What if truth was merely a linguistic property? Certainly it seems like this might be the case, after all, the only things it makes sense to predicate truth of are sentences in some language. Of course this doesn’t explain what truth is, it simply puts us on the path to an answer; we still have to say why one sentence is true while another is false.
The first idea that springs into everyone’s mind is to appeal to accuracy. That is we want to say that a sentence is true if it accurately portrays its objects (without error). But then we must define what accuracy consists of, and we might be tempted to think that it is some kind of correspondence, between the way things actually are and the propositions expressed by the sentence. This is essentially the correspondence theory of truth, and its problems are well known, specifically it is hard to say what certain true statements, like true mathematical statements, could correspond to.
Another possibility is to define accuracy in terms of other people, specifically to claim that an accurate sentence is one that all people would agree with (or a majority of people). This certainly has some appeal; we no longer have to worry about how to define the connection between true statements and how the world really is, as we assume that if everyone agrees to the statement there must be something that causes this agreement. And such a definition is not inconsistent, but unfortunately it doesn’t capture what we mean by truth either. I think we can all agree that there are many true statements that are true independently of what people believe (for example: “the earth orbits the sun”). A definition that relies exclusively on people cannot capture this property of truth.
Let me propose a third possibility then, that what we mean when we say that a sentence is true is that, if the sentence is correctly understood, everything that the listener has experienced, and can in principle experience, will agree with it. This definition of course leans upon our ability to understand the meaning of sentences. Although defining what meaning is, and how we come to grasp it, may be problematic I do not see any reason to think that understanding this ability will rely on truth (and thus this definition isn’t circular). This definition certainly seems acceptable for the “normal” cases (although most theories of truth are). For example, if I claim that “‘some cats are white’ is true” then I am asserting that one could possibly encounter a white cat. If one couldn’t encounter a white cat then that would mean that there were no white cats, which would mean that I was incorrect in asserting “‘some cats are white’ is true”, meaning that the statement is false, which would really be the case. Now we might worry that this definition relies too heavily on our senses, and that “truth” might then differ for a blind man. This is really not the case, because the experiences we are referring to are experiences possible in principle, meaning that the blind man could use instruments, or even a reliable reporter of events, to experience the existence of a white cat; he doesn’t have to see it.
So let me turn to the cases that are typically problematic, specifically the cases of mathematical truths and recursive truth claims (i.e. sentences of the form “‘X is true’ is true”). To determine how this definition of truth handles cases of mathematical truth we must explicate how one can experience a mathematical statement. I am not a mathematical realist; I don’t think that formula and numbers are the kinds of things that can be experienced. I do think, however, that we can experience the proof of a statement in mathematics (for example, by seeing that proof written down, or by thinking it up). Thus, if X is some mathematical assertion, I think that to say “X is true” is really to mean “‘X can be proven’ is true”. And this statement is not problematic, because it either is or is not the case that we can experience a valid proof of X from some axiom set, in some logical system (I assume that those constraints are determined by context). Finally then we come to the case of recursive truth claims. To see how the definition of truth presented here handles these we must unpack them. “‘X is true’ is true” thus becomes: “In principle we can experience that ‘X is true’”, which becomes “In principle we can experience that ‘In principle we can experience X’”. This means that the initial claim is true if we can experience experiencing X, which is only possible if we can experience X. And thus the statement means the same thing as “X is true”, as it should. So neither mathematical truth nor recursive truth claims give this definition of truth problems, which is surely to its credit.
To conclude I would like to make two observations about this definition of truth. The first is that although this definition has some similarities to verificationism it is not a version of that school of thought because it deals with what can in principle be experienced versus what can actually be experienced, which makes a world of difference (for example, a verificationist would be unable to make claims about things that they did not have the instruments to detect). The second is that given this definition of truth there are, strictly speaking, some statements that are neither true nor false. Specifically, statements about objects that are, even in principle, unobservable have this property (for example “undetectable pink unicorns exist” is neither true nor false). However, because the objects these sentences are about are undetectable they must also be unable to have a causal effect on the world (see here), and thus our inability to speak about them is not entirely unexpected, since in many ways such objects are nonsense, and a sentence that can’t be understood isn’t true or false either.