XPost: comp.theory, sci.logic, sci.math   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 1/16/2026 2:34 PM, Richard Damon wrote:   
   > On 1/16/26 3:24 PM, olcott wrote:   
   >> On 1/16/2026 1:34 PM, Richard Damon wrote:   
   >>> On 1/16/26 2:16 PM, olcott wrote:   
   >>>> On 1/16/2026 12:52 PM, Richard Damon wrote:   
   >>>>> On 1/16/26 12:47 PM, olcott wrote:   
   >>>>>> The system uses proof-theoretic semantics, where the   
   >>>>>> meaning of a statement is determined entirely by its   
   >>>>>> inferential role within a theory. A theory T consists   
   >>>>>> of a finite set of basic statements together with   
   >>>>>> everything that can be derived from them using the   
   >>>>>> inference rules. The statements derivable in this   
   >>>>>> way are the theorems of T. A statement is true in   
   >>>>>> T exactly when T proves it. A statement is false   
   >>>>>> in T exactly when T proves its negation. Some   
   >>>>>> statements are neither true nor false in T. These   
   >>>>>> are the non-well-founded statements: statements   
   >>>>>> whose inferential justification cannot be grounded   
   >>>>>> in a finite, well-founded proof structure. This includes   
   >>>>>> self-referential constructions such as Gödel-type sentences.   
   >>>>>>   
   >>>>>> *Proof Theoretic Semantics Blocks Pathological Self-Reference*   
   >>>>>> https://philpapers.org/archive/OLCPTS.pdf   
   >>>>>>   
   >>>>>   
   >>>>> WHAT system?   
   >>>>>   
   >>>>> WHAT can you do in it?   
   >>>>>   
   >>>>> Can you actually prove that, or is it just more of your lies.   
   >>>>>   
   >>>>   
   >>>> You have to actually read the paper.   
   >>>   
   >>> I did. Where do you actually define the initial axioms of your syste,/   
   >>>   
   >>>>   
   >>>>> Your problem is that you system is based on a criteria that matches   
   >>>>> your own definition of non-well-founded.   
   >>>>>   
   >>>>   
   >>>> What does not well-founded mean in proof-theoretic semantics?   
   >>>   
   >>> So. how is your definition of the criteria to be non-well-founded not   
   >>> non-well-founded for some questions?   
   >>>   
   >>> Note, asking LLMs for a definition doesn't define it in your system.   
   >>>   
   >>>>   
   >>>> In proof‑theoretic semantics, a statement is not well‑founded when   
   >>>> its justification cannot be grounded in a finite, well‑structured   
   >>>> chain of inferential steps. It lacks a terminating, well‑ordered   
   >>>> proof tree that would normally establish its truth or falsity. This   
   >>>> often happens with self‑referential or circular statements whose   
   >>>> “proofs” loop back on themselves rather than bottoming out in basic   
   >>>> axioms or introduction rules. // Copilot   
   >>>>   
   >>>> In proof-theoretic semantics, saying that something is “not well-   
   >>>> founded” means that the structure used to define or justify meanings   
   >>>> does not rest on a base case that is independent of itself. Instead,   
   >>>> it involves circular or infinitely descending dependencies among   
   >>>> rules or proofs. // ChatGPT   
   >>>>   
   >>>> In proof-theoretic semantics, not well-founded typically refers to   
   >>>> derivations or proof structures that contain infinite descending   
   >>>> chains or circular dependencies, violating the well-foundedness   
   >>>> property.   
   >>>> In classical proof theory, well-founded derivations have a clear   
   >>>> hierarchical structure where every inference rule application   
   >>>> depends only on "smaller" or "simpler" premises, eventually   
   >>>> bottoming out in axioms or basic rules. This ensures that proofs are   
   >>>> finitely constructible and verifiable. // Claude AI   
   >>>>   
   >>>> A set of introduction rules (definitional clauses) for an atom P is   
   >>>> called well-founded if every chain of successive "definitions"   
   >>>> (unfoldings) eventually terminates — i.e., there is no infinite   
   >>>> descending chain of definitional dependencies.   
   >>>> Intuitively:   
   >>>> The meaning of P is ultimately grounded in basic facts or in logical   
   >>>> structure after finitely many unfoldings. // Grok   
   >>>>   
   >>>>   
   >>>   
   >>> And, thus, your "definition" of non-well-founded   
   >>   
   >> Is the standard definition in truth theoretic semantics making   
   >> "true on the basis of meaning expressed in language"   
   >> reliably computable for the entire body of knowledge.   
   >>   
   >> This includes expressing all of PA in a complete system.   
   >>   
   >   
   > I think not.   
   >   
   > One problem you are going to run into is that this "entire body of   
   > knowledge" is itself not built on those semantics,   
   >   
      
   I knew that this would be philosophically too deep   
   for you so I am using PA to build a bridge.   
      
   > It is a problem trying to process "knowledge" based on a different logic   
   > than the logic you are trying to process it.   
   >   
   > Also, part of our knowledge is about mathematics, which, for instance   
   > will assert that the Goldbach Conjecture is one of the great puzzles of   
   > mathematics, and must either be true or false, but that FACT is   
   > incompatible with proof-theoretic semantics, as mathematics can show   
   > that some true statements do not have proofs in the system.   
   >   
      
   You seem to keep forgetting the specified domain   
   is the body of knowledge that is   
   "true on the basis of meaning expressed in language"   
      
   > Thus, your system colapses in a contradiction that the statement might   
   > be not-well-founded, but that classification might be not-well-founded,   
   > and that determination may be not-well-founded, and so on, so your   
   > attempt to define you system runs into a possibly infinite loop of   
   > asking if we can even talk about the statement.   
   >   
      
   My paper already explains all of the details of that.   
      
   Proof Theoretic Semantics Blocks Pathological Self-Reference   
   https://philpapers.org/archive/OLCPTS.pdf   
      
   > If you disagree, it falls upon YOU to figure out how to handle that   
   > issue, you can't just assume it can be done.   
   >   
      
      
   --   
   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)