From: pdugan (pdugan@vt.edu)
Date: Wed Jan 25 2006 - 21:07:59 MST
>===== Original Message From Ben Goertzel <ben@goertzel.org> =====
>Marc,
>
>Inconsistentism also seems to tie in with G. Spencer Brown's notion of
>modeling the universe using "imaginary logic", in which contradiction
>is treated as an extra truth value similar in status to true and
>false.
>
Interestingly, the most promising pointer to a proof of Riemann's hypothesis
lies in proving the theorem R[s] = 1/2 a contradiction, that is undecidable.
The nature of the hypothesis hinges on a non-commutative logic, so if the
theorem is unprovable then its true, because if it were false it would be
disprovable.
Riemann's hypothesis is a sort of statement of consistency for number
theory, and thus mathmatics in general. Yet, it can't be proven true in a
time-ful perspective, there'll always be more zeroes ahead. In a timeless
sense, it can be proven by a sort of imaginary logic. It strikes me that this
is a reversal of Brown's distinction, where the timeless is consistent and the
the timeful is not.
Patrick Dugan
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