XPost: comp.theory, sci.math, sci.lang   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 2/6/2026 5:18 PM, Richard Damon wrote:   
   > On 2/6/26 3:00 PM, olcott wrote:   
   >> On 2/6/2026 12:15 PM, Richard Damon wrote:   
   >>> On 2/6/26 10:30 AM, olcott wrote:   
   >>>> On 2/6/2026 3:01 AM, Mikko wrote:   
   >>>>> On 05/02/2026 18:55, olcott wrote:   
   >>>>>   
   >>>>>> Changing the foundational basis to Proof Theoretic Semantics   
   >>>>>> Tarski Undefinability is overcome   
   >>>>>>   
   >>>>>> x ∈ Provable ⇔ x ∈ True // proof theoretic semantics   
   >>>>>   
   >>>>> A definition in terms of an undefined symbol does not really define.   
   >>>>>   
   >>>>   
   >>>> It is an axiom: ∀x (Provable(x) ⇒ True(x))   
   >>>   
   >>> But the axiom uses ⇒ which goes in just one direction, while you   
   >>> statements used ⇔ which attempts to go both ways.   
   >>>   
   >>   
   >> This was corrected by an expert that seems   
   >> to really know these things.   
   >>   
   >> This same expert agrees that with within PTS:   
   >> "if x is provable, then it is true."   
   >>   
   >   
   > Right, Provable leads to Truth. But Not Provable does not mean not true,   
   > or Truth require provability by the axiom.   
   >   
   > I gues you are just admitting that you are just a pathetic liar.   
   >   
   >   
   >>>   
   >>>>   
   >>>> There are dozens of papers needed to verify this.   
   >>>> It will take me quite a while to form proper citations   
   >>>> of these papers. It is anchored in proof theoretic semantics.   
   >>>> Generic PTS states that ~Provable(x) ⇔ Meaningless(x).   
   >>>> Model theory and truth conditional semantics are rejected.   
   >>>>   
   >>>   
   >>> And, I think your problem is you don't actually understand what you   
   >>> are reading. This shows in that you have been making the claim for   
   >>> years, but you are now admitting you can't ACTUALLY show why it is   
   >>> (yet).   
   >>>   
   >>   
   >> ∀x  (~Provable(x) ⇔ Meaningless(x))   
   >> Seems to be exactly and precisely what Proof Theoretic   
   >> Semantics actually says. Since the SEP article was   
   >> written by the guy that coined the term:   
   >> "Proof Theoretic Semantics"   
   >> It should be pretty definitive.   
   >   
   > No, which is part of your problem. Proof-Theoretic Semantics say we   
   > can't talk about the truth of a statement we can not prove, NOT that the   
   > statement can't be true without the proof, just we can't talk about it.   
   >   
      
   Lets try to say this exactly accurately.   
   In PTS expressions that are unprovable are   
   ungrounded in semantic meaning.   
      
   When I refer to a formal system I am referring to   
   Russell's atomic facts written down and placed in   
   a simple Type Hierarchy.   
      
      atomic facts, which consist either of a simple   
      particular exhibiting a quality, or multiple   
      simple particulars standing in a relation.   
   https://plato.stanford.edu/entries/logical-atomism/   
      
   > Proof-Theoretic Semantics limits our way of looking at things to what   
   > can be proven, and things outside of what can be proven are just outside   
   > the domain of discussion.   
   >   
      
   "true on the basis of meaning expressed in language"   
   necessarily includes the entire body of knowledge   
   expressed in language.   
      
   > The problem of using this Philosophical view in Formal Logic systems   
   > that have the power to create the Natural Number system is that we   
   > suddenly find we can't know if we can talk about a given statement until   
   > we solve it.   
   >   
   >>   
   >> https://plato.stanford.edu/entries/proof-theoretic-semantics/   
   >>   
   >>> Your problem is it seems you fundamentally don't understand how   
   >>> semantics work, and why it is important to put things into context.   
   >>>   
   >>   
   >> Not at all. It all in "Proof Theoretic Semantics"   
   >   
   > Which you don't understand, as that is all discussion in PHILOSOPHY, not   
   > FORMAL LOGIC, particularly those systems that can create infinite   
   > domains of reguard.   
   >   
   >>   
   >>> This shows in part because you keep on trying to apply principles for   
   >>> general Philosophy to Formal Logic, where they do not apply.   
   >>>   
   >>   
   >> Try saying that after you spend three hours carefully studying   
   >> the linked article. That article is not the end-all be-all   
   >> of "Proof Theoretic Semantics", yet it does seem to be the   
   >> most definitive single source.   
   >   
   > Maybe you should notice how many times they talk about removing things   
   > like in standard logic. Since Formal Logic system include in there   
   > definitions, the mode of interpreation of the logic, you aren't allowed   
   > to change that and keep the system being "the same".   
   >   
   > In other words, if you want to change to your "Proof-Theoretic   
   > Semantics", you FIRST need to show how much of the system services the   
   > change of rules.   
   >   
   > Since the definition of arithmatic of Natural Numbers falls apart if you   
   > try to force this on it, all you are doing is saying that you logic   
   > can't handle mathematics.   
   >   
      
   ∀x (Provable(PA, x)  ⇒ True(PA, x))   
   ∀x (Provable(PA, ~x) ⇒ False(PA, x))   
   ∀x (~True(PA, x) ∧ ~False(PA, x) ⇔ ~Truth_Apt(PA, x))   
      
      
   --   
   Copyright 2026 Olcott

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

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