[FOM] intuitionism and the liar paradox
Nik Weaver
nweaver at math.wustl.edu
Sat Apr 17 12:33:20 EDT 2010
Panu Raatikainen wrote:
> Nik Weaver advertized his solution to the Liar paradox. It is
> essentially based on the intuitionistic conception of truth.
>
> I would now challenge Weaver to explain, to us non-initiated, what,
> more exactly, is the intuitionistic understanding of truth -
> non-circularly.
This criticism isn't really specific to my paper. It doesn't address
my central insight that there is a problem with the inference "A is
true implies A" under the proof interpretation of the logical symbols.
Rather, the paper Panu cites is a broad critique of the semantic
notion of a valid proof. Is Panu a strict formalist? If not, can he
explain "to us non-initiated" how mathematics can be anything more than
a formal game with symbols if we have no general notion of validity
of proofs, i.e., if the only notion of validity we have is syntactic
validity within a particular formal system?
Turning to his "challenge", I have looked at his paper and I don't
see the circularity. His argument at the bottom of page 140 seems to
presume that proof validity is decidable, which I don't accept. If I
am mistaken that decidability is assumed here, perhaps he can clarify.
Nik
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