[FOM] Platonism and undecidability
Neil Tennant
neilt at mercutio.cohums.ohio-state.edu
Thu Nov 6 19:38:03 EST 2003
Reply to Sambin and Friedman.
I suggest that you forget my tongue-in-cheek question whether one should
conclude that intuitionists are not people! I apologize if my attempt to
inject some levity into the discussion has led to any misunderstandings.
Let's return to Harvey's claim:
> I was proposing that it is hard to convince people that "every sentence
> has a determinate truth value" if truth values cannot be found, or if
> truth values are known to be non findable, or there is absolutely no
> evidence that truth values can be found, or there is no plan or idea for
> finding truth values, etc.
The proposal is of the form
It is hard to convince people that P if Q, or if R, or if S or if T.
This would validate the inference
R;
so, it is hard to convince people that P.
Here, the premise R is "the truth value of some proposition (X, say) is
known to be non findable"; and P is "every statement has a determinate
truth value".
So Harvey's proposal would validate the following inference:
For some proposition X, the truth value of X is known to be
non-findable;
therefore,
It is hard to convince people that every statement has a
determinate truth value.
My point was simply that for an intuitionist, the premise is inconsistent.
So it cannot figure in any sound argument for the conclusion.
Of course, the intuitionist is not out to convince anyone that every
statement has a determinate truth value! On the contrary---the
intuitionist will want to argue that NOT every statement has a determinate
truth value.
But what the intuitionist CANNOT do, when arguing for a denial of the
universal claim, is make out that there is a counterexample to it.
That's all.
Neil Tennant
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