XPost: comp.theory, sci.math, sci.lang   
   From: 046-301-5902@kylheku.com   
      
   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 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.   
      
   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.   
      
   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?   
      
   What language is that, and what are examples? What happens   
   when you try to make a false sentence?   
      
   Is it possible to utter conjectures which later turn out false;   
   and if so, then what happens?   
      
   >>>> 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.   
      
      
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