p and not-p nor neither p nor not-p. We thus think nothing at all. If we could not contradict ourselves we could not think. We think a contradiction only when we think it as such, as thought that cancels itself. In thinking a contradiction without think- ing it as such, we fail to think anything at all—we are illogical. (Thompson, 1981, p. 471, fn. 8)

One point he might be intending to make here is that, supposing we can take contradictions to be true in thought, if the minimal principle of contradiction were not presupposed, we would have to take not only the contradiction to be true, but its negation, and so on and so forth. But this kind of result might be taken to follow from a failure of MPC in any case. If everything is true, and I think that p is true, then I must also think that ¬p is true, and so on and so forth. But that is not a problem peculiar to thinking contradictions.

The point specific to contradictions appears to be that in thinking p and ¬p, these contradictory propositions cancel each other out, hence there is no thought at all. If for every proposition p we think both p and ¬p, this would

then amount to cancelling all (propositional) thought. This cancellation view of contradictions is illustrated nicely by Strawson.21

Suppose a man sets out to walk to a certain place; but, when he gets half-way there, turns round and comes back again. This may not be pointless. He may, after all, have wanted only exer- cise. But from the point of view of a change of position, it is as if he had never set out. And so a man who contradicts himself may have succeeded in exercising his vocal chords. But from the point of view of imparting information, of communicating facts (or falsehoods) it is as if he had never opened his mouth. He utters words, but does not say anything. Or he might be com- pared with a man who makes as if to give something away and then takes it back again. He arouses expectations which he does not fulfil; and this may have been his purpose. Similarly, it may have been the purpose of a man who contradicts himself just to create puzzlement. The point is that the standard purpose of speech, the intention to communicate something, is frustrated by self-contradiction. Contradicting oneself is like writing some- thing down and then erasing it, or putting a line through it. A contradiction cancels itself and leaves nothing. (Strawson, 1952, pp. 2–3)

I turn again to my arguments of section 3.3.3. Proponents of this view of contradictions have to explain how it is that we succeed in thinking and understanding contradictions to the point that we can (a) recognize that they are contradictions, (b) claim that they are false, and (c) correct our- selves when contradictions are pointed out to us in a reasonable and rational manner.