[FOM] Platonism and undecidability
Harvey Friedman
friedman at math.ohio-state.edu
Thu Nov 6 12:20:18 EST 2003
Reply to Tennant.
Tennant comments on what I wrote:
Friedman:
>> 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.
There is no trouble criticizing this statement on one grounds or another. I
know of no interesting statement of this rough form that cannot be
criticized on one ground or another. Then that starts a process of
refinement, typical of f.o.m./philosophy interaction, where it typically can
lead to good new f.o.m.
However, I don't see that Tennant has made any legitimate criticism of this
statement, as I indicate.
On 11/6/03 7:05 AM, "Neil Tennant" <neilt at mercutio.cohums.ohio-state.edu>
wrote:
> I want to focus on the part
>
> it is hard to convince people that "every sentence
> has a determinate truth value" if ...
> truth values are known to be non findable
>
> and then substitute "intuitionists" for "people" (if I may):
>
> it is hard to convince intuitionists that "every sentence
> has a determinate truth value" if ...
> truth values are known to be non findable
>
> At this point one has a problem.
I don't see any problem.
>For an intuitionist, the claim
>
> the truth-value of p is known to be non findable
>
> is inconsistent, hence cannot play any role in making an *intuitionist*
> reluctant to believe that every sentence has a determinate truth value.
> Should I conclude that intuitionists are not people? :-)
Under the suggestion that we might conclude that intuitionists are not
people, Tennant seems to be taking my statement as false - in particular,
false for intuitionists.
The if part is viewed by intuitionists as absurd. The "every sentence has a
determinate truth value" is also viewed as absurd by intuitionists - or at
least viewed as false. The fact that there may or may not be a connection
between the two is not a criticism of my statement.
This is somewhat analogous to criticizing a statement of the form
(forall x)(P(x) implies Q(x))
on the grounds that
for some x, P(x) is absurd
or on the grounds that
for some x, P(x) has nothing to do with Q(x).
Tennant's "criticism", at least in the form he has presented it, is not
sufficiently coherent to be productive for f.o.m. In fact, I do not see the
coherence in it at all.
I repeat what I said at the outset: there is no difficulty in legitimately
and productively criticizing any interesting statement of roughly this form.
NOTE: Of course, I wasn't thinking of intuitionists at all when I made this
statement, since I regard them as not even contemplating the idea that every
sentence of classical set theory has a determinate truth value. That is
because they don't accept the coherence of classical set theory in the first
place. On the other hand, there may be some formulation of "every sentence
has a determinate truth value" that at least some intuitionists regard as
plausible. I have never heard this view.
Harvey Friedman
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