XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 11/28/2025 4:54 PM, Alan Mackenzie wrote:   
   > [ Followup-To: set ]   
   >   
   > In comp.theory olcott  wrote:   
   >> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:   
   >>> dart200  wrote:   
   >>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:   
   >>>>> dart200  wrote:   
   >>>>>> does the logical construction:   
   >   
   >>>>>> "this sentence is false"   
   >   
   >>>>>> place a hard limit on our ability to understand truth:   
   >   
   >>>>>> yes/no???   
   >   
   >>>>> No, not at all.  Anybody beyond early childhood will recognise it as a   
   >>>>> mere frivolous distraction from any seeking after the truth.   
   >   
   >>>> so why does anyone think such a construct places a meaningful limit in a   
   >>>> formal system then?   
   >   
   >>> People, in general, don't, apart from one or two exceptions.   
   >   
   >>>> "this sentence has no proof"   
   >   
   >>> That is a world apart from "This sentence is false.".  It's the kernel   
   >>> of Gödel's proof (as you know, of course).  "This sentence has no proof"   
   >>> turns out to be true and unprovable (for a precisely defined meaning of   
   >>> "unprovable").   
   >   
   >   
   >> *Within A new foundation for correct reasoning*   
   >   
   >> (a) Every element of the body of knowledge that can   
   >>      be expressed in language is entirely composed of   
   >>    (1) A finite set of atomic facts   
   >>    (2) Every expression of language that is semantically   
   >>        entailed by (1)   
   >> (b) a formal language based on Rudolf Carnap Meaning   
   >>      Postulates combined with The Kurt Gödel definition   
   >>      of the "theory of simple types"   
   >>      https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944   
   >>      Where every semantic meaning is fully encoded syntactically   
   >>      as one fully integrated whole not needing model theory   
   >   
   >> We have now totally overcome Gödel Incompleteness   
   >> and Tarski Undefinability for the entire body if   
   >> knowledge that can be expressed in language. It   
   >> is now a giant semantic tautology.   
   >   
   > You can't "overcome" these theorems, since they're not obstacles.   
   > They're fundamental truths.   
   >   
      
   I just showed the detailed steps making both of   
   them impossible in the system that I just specified.   
   A counter-example is categorically impossible.   
      
   >>>> "this program loops forever iff it's decided that it halts"   
   >   
   >>> As you also know, this is the contradiction reached in one of the proofs   
   >>> of the Halting Theorem.  This is also not the same as "This sentence is   
   >>> false.", though it is inspired by that nonsense.   
   >   
   >   
   >> It is isomorphic.   
   >   
   > Stop using mathematical terms you don't understand.  There is no   
   > isomorphism here.  Your assertion is a category error.   
   >   
   I used that term correctly and you cannot actually   
   show otherwise.   
      
   >>> None of these sentences/nonsenses limit our ability to understand truth.   
   >>> They are part of the truth that we understand.  They delineate   
   >>> fundamental boundaries of what can be known and proven, in particular   
   >>> that truth is more subtle than provability.   
   >   
   >   
   >> That is bullshit as I have just proven.   
   >   
   > Every time you use the word "proven" you appear to be lying.  I can't   
   > recall any occurrence where you were telling the truth.   
   >   
      
   When a counter-example to my claim is categorically   
   impossible then I have proven this claim even if   
   you fail to understand that this is the generic   
   way that all actual proof really works.   
      
   >> Within the giant semantic tautology of knowledge that   
   >> can be expressed in language everything is proven or   
   >> not an element of this body.   
   >   
   > Your scheme is limited indeed, in that it is not powerful enough to   
   > represent unprovable propositions.   
      
   In other words "the entire body of knowledge that   
   can be expressed in language" uses big words that   
   you cannot understand?   
      
   What is left out of:   
   "the entire body of knowledge that can be expressed in language" ?   
      
   What is left out of:   
   "the entire body of knowledge that can be expressed in language" ?   
      
   What is left out of:   
   "the entire body of knowledge that can be expressed in language" ?   
      
   What is left out of:   
   "the entire body of knowledge that can be expressed in language" ?   
      
   What is left out of:   
   "the entire body of knowledge that can be expressed in language" ?   
      
   >  I (along with the vast majority of   
   > mathematicians, scientists, philosophers, ....) do not accept such   
   > limitations.  These limitations involve not being able to do arithmetic   
   > at all.   
   >   
   >>> This opens the possibility that some mathematical conjectures may be   
   >>> true but unprovable.  That's just part of existence.   
   >   
   >>>> --   
   >>>> a burnt out swe investigating into why our tooling doesn't involve   
   >>>> basic semantic proofs like halting analysis   
   >   
   >>>> please excuse my pseudo-pyscript,   
   >   
   >>>> ~ nick   
   >   
   >> --   
   >> Copyright 2025 Olcott   
   >   
   >> My 28 year goal has been to make   
   >> "true on the basis of meaning" computable.   
   >   
   >> This required establishing a new foundation   
   >> for correct reasoning.   
   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)