XPost: comp.theory, sci.math, sci.lang   
   From: polcott333@gmail.com   
      
   On 11/29/2025 3:39 PM, Kaz Kylheku wrote:   
   > On 2025-11-29, olcott  wrote:   
   >> On 11/29/2025 2:23 PM, Kaz Kylheku wrote:   
   >>> On 2025-11-29, olcott  wrote:   
   >>>> On 11/29/2025 11:53 AM, Kaz Kylheku wrote:   
   >>>>> On 2025-11-29, olcott  wrote:   
   >>>>>> Any expression of language that is proven true entirely   
   >>>>>> on the basis of its meaning expressed in language is   
   >>>>>> a semantic tautology.   
   >>>>>   
   >>>>> A tautology is an expression of logic which is true for all   
   >>>>> combinations of the truth values of its variables and propositions,   
   >>>>> which is, of course, regardless of what they mean/represent.   
   >>>>   
   >>>> I did not say tautology. I said semantic tautology.   
   >>>> I am defining a new thing under the Sun.   
   >>>   
   >>> The existing tautology is already semantic. You have to know the   
   >>> semantics (the truth tables of the logical operators used in the   
   >>> formula, and the workings of quantifiers and whatnot) to be able to   
   >>> conclude whether a formula is a tautology.   
   >>>   
   >>   
   >> Try and show how Gödel incompleteness can be   
   >> specified in a language that can directly encode   
   >> self-reference and has its own provability operator   
   >> without hiding the actual semantics using Gödel numbers.   
   >   
   > The numbers are essential, because Gödel Incompleteness is   
   > about number theory.   
   >   
      
   The generalization Gödel incompleteness applies to   
   every formal system that has arithmetic or better.   
      
   > The Gödel Theorem involves a proof in which a certain number,   
   > the "Gödel number" that may be called G, is asserted to have   
   > a number-theoretical property.   
   >   
      
   G := (F ⊬ G) // G says of itself that it is unprovable in F   
      
   > An example of a number-theoretical property is "25 is a perfect   
   > square". Except we need it in more formal language.   
   >   
   > Gödel discovered that you can encode statements of number theory as   
   > integers, and manipulate them (e.g. do derivation) by arithmetic.   
   >   
      
   That simply abstracts away the underlying semantics.   
   G is unprovable in F because G is semantically unsound,   
   We can't see that with Gödel numbers.   
      
   > Then it became obvious that whether or not a formula is a theorem   
   > is a property of its Gödel number: a number-theoretical property.   
   >   
   > There are theorem-numbers and non-theorem-numbrers.   
   >   
   > The Gödel sentence says somethng like "The Gödel number   
   > calculated by the expression G is not a theorem-number."   
   >   
   > But G turns out to be the Gödel number of that very sentence   
   > itself.   
   >>   
   >>> Pick another word. Since only dimwitted crackpots like yourself will   
   >>> want to discuss anything using that word, keep the syllable count low   
   >>> and make sure there aren't too many off-centre vowels.   
   >>   
   >> Ad hominem the first choice of losers.   
   >   
   > I'm not making an argument; I'm suggesting a way of choosing   
   > an alternative word, since "tautology" is taken.   
   >   
   >>>> *Semantic tautology is stipulated to mean*   
   >>>   
   >>> Reject; call it something else.   
   >>>   
   >>>> Any expression of language that is proven true entirely   
   >>>> on the basis of its meaning expressed in language.   
   >>>   
   >>> You are gonna need to supply an example.   
   >>   
   >> The key is that a counter-example is categorically   
   >> impossible.   
   >   
   > So you are saying every expression in a certain language   
   > is proven true, so that its syntax admits no false sentences?   
   >   
      
   It syntax admits anything that any human can   
   say in any language comprised of symbols.   
      
   > What language is that, and what are examples? What happens   
   > when you try to make a false sentence?   
   >   
      
   English, Second Order Predicate logic, C++...   
      
   > Is it possible to utter conjectures which later turn out false;   
   > and if so, then what happens?   
   >   
      
   Conjectures are not elements of the body of knowledge.   
      
   >>>>> You would need to have tremendous stature in logic to   
   >>>>> be able to dictate a redefinition of a deeply entrenched,   
   >>>>> standard term.   
   >>>>   
   >>>> Or I could simply prove that I am correct on the   
   >>>   
   >>> Your intellectual track record shows that you couldn't prove correct   
   >>> your way out of a wet paper bag.   
   >>   
   >> Ad hominem the first choice of losers.   
   >   
   > But anyway, your intellectual track record shows that you couldn't prove   
   correct   
   > your way out of a wet paper bag.   
   >   
   > This is entirely relevant.   
   >   
   > You've never proven anything and never will.   
   >   
   > That contradicts your above claim that "I could simply prove ...".   
   >   
   > All evidence points to: no, you couldn't.   
   >   
   >>> You are already wrong. The definition of word is neither correct   
   >>> nor incorrect. It's just accepted or not. A bad definition ahs   
   >>> some issue like circularty or inconsistency, but if there is no   
   >>> such problem, then the rest is just a matter of convention.   
   >>   
   >> There you go, you are getting it now.   
   >> circularity, inconsistency, and incoherence.   
   >   
   > The existing definition of "tautology" doesn't have these issues.   
   >   
   >   
      
   It also is not rich enough to express anything   
   that anyone can possibly say about anything.   
      
      
   --   
   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)