XPost: comp.theory, sci.logic, sci.math   
   XPost: comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/15/2026 9:28 PM, Richard Damon wrote:   
   > On 1/15/26 6:45 PM, olcott wrote:   
   >> On 1/15/2026 5:50 AM, Richard Damon wrote:   
   >>> On 1/15/26 12:30 AM, olcott wrote:   
   >>>> On 1/14/2026 9:44 PM, Richard Damon wrote:   
   >>>>> On 1/14/26 4:36 PM, olcott wrote:   
   >>>>>> Interpreting incompleteness as a gap between mathematical truth   
   >>>>>> and proof depends on truth-conditional semantics; once this is   
   >>>>>> replaced by proof-theoretic semantics a framework not yet   
   >>>>>> sufficiently developed at the time of Gödel’s proof the notion of   
   >>>>>> such a gap becomes unfounded.   
   >>>>>>   
   >>>>>   
   >>>>> But that isn't what Incompleteness is about, so you are just   
   >>>>> showing your ignorance of the meaning of words.   
   >>>>>   
   >>>>> You can't just "change" the meaning of truth in a system.   
   >>>>>   
   >>>>   
   >>>> Yet that is what happens when you replace the foundational basis   
   >>>> from truth-conditional semantics to proof-theoretic semantics.   
   >>>   
   >>> Which isn't allowed.   
   >>>   
   >>> You don't seem to understand that "changing the basis" means you have   
   >>> a different system.   
   >>>   
   >>   
   >> Yes just like you always said that I needed.   
   >> A formal system such that   
   >> "true on the basis of meaning expressed in language"   
   >> is always reliably computable.   
   >>   
   >   
   > So, go ahead and try to do it.   
   >   
   > The problem is your system now can't encode "all human knowledge", as   
   > that doesn't work in the system.   
   >   
      
   We start with the smaller goal a defining PA without   
   Gödel Incompleteness.   
      
   > The problem is that the knowledge is based on logic that isn't   
   > compatible with you logic system.   
   >   
   > All you could do is try to encode the human knowledge that is still true   
   > under the restrictions, which can't include details about the real   
   > world, as that is inherently truth-conditional, as we don't know the   
   > "axioms" the world works on.   
   >   
   > Thus, your "all human knowledge" just fails to be available.   
      
   Actual "true on the basis of meaning expressed in language"   
   has always been proof-theoretic semantics.   
      
   --   
   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)