Re: FOL, ZFC, NGB and Prolog

tom wrote:
(I thought Goedel equated provability and truth).

to which aatu koskensita responded:
Quite the opposite, really, provided we're speaking about formal
provability.


that is not quite true
goedel, like many mathematicians of the time, struggled with the
definition of truth
and at times he did study the "truth as proof" school
but his conceptions of its meaning was not a necessary component to his
major arguments in metamathematics

however, the constructivists of the time equated truth and provability
and this later was incorporated into the foundations of computation
which express the incompleteness theorems much more directly

the key concept is inaccesibility
(or the dual notion of platonic truth)

to tom:
if you are truly interested in the connections between computation and
proof theory
start with the curry-howard isomorphism
it is the centerpiece on which the connection is made formal



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galathaea: prankster, fablist magician, liar

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