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|    sci.math.symbolic    |    Symbolic algebra discussion    |    10,432 messages    |
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|    Message 10,429 of 10,432    |
|    olcott to Richard Damon    |
|    Re: Well-founded proof theoretic semanti    |
|    24 Jan 26 13:28:25    |
      XPost: comp.theory, sci.logic, sci.math       XPost: comp.lang.prolog       From: polcott333@gmail.com              On 1/24/2026 1:23 PM, Richard Damon wrote:       > On 1/24/26 12:56 PM, olcott wrote:       >> On 1/24/2026 11:17 AM, Richard Damon wrote:       >>> On 1/22/26 7:15 PM, olcott wrote:       >>>> On 1/22/2026 6:09 PM, Richard Damon wrote:       >>>>> On 1/22/26 12:40 PM, olcott wrote:       >>>>>> Well-founded proof theoretic semantics where True(L, x)       >>>>>> is anchored in provability from the axioms of formal       >>>>>> system L seems to eliminate the undecidability that       >>>>>> model theoretic semantics encounters when truth is       >>>>>> measured from outside of the formal system in a separate       >>>>>> model.       >>>>>       >>>>> But GOdel's proof wasn't based on a truth outside the system.       >>>>>       >>>>> The proof was based outside the system,       >>>> Hence requiring provability in the system has       >>>> always been totally wrong-headed.       >>>>       >>>       >>> Nope, when in the system, that is all you know.       >>>       >>       >> So you think that inside and outside are the same thing?       >>       >       > No, but the outside can know everything about the inside, and make       > things that work on the inside.       >              Only because outside you have meta-math to       look at these things and inside you only have PA.              --       Copyright 2026 Olcott |
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