Re: Simple yet Profound Metatheorem


Barb Knox wrote:

> If you want provability and truth to be the same, you can dispense with
> all the modal machinery and just use some existing well-thought-out
> constructive logic (e.g. Intuitionistic).
>
False. Truth and provability are *not* the same in
intuitionistic/constructive logics. If you claim otherwise, show me a
valid proof of the law of non-contradiction i.e., of ~(P&~P), in these
logics. Any "proof" of ~(P&~P) that you produce from contradictory
premises is not a valid proof in these logics. E.g. see Appendix A of

http://arxiv.org/abs/math.LO/0506475

which reproduces the argument given in my published paper in IJQI, Vol.
3, No. 1 (2005) pp. 263-267 ("The quantum superposition principle
justified in new non-Aristotelian finitary logic").

Regards, RS

.

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