The position of what’s sometimes called semantic realism is that every (grammatically-acceptable) statement (or proposition) is bivalent (i.e., it’s determinately true or false); as well as being evidence-transcendent (i.e., it’s true or false independently of our means of establishing its truth-value).
Thus if we take any given p, we can state this:
Proposition p is determinately true (or false) regardless of any proof, evidence, experimental data, etc. we may (or may not) have for it.
This immediately elicits two questions:
1) Can a statement (or proposition) be determinately true (or false) regardless of whether we know it to be true (or false)?
2) Can a statement be true (or false) regardless of how we can show it to be true (or false)?
Despite those two questions, even if any given proposition p is determinately true (or false) regardless… so what? That supposedly determinate truth-value doesn’t seem to have any epistemic or metaphysical point. What I mean by that is if we can’t establish a procedure for determining p’s truth-value, then what purpose does the locution “Proposition p is determinately true or false” serve? That realist truth is effectively a “an idle wheel in the mechanism” that doesn’t have a function (to use a phrase from Wittgenstein).
So now let’s put some flesh on this so-far rather abstract problem.
“If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.”
Admittedly, it doesn’t really help matters that Russell gave us a silly (or simply humorous) example of a flying teapot between Earth and Mars. (Any other example/statement can do the same job just as well.) In any case, this is the central proposition in the quote above:
Between Earth and Mars there is a china teapot which is revolving about the sun in an elliptical orbit.
Now is that statement determinately true (or false) at this moment in time?
My point here — perhaps unlike Russell’s own central point — isn’t really about the epistemic nature of any possible (or impossible) proof (or demonstration) of the truth or falsehood of that statement. After all, the semantic realist is claiming that proposition p is determinately true (or false) regardless of proof or lesser kinds of demonstration. In other words, his point isn’t about our epistemic means (or lack thereof) of demonstrating a proposition’s truth (or falsehood). And the sceptic’s position isn’t relevant here either in that — to the realist at least — even if a demonstration occurred in the future, proposition p would still be determinately true (or false) at this present moment in time.
Now at present there’s no way of determining the truth (or falsehood) of the statement “There is a teapot between Earth and Mars which is revolving about the sun in an elliptical orbit”. Still, according to the realist, the statement is either true or false — determinately and at this moment in time. And any other given p is also determinately true (or false) at this moment in time.
But what if it does indeed matter how we determine any given statement’s truth (or falsehood)?
A semantic anti-realist can settle for saying that a proposition (or statement) is truth-apt at this moment in time. However, a proposition can (or could) have its precise truth-value determined in the future and then it will “become” — simply — true. The realist, on the other hand, will counter that by arguing that proposition p is both truth-apt and true at this moment in time. (Later, the mathematician, logician, philosopher, scientist, etc. may come to determine its truth or falsity.)
To take just one often-cited example. What about the famous case of Fermat’s Last Theorem?
This is what the semantic realist will state:
Surely the proof of Fermat’s Last Theorem didn’t (as it were) bring about its truth.
(It was actually proved in 1993 by Andrew Wiles.)
The anti-realist (of which there are many kinds), on the other hand, would have said that Fermat’s Last Theorem had no truth until it was proved in 1993. Thus, to such an anti-realist, truth = proof.
The problem here is a proposition may be determinately true (or false) if it’s about a flying teapot flying around the sun. However, it may not be determinately true (or false) when it comes to an unproven mathematical statement or theorem. These two cases seem very different.
Having made all those anti-realist points above, it can still be argued that the rejection of bivalence isn’t actually a genuine rejection. That is, to argue that there’s a third truth-value (which is indeterminate) isn’t actually a rejection of a proposition’s being determinately true or false. What I mean by that is even if the truth-value of proposition p is indeterminate at this moment of time, then that simply tells us about our epistemic situation at this moment in time. In other words, even a realist can accept that any given proposition does indeed have an indeterminate truth-value for us right now. However, such a proposition is still determinately true (or false) right here and right now.