XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 2/8/2025 4:45 AM, Mikko wrote:   
   > On 2025-02-07 16:21:01 +0000, olcott said:   
   >   
   >> On 2/7/2025 4:34 AM, Mikko wrote:   
   >>> On 2025-02-06 14:46:55 +0000, olcott said:   
   >>>   
   >>>> On 2/6/2025 2:02 AM, Mikko wrote:   
   >>>>> On 2025-02-05 16:03:21 +0000, olcott said:   
   >>>>>   
   >>>>>> On 2/5/2025 1:44 AM, Mikko wrote:   
   >>>>>>> On 2025-02-04 16:11:08 +0000, olcott said:   
   >>>>>>>   
   >>>>>>>> On 2/4/2025 3:22 AM, Mikko wrote:   
   >>>>>>>>> On 2025-02-03 16:54:08 +0000, olcott said:   
   >>>>>>>>>   
   >>>>>>>>>> On 2/3/2025 9:07 AM, Mikko wrote:   
   >>>>>>>>>>> On 2025-02-03 03:30:46 +0000, olcott said:   
   >>>>>>>>>>>   
   >>>>>>>>>>>> On 2/2/2025 3:27 AM, Mikko wrote:   
   >>>>>>>>>>>>> On 2025-02-01 14:09:54 +0000, olcott said:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> On 2/1/2025 3:19 AM, Mikko wrote:   
   >>>>>>>>>>>>>>> On 2025-01-31 13:57:02 +0000, olcott said:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> On 1/31/2025 3:24 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>> On 2025-01-30 23:10:18 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> Within the entire body of analytical truth any   
   >>>>>>>>>>>>>>>>>> expression of language that has no sequence of   
   >>>>>>>>>>>>>>>>>> formalized semantic deductive inference steps from the   
   >>>>>>>>>>>>>>>>>> formalized semantic foundational truths of this system   
   >>>>>>>>>>>>>>>>>> are simply untrue in this system. (Isomorphic to   
   >>>>>>>>>>>>>>>>>> provable from axioms).   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>> If there is a misconception then you have misconceived   
   >>>>>>>>>>>>>>>>> something. It is well   
   >>>>>>>>>>>>>>>>> known that it is possible to construct a formal theory   
   >>>>>>>>>>>>>>>>> where some formulas   
   >>>>>>>>>>>>>>>>> are neither provble nor disprovable.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> This is well known.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> And well undeerstood. The claim on the subject line is   
   >>>>>>>>>>>>>>> false.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> a fact or piece of information that shows that something   
   >>>>>>>>>>>>>> exists or is true:   
   >>>>>>>>>>>>>> https://dictionary.cambridge.org/us/dictionary/english/proof   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> We require that terms of art are used with their term-of-   
   >>>>>>>>>>>>> art meaning and   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> The fundamental base meaning of Truth[0] itself remains the   
   >>>>>>>>>>>> same   
   >>>>>>>>>>>> no matter what idiomatic meanings say.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Irrelevant as the subject line does not mention truth.   
   >>>>>>>>>>> Therefore, no need to revise my initial comment.   
   >>>>>>>>>>   
   >>>>>>>>>> The notion of truth is entailed by the subject line:   
   >>>>>>>>>> misconception means ~True.   
   >>>>>>>>>   
   >>>>>>>>> The title line means that something is misunderstood but that   
   >>>>>>>>> something   
   >>>>>>>>> is not the meaning of "true".   
   >>>>>>>>   
   >>>>>>>> It is untrue because it is misunderstood.   
   >>>>>>>   
   >>>>>>> Mathematical incompleteness is not a claim so it cannot be untrue.   
   >>>>>>   
   >>>>>> That mathematical incompleteness coherently exists  claim.   
   >>>>>   
   >>>>> Yes, but you didn't claim that.   
   >>>>>   
   >>>>>> The closest that it can possibly be interpreted as true would   
   >>>>>> be that because key elements of proof[0] have been specified   
   >>>>>> as not existing in proof[math] math is intentionally made less   
   >>>>>> than complete.   
   >>>>>   
   >>>>> Math is not intentionally incomplete.   
   >>>>   
   >>>> You paraphrased what I said incorrectly.   
   >>>   
   >>> No, I did not paraphrase anything.   
   >>>   
   >>>> Proof[math] was defined to have less capability than Proof[0].   
   >>>   
   >>> That is not a part of the definition but it is a consequence of the   
   >>> definition. Much of the lost capability is about things that are   
   >>> outside of the scope of mathemiatics and formal theories.   
   >>>   
   >>   
   >> When one thinks of math as only pertaining to numbers then math   
   >> is inherently very limited.   
   >   
   > That's right. That limited area should be called "number theory",   
   > not "mathematics".   
   >   
   >> When one applies something like   
   >> Montague Grammar to formalize every detail of natural language   
   >> semantics then math takes on much more scope.   
   >   
   > It is not possible to specify every detail of a natural language.   
   > In order to do so one should know every detail of a natural language.   
   > While one is finding out the language changes so that the already   
   > aquired knowledge is invalid.   
   >   
   >> When we see this then we see "incompleteness" is a mere artificial   
   >> contrivance.   
   >   
   > Hallucinations are possible but only proofs count in mathematics.   
   >   
   >> True(x) always means that a connection to a semantic   
   >> truthmaker exists. When math does this differently it is simply   
   >> breaking the rules.   
   >   
   > Mathematics does not make anything about "True(x)". Some branches care   
   > about semantic connections, some don't. Much of logic is about comparing   
   > semantic connections to syntactic ones.   
   >   
   >>>>> Many theories are incomplete,   
   >>>>> intertionally or otherwise, but they don't restrict the rest of math.   
   >>>>> But there are areas of matheimatics that are not yet studied.   
   >>>>>   
   >>>>>> When-so-ever any expression of formal or natural language X lacks   
   >>>>>> a connection to its truthmaker X remains untrue.   
   >>>>>   
   >>>>> An expresion can be true in one interpretation and false in another.   
   >>>>   
   >>>> I am integrating the semantics into the evaluation as its full context.   
   >>>   
   >>> Then you cannot have all the advantages of formal logic. In particular,   
   >>> you need to be able to apply and verify formally invalid inferences.   
   >>   
   >> All of the rules of correct reasoning (correcting the errors of   
   >> formal logic) are merely semantic connections between finite strings:   
   >   
   > There are no semantic connections between uninterpreted strings.   
   > With different interpretations different connections can be found.   
   >   
      
   When we do not break the evaluation of an expression of language   
   into its syntax and semantics such that these are evaluated   
   separately and use something like Montague Semantics to formalize   
   the semantics as relations between finite strings then   
      
   it is clear that any expression of language that lacks a connection   
   through a truthmaker to the semantics that makes it true simply remains   
   untrue.   
      
   In the big picture way that truth really works there cannot   
   possibly be true[0](x) that is not provable[0](x) where x   
   is made true by finite strings expressing its semantic meanings.   
      
   >> When one finite string expression of language is known to be true   
   >> other expressions are know to be semantically entailed.   
   >   
   > Only if they are connected with (semantic or other) connections that   
   > are known to preserve truth.   
   >   
      
      
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