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Mathematical Logic And G\"odel

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Posted by R. Stephen Newberry on December 1, 2003 18:09:21 UTC


The Anatomy and Ultimate nature of "True-but-Unprovable Propositions"

can be found at mathpreprints.com

http://www.mathpreprints.com/math/Preprint/stevnewb/20031020/5/

ABSTRACT

Presents a very crude, very basic view of the Logical Universe from the perspective of Classical Logic and Henkin General Models semantics. Not only is the equivalence-class of such sentences [and their negations]derived by a method of such simplicity that it is self-evidently correct, but the ontological and epistemological 'raison d'etre' for such sentences is demonstrated in a comparably self-evident manner.

The key to the puzzle is that there are two flavors of mathematical truth: (1) Tautological truth, "u-validity, (= universal validity, absolute truth in EVERY universe) ; and (2) Contingent truth, "n-validity" (= validity on all-and-only finite domains; with satisfiability on an infinite domain (by compactness), but admitting an infinite counter-model.)

The essay has been submitted for publication in JSL. Comments are solicited.

stevnewb@ix.netcom.com


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