Some of us of a realist persuasion hold that at least some truths have need of worldly correlates that 'make them true.' This notion that (some) truths need truthmakers is a variation on the ancient theme that truth implies a correspondence of what-is said or what-is-thought with what-is. You all know the passages in Aristotle where this theme is sounded.
Example. Having just finished my drink, the thought expressed by an assertive utterance of 'My glass is empty' is true. But the thought is not just true; it is true because of the way things are 'outside' my mind. The glass (in reality) is (in reality) empty. So the realist says something like this: the thought (proposition, judgmental content, etc.) is true in virtue of the obtaining of a truthmaking state of affairs or fact. The thought is true because the fact obtains or exists, where 'because' does not have a causal sense but expresses the asymmetrical relation of truthmaking. The fact is the ontological ground (not the cause) of the thought's being true.
One might wonder whether this realist theory of truth leads to an infinite regress, and if it does, whether the regress is vicious. Some cryptic remarks in Gottlob Frege's seminal article, "The Thought: A Logical Inquiry," suggest a regress argument against the correspondence theory of truth.
For Frege, a thought (Gedanke) or proposition is the sense (Sinn) of a context-free declarative sentence. 'Snow is white' and its German translation Schnee ist weiss are examples of context-free declarative sentences. 'Context-free' means that all indexical elements have been extruded including verb tenses. When we say that a sentence such as 'Snow is white' is true, what we are really saying is that the sense of this sentence is true. The primary truth-vehicles are propositions, sentences being truth-bearers only insofar as they express true propositions.
Now could the being-true of a sentential sense consist in its correspondence to something else? Frege rejects this notion: "In any case, being true does not consist in the correspondence of this sense with something else, for otherwise the question of truth would reiterate itself to infinity." (Philosophical Logic, ed. Strawson, p. 19) A little earlier, Frege writes,
For what would we then have to do to decide whether something were true? We should have to enquire whether it were true that an idea and a reality, perhaps, corresponded in the laid-down respect. And then we should be confronted by a question of the same kind and the game could begin again. So the attempt to explain truth as correspondence collapses. And every other attempt to define truth collapses too. (Ibid.)
What exactly is Frege's argument here? We begin by noting that
1. Necessarily, for any proposition p, it is true that p iff p.
This equivalence, which I hope nobody will deny, gives rise to an infinite regress, call it the truth regress. For from (1) we can infer that if snow is white, then it is true that snow is white, and
iterating the operation, if it is true that snow is white, then it is true that it is true that snow is white, and so on without end. This is an infinite regress all right, but it is obviously benign. For if
we establish the base proposition, Snow is white, then we ipso facto establish all the iterations. Our establishing that snow is white does not depend on a prior establishing that it is true that snow is white. In general, our establishing of any proposition in the infinite series does not depend on having first established the next proposition in the series. The truth regress, though infinite, is benign.
Note that if the truth-regress were vicious, then the notion of truth itself would have been shown to be incoherent. For the truth-regress is a logical consequence of the equivalence principle (1) above, a principle that simply unpacks our understanding of 'true.' So if the truth-regress were vicious, then (1) would not be unproblematic, as it surely is.
It follows that if Frege's Regress is to amount to a valid objection to the definition of truth as correspondence, "and [to] every other attempt to define truth," then Frege's Regress must be different from the truth regress. In particular, it must be a vicious regress. Only vicious infinite regresses have the force of philosophical refutations. But then what is Frege's Regress? Consider
2. Necessarily, for any p, it is true that p iff *p* corresponds to reality.
One can think up counterexamples to (2), but the precise question before us is whether (2) issues in a vicious infinite regress. Now what would this regress (progress?) look like? Let 'T(p)' abbreviate
'it is true that p.' And let 'C*p*' abbreviate '*p* corresponds to reality.' (The asterisks function like Quine's corners.) The regress, then, looks like this:
3. p iff T(p) iff C*p* iff T(C*p*) iff C(T(C*p*)) iff T(C(T(C*p*) iff C(T(C(T(C*p*)) . . .
Is (3) a vicious regress? It would be vicious if one could establish T(p) only by first establishing C*p* and so on. But if these two terms have the same sense, in the way that the first and second terms have the same sense, then (3) will be as benign as the truth regress. Suppose that 'It is true that p' and '*p* corresponds to reality' have the same sense. Suppose in other words that the correspondence theory of truth is the theory that the sense or meaning of these distinct sentences is the same. It would then follow that to establish that it is true that p and to establish that *p* corresponds to reality would come to the same thing, whence it would follow that the regress is benign.
For the regress to be vicious, the second and third terms must differ in sense. For again, if the second and third terms do not differ in sense, then to establish one is to establish the other, and it would not be case that to establish that it is true that p one would first have to establish that *p* corresponds to reality or to some chunk of reality. But if the second and third terms do not differ in sense, then it appears that the regress doesn't get started at all. For the move from the second term to the third to be valid, the entailment must be grounded in the sense of the second term: the third term must merely unpack the sense of the second term. If, however, the two terms are not sense-connected, then no infinite regress is ignited.
My interim conclusion is that it is not at all clear that Frege's Regress is either benign, or not a regress at all, and therefore not at all clear that it constitutes a valid objection to theories of truth, in particular to the theory that truth resides in correspondence.
REFERENCE: Peter Carruthers, "Frege's Regress," Proc. Arist. Soc., vol. LXXXII, 1981/1982, pp. 17-32.
