FOM: Intuitionism (Tait)
Jay Halcomb
jhalcomb8 at attbi.com
Mon Jun 17 19:28:35 EDT 2002
Charlie Volkstorf wrote:
>Must the proof of P be the same as the proof that this proof proves P?
What is a proof? What is a proof which demonstrates that something is a
proof?
Doesn't intuitionism, fundamentally and historically, involve a theory about
how proofs (or mathematical entities in general) are presented to the
consciousness, which is always individual, and which vary greatly?
Perhaps one should explicitly relativize this talk of proofs to languages
and logics. A communicated proof "that P" is always communicated in some
language, formal or informal -- usually a combination, and with respect to
some system of logic (not to mention other background assumptions).
Jay
Jay Halcomb
Interests: logic and computability
http://www.sonic.net/~halcomb
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