Thursday, March 3, 2011

A Refutation of the Coherence Theory of Truth

Davidson famously made a supposed knock-down argument against the correspondence theory of truth. It came to be known as the sling-shot argument because of its "disarming simplicity". Without getting into the details of that argument, I want to propose a similarly simple, and disarming, argument against the coherence theory of truth. I take it that my argument is more swiftly disarming than Davidson's, so call it the "Golden Gun Argument".

The coherence theory of truth amounts to the claim that some proposition p is true if and only if p coheres (fits with, etc.) the rest of one's beliefs, which themselves also must be mutually coherent. Depending on the theory, each belief must either be entailed by, or more modestly compatible with, the rest of one's beliefs. I want to claim that this theory is itself incoherent, and I employ two distinct arguments to demonstrate this. The first of these arguments concludes that the coherence theory ought not be believed, in an epistemically normative sense. The second argument, however, leads to a much stronger conclusion: That the coherence theory is necessarily false. Because I see the latter argument as the stronger, we will call this one the Golden Gun Argument. Accordingly, we will call the former argument the Target Practice Argument.


1. Target Practice

For this first argument, as I said, I will try to show that the coherence theory ought not be believed. That is, it would not be epistemically virtuous, or responsible, to believe it. The argument will hinge on the following normative claim:

(N) One ought not believe some universally quantified proposition p true if p could trivially fail to obtain.

Obviously, the claim of N needs some clarifying. What I mean by "trivially fail to obtain" is something like the following: That some not-unexpected circumstantial fact, or occurrence, could render your belief that p false. Because N is largely intuitive, and therefore difficult to give a precise explanation of, I think we should consider an example. Say I believe the universal claim "All citizens of nation X will continue to stand within the borders of nation X". Now, even if I have good reason to believe citizens of X are fervent patriots, have no desire to go elsewhere, and are generally apathetic about moving their bodies, I still should not believe the universal claim. Why? Because a quite trivial, easily actualized occurrence could render it false: One citizen stepping outside the borders of X. So although the evidence may be strong that the citizens generally love their country, hate moving, and etc., the fact that it wouldn't be immensely unexpected for just one citizen to step out, and indeed easy for them to do so, renders my belief irresponsible in some way. I hope the intuition behind N is now sufficiently clear.

Here, then, is the argument:

P1. The coherence theory is a universal claim concerning the nature of truth.
P2. Any universal claim that could trivially fail to obtain should not be believed (by N).
P3. The coherence theory could trivially fail to obtain.
Conclusion: Therefore, the coherence theory should not be believed.

Now we may address the heart of the argument, which is found in (P3). The reason that the coherence theory could trivially fail to obtain is easy to see: If it is true, then the coherence theory itself by definition needs to fit in (cohere, be entailed by, etc.) the rest of our beliefs. But what guarantees that it will? Sure, under some people's system of beliefs the coherence theory may cohere with the rest, but surely not all people's. It seems highly plausible that there could be multiple, and equally "coherent" and "justified", systems of beliefs that themselves conflicted with the coherence theory. But, if such systems of beliefs did conflict with the coherence theory, then the coherence theory would turn out false under those systems. Thus it seems that the coherence theory has the capacity to fail its own criterion for truth. Indeed, a quite trivial and easily actualizable fact could render it false: A coherent, justified system of beliefs being held that itself did not cohere with the coherence theory of truth.

So much for Target Practice.


2. The Golden Gun Argument

This argument will depend heavily upon the modal notions of necessity and possibility. In particular, it depends on the S5 axiom of modal logic: That is, if possibly necessarily p, then necessarily p. I will , however, be using the logically equivalent axiom: If possibly necessarily ~p, then necessarily ~p.

Here's the argument:

P1. The coherence theory is possibly self-refuting.
P2. For any x, if x is self-refuting then x is necessarily false.
P3. Therefore, the coherence theory is possibly necessarily false.
Conclusion: Therefore, the coherence theory is necessarily false.

(P1) is supported by the fact that, as mentioned before, if the coherence theory is correct then under certain systems of beliefs it will be self-refuting. That is, under those systems the following conditional will obtain: 'If the coherence theory of truth is true, then the coherence theory of truth is false'. Thus it is possibly self-refuting. (P2) is self-evident (i.e., not only are statements like "This is not a sentence" self-refuting, but they are also, ipso facto, necessarily false). (P3) follows from (P1) and (P2), and, of course, the conclusion follows by an application of S5.

If this reasoning is correct, then the coherence theory is in big trouble. Not only is it false, but it is impossible that it be true (under suitable assumptions). Thus the Golden Gun Argument achieves a head-shot.



NOTE: It's worth mentioning, I think, that the coherence theory of truth implies the possibility of the correspondence theory of truth being true (if it happened to cohere with a mutually fitted web of belief). Yet, the correspondence theory of truth implies, at most, that the coherence theory of truth be justified, or coherent, thus retaining its own integrity. Correspondence appears to come out on top.