XPost: comp.theory, sci.math, sci.lang   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 2/6/2026 7:54 PM, Richard Damon wrote:   
   > On 2/6/26 8:13 PM, olcott wrote:   
   >> On 2/6/2026 6:23 PM, Richard Damon wrote:   
   >>> On 2/6/26 7:10 PM, olcott wrote:   
   >>>> 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.   
   >>>   
   >>> Right, which means you can't talk about them.   
   >>>   
   >>   
   >> Your way of saying it is way too weak.   
   >> Is gibberish nonsense is more accurate.   
   >   
   > Nope, just because it doesn't know the answer, doesn't mean the question   
   > is "gibberish".   
   >   
   > That is the flaw in your thinking.   
   >   
      
   What is an expression of language that has no meaning?   
      
   > Unless the system can KNOW that the statement can not be proven, it   
   > doesn't know that the statement is actually gibberish, or just to   
   > difficult to understand.   
   >   
   > Just like Tarski's proof that a Truth Primative can't exist, or Godel's   
   > proof that formal logic system that can handle the mathematcis is   
   > incomplete SEEM LIKE GIBBERISH TO YOU, but are actually full of meaning   
   > to those that actually understand their meaning.   
   >   
   > Proof-Theoretic Semantics understands that just because we haven't found   
   > a proof, doesn't make it non-well-founded, and accepts it.   
   >   
   > Godel's proof shows the limitiation of Proof-Theoretic Semantics in a   
   > mathematical system.   
   >   
      
   Not in the least little bit.   
      
   > He creates a perfectly semantic statement   
      
   In the wrong semantic system.   
      
   > as a relationship that can be   
   > finitely tested for any number. He then ask a complete semantically   
   > reasonable question about that relationship, does a number exist that   
   > satisfies it, making an assertion that it does not.   
   >   
   > This SHOULD have meaning in a system that understands the mathematics.   
   >   
   > But, by the rules of proof-theoretic semantics, The statement can only   
   > be considered to be true if we could prove it, and false if we could   
   > prove its converse, or declared non-well-founded if we could prove that   
   > neither of those can be shown,   
      
   Yes.   
      
   > but it turns out that there is no proof   
   > in the system for ANY of those options, and thus a statement that HAS   
   > semantic meaning by the structure of the system can't be given a PT   
   > semantics.   
   >   
      
   My system involves a type hierarchy with unlimited finite levels of   
   indirect reference.   
      
   > It turns out that Proof-Theoretic Semantics just fail for system that   
   > handle mathematics as there exists statements like this that can not be   
   > proven true, can not be proven false, and can't be proven to not be able   
   > for make either of those proofs.   
   >   
   > But then, this comes out as a somewhat natural result of the axiom of   
   > induction, which defines a way to answer SOME truth-conditional   
   > statements, but not all, and thus admits them into its semantics.   
   >   
   >>   
      
      
      
      
   >> *THE MEANING IN ALL FORMAL MATHEMATICAL AND NATURAL LANGUAGES*   
   >   
   > Then you accept the Formal Logic definition of "Truth" that means what   
   > can be demonstrated by an infinite sequence of steps, and thus reject   
   > you proposition that something is only true if it can be proven.   
   >   
   >   
      
   We have been over this quite a few time now.   
   Anything requiring an infinite number of steps   
   is outside the domain of knowledge.   
      
      
      
   >>   
   >> *Good job, you got the most important point exactly correctly*   
   >> Non-well-founded means not truth-apt.   
   >   
   > So, you accept that your "Proof-Theoretic" system uses Truth-Conditional   
   > meaning, as you can't actually PROVE that something is Truth_Apt.   
   >   
      
   ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???   
   ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???   
   ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???   
      
   Truth conditional semantics has always been TOTALLY WRONG HEADED !!   
      
   >   
   > Sorry, you are just showing your world is just an imaginary fantasy.   
   >   
   >>   
   >>> You might not be able to do any of the above, in which case you can't   
   >>> talk about the statement and it truth.   
   >>>   
   >>   
   >> The key thing is that PTS rejects cases of pathological   
   >> self-reference as lacking a well-founded justification   
   >> tree thus semantically ill-formed within PTS.   
   >   
      
   [continued in next message]   
      
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