Is Fitch's Paradox fatal for verificationism, or epistemic theories of meaning generally?
For various reasons, dealt with elsewhere, philosophers have at various times felt themselves drawn to epistemic theories of truth. An epistemic theory of truth is one that defines what it is for a proposition to be true by reference to what it takes to know it to be true (the reference to knowledge here is sometimes replaced by a reference to justified belief or some other epistemic concept).
The classic example of an epistemic theory of truth comes from verificationism, the claim that a statement has meaning only if it can be verified. Since only statements that have meaning can be true or false, this makes a statement's meaning depend on the conditions for its verification. By this definition, verificationism originally only asserts a condition for meaningfulness, and its origins do lie in this so-called 'verification principle'. However it naturally leads to a full-blown account of what meaning is in terms of verification conditions. And since to give the meaning of a sentence is to give the conditions for its truth, this involves the identification of truth conditions with verification conditions.
Verificationism is subject to many criticisms, but one of the neatest comes from Frederic Fitch, and goes by the name of Fitch's Paradox. A full presentation can be found in the Stanford Encyclopaedia of Philosophy, but for present purposes we can phrase it as an argument that if all truths are knowable, then all truths are actually known - an absurd result that we can and must avoid by denying that all truths are knowable. The argument runs thus:
- All truths are knowable
- No one can know that a proposition P is both true and not known to be true
- Therefore it cannot be true that a proposition P is both true and not known to be true
The second premise of this argument is obviously true because if we know that P is true then it is known to be true - by us. The conclusion follows because if it were true that P was both true and not known to be true, it would thus be a counterexample to the claim that all truths are knowable, since we have just seen that this conjunctive truth cannot be knowable.
This is not the sort of truth that the original verificationists meant to rule out. They had in their sights opaque metaphysical claims such as the British idealist F.H. Bradley's notorious pronouncement that “the Absolute enters into, but is itself incapable of, evolution and progress”. (This sentence was cited as a classic example of grandiose metaphysical nonsense by the logical positivist A.J. Ayer, who claimed to take it “at random” from Bradley's Apperance and Reality - managing to sound spectacularly dismissive in two words.) Such claims were characteristically devoid of any implications for the down-to-earth realm of perceptual experience, and could not be explained in terms of this to those puzzled by what they meant. By contrast, if the proposition P referred to in the conjunctive proposition above is clear - if, for example, it is simply that a tree has fallen in an uninhabited forest - then that conjunctive proposition is also clear, and readily explained in terms of things we understand from experience, such as falling trees and the absence of knowledge.
This suggests that if the verification principle was intended to dismiss the meaningfulness of flighty metaphysical claims unconnected to experience, it was phrased too strongly, as it also rules out clearly meaningful propositions that are made up of concepts we understand from experience. And in fact this has always been a criticism of verificationism. The claim that a proposition P is both true and not known to be true is not the only one ruled out. Others may include claims about past events which have left no trace and about the internal mental states of other people, which plausibly cannot be verified. A surer example comes from Isaiah Berlin: the claim that if I look up, I will see a blue patch and if I don’t, I won’t cannot be verified without straddling two positions simultaneously, which is logically impossible. This is particularly embarassing for verificationists, who typically offer a 'phenomenalist' analysis of statements about material objects, which involves similar conjunctions of counterfactual claims about the experiences we would have of them in different situations.
The diagnosis that the verification principle is stronger than it needs to be to serve verificationists' anti-metaphyical intentions is made yet more plausible by the fact that they rarely offered direct arguments for it; more often, they were searching for a way to capture their sense that claims like Bradley's were meaningless, and latched onto the verification principle as a plausible candidate for this. Edward Craig observes that "one finds in the literature of Logical Positivism no great wealth of argument in favour of verificationism, for in the heyday of the Vienna Circle it seems to have been felt sufficiently persuasive just to postulate the Verification Principle and display its anti-metaphysical consequences".
This means that if we can find an epistemic theory of truth and meaning that rules out only clearly meaningless claims, it will have all the advantages of verificationism with none of its disadvantages, vulnerability to Fitch's Paradox included. Intuitively, it seems that we should be able to devise some such theory, because it is perfectly coherent to say that meaningful sentences all have some epistemic property while denying that they are all actually known to be true.
As it happens, it is relatively easy to modify verificationism to avoid Fitch's Paradox. Consider that this Paradox exploits the fact that our coming to know of P's unknownness makes it cease to hold. The obvious solution is to drop the requirement - which may not even have been intended by the original verificationists - that we can know that statements are true while they still hold. Suppose it is true on the first day of 2011 that a particular tree has toppled and that nobody knows that it has done so. We could at some later point come to know that this was true without making it cease to be true - the proposition that we will have stopped being true is the quite distinct one that this tree has toppled and that nobody knows that it has done so now.
There are other epistemic theories of truth also avoid Fitch's Paradox, and move yet further from verificationism. The simplest permutations replace the reference to knowability above with one to justifiability or another epistemic status. Others require only that meaningful sentences be verifiable or justifiable by some actual or hypothetical 'Ideal Observer', rather than by us as we are trying to comprehend them. This Ideal Observer is supposed to be free of some of our epistemic limitations, in order to get around the problem that verificationists had with claims outside our purview, such as those about events outside our light cone. It is not easy to define precisely what epistemic limitations it should be free of, as if we grant it God's alleged unmediated knowledge of all truths, the theory collapses into triviality, stating only that all truths are true, and all meaningful statements are potentially true. And this particular theory faces other problems. But the point here is only that it is yet another epistemic theory of truth unaffected by Fitch's Paradox.
So we have seen that while Fitch's Paradox afflicts verificationism as traditionally understood, the verificationist can escape it with a relatively simple modification of her position, and it is not fatal for epistemic theories of truth and meaning generally. The question of whether these theories are correct, and whether they correctly capture the widespread intuition that some connection to the world of experience is required for meaningfulness, remains open.
 Edward Craig, 'Meaning, Use and Privacy' in Mind (No. 91, October 1982), p541
 The demand that all meaningful statements are potentially true would rule out statements such as 'Cairo both has Pyramids and does not have Pyramids', as this cannot be true. In one sense this statement is nonsensical, but we presumably want to allow that we can in some sense understand it. In this case, the epistemic theory of meaning must impose its requirement only on atomic propositions, such as the conjuncts and disjuncts into which statements like the above can be analysed. In this case, 'Cairo both has Pyramids and does not have Pyramids' can be analysed as the conjunction of the two atomic propositions 'Cairo has Pyramids' and 'Cairo does not have Pyramids', each of which is indeed potentially true.