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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

              My 28 year goal has been to make
       "true on the basis of meaning expressed in language"
       reliably computable.

              This required establishing a new foundation
              --- SoupGate-Win32 v1.05        * Origin: you cannot sedate... all the things you hate (1:229/2)   

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