“pis true/false in realism regardless of any conscious experience, which meanspalways has a truth-value.”

Can't
you respond to that in the following way?

Sure,
a statement is determinately true regardless of whether we know it to
be true or how we know it's true... So what? That determinate
truth-value doesn't have any epistemic or even metaphysical point.

What
I mean by that is if we can't establish a procedure for determining
its truth, then what purpose does the locution “

*p*is determinately true or false” serve?
That
realist's truth is “a wheel in the mechanism that doesn't have a
function”, as Wittgenstein put it (though about something else).

I
think it was Bertrand Russell (or Michael Dummett) who made
this statement:

“There's a flying teapot floating around a distant star X in a distant galaxy Y.”

Now
there's no way of determining the truth or falsehood of this
statement. (It didn't help the matter by saying it's a teapot.)
Still, the statement “There is a teapot floating around star X in
galaxy Z” is either true or false – determinately.

*p*is determinately true or false either way. However, what matters is how we

*determine*its true. What doesn't seem to matter is that it's determinately true or false regardless; especially since we don't know its truth-vale and therefore, from the realist's perspective, that may be the end of the story.

The
anti-realist can say that a proposition is “truth-apt” now;
though it can have its precise truth-value determined in the future.
However, the realist will still say that it's both truth-apt now; as
well as true now. Later, the mathematician or philosopher may come to
determine its truth (or falsity); though it's still true (or false) now.

*)
The case of Fermat's Last Theorem, for example, adds more
difficulties to this. Though the point of this example is – is it?
- that the proof brought/brings the theorem's truth into existence (as it were).
Though this is what the realist – will he? - disputes. The
intuitionists or constructivists would have said that Fermat's
theorem had no truth until it was/is proved. Thus truth = proof.

The
problem here is that

*p*may be determinately true or false when it comes to the case of the flying teapot though not determinately true or false when it comes to an unproven (or any) mathematical statement or theorem.**Bivalence**

I've
never really seen the anti-realist rejection of bivalence as, well, a
genuine rejection. What I mean by that is that to argue that there's
a third truth-value (which is

*indeterminate*) isn't really a rejection of a proposition's being determinately true or false. That is, even if the truth value of*p*is indeterminate, that simply tells us about our epistemic situation. It does have an indeterminate truth-value*for us*. However, it's still determinately true or false (though for whom - fo no one?).
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