XPost: sci.logic, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 10/5/2025 5:06 AM, Mikko wrote:   
   > On 2025-10-04 13:34:07 +0000, olcott said:   
   >   
   >> On 10/4/2025 5:25 AM, Mikko wrote:   
   >>> On 2025-10-02 10:07:33 +0000, olcott said:   
   >>>   
   >>>> On 10/2/2025 4:38 AM, Mikko wrote:   
   >>>>> On 2025-10-01 15:40:06 +0000, olcott said:   
   >>>>>   
   >>>>>> On 10/1/2025 5:12 AM, Mikko wrote:   
   >>>>>>> On 2025-10-01 01:46:15 +0000, olcott said:   
   >>>>>>>   
   >>>>>>>> On 9/30/2025 7:48 AM, Mikko wrote:   
   >>>>>>>>> On 2025-09-29 12:21:25 +0000, olcott said:   
   >>>>>>>>>   
   >>>>>>>>>> On 9/27/2025 5:05 AM, Mikko wrote:   
   >>>>>>>>>>> On 2025-09-26 01:08:45 +0000, olcott said:   
   >>>>>>>>>>>   
   >>>>>>>>>>>> On 9/25/2025 2:15 AM, Mikko wrote:   
   >>>>>>>>>>>>> On 2025-09-24 14:27:00 +0000, olcott said:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> On 9/24/2025 2:12 AM, Mikko wrote:   
   >>>>>>>>>>>>>>> On 2025-09-23 16:04:38 +0000, olcott said:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> On 9/23/2025 4:21 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>> On 2025-09-23 00:56:19 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> On 9/21/2025 4:22 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>>>> On 2025-09-20 14:57:20 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>>>> On 9/20/2025 4:31 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>> Gödel's sentence is not really self-referential. It   
   >>>>>>>>>>>>>>>>>>>>> is a valid   
   >>>>>>>>>>>>>>>>>>>>> sentence in the first order language of Peano   
   >>>>>>>>>>>>>>>>>>>>> arithmetic. That   
   >>>>>>>>>>>>>>>>>>>>> the value of an arithmetic expression in that   
   >>>>>>>>>>>>>>>>>>>>> sentence evaluates   
   >>>>>>>>>>>>>>>>>>>>> to the Gödel number of the sentence has no   
   >>>>>>>>>>>>>>>>>>>>> arithmetic significance.   
   >>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>> Yes that is the moronic received view yet these stupid   
   >>>>>>>>>>>>>>>>>>>> people stupidly ignore Gödel's own words.   
   >>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>> It is what Gödel said and proved.   
   >>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>> The most important aspect of Gödel's 1931   
   >>>>>>>>>>>>>>>>>>>> Incompleteness theorem   
   >>>>>>>>>>>>>>>>>>>> are these plain English direct quotes of Gödel from   
   >>>>>>>>>>>>>>>>>>>> his paper:   
   >>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>> ...there is also a close relationship with the   
   >>>>>>>>>>>>>>>>>>>> “liar” antinomy,14 ...   
   >>>>>>>>>>>>>>>>>>>> ...14 Every epistemological antinomy can likewise be   
   >>>>>>>>>>>>>>>>>>>> used for a similar undecidability proof...   
   >>>>>>>>>>>>>>>>>>>> ...We are therefore confronted with a proposition   
   >>>>>>>>>>>>>>>>>>>> which asserts its own unprovability. 15 ...   
   >>>>>>>>>>>>>>>>>>>> (Gödel 1931:40-41)   
   >>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>> Gödel, Kurt 1931.   
   >>>>>>>>>>>>>>>>>>>> On Formally Undecidable Propositions of Principia   
   >>>>>>>>>>>>>>>>>>>> Mathematica And Related Systems   
   >>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>> The most important aspect is the theorem itself:   
   >>>>>>>>>>>>>>>>>>> every theory that   
   >>>>>>>>>>>>>>>>>>> has the symbols and axioms of the first order Peano   
   >>>>>>>>>>>>>>>>>>> arithmetic is   
   >>>>>>>>>>>>>>>>>>> either incomplete or inconsistent.   
   >>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> That never has been the important part.   
   >>>>>>>>>>>>>>>>>> That has always been bullshit misdirection   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>> It is important because people consider it important.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> Prior to Pythagoras there was a universal consensus   
   >>>>>>>>>>>>>>>> that the Earth is flat.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> To think the Earth as flat is simpler and good enough for   
   >>>>>>>>>>>>>>> many   
   >>>>>>>>>>>>>>> purposes. For a long time there was no need to think   
   >>>>>>>>>>>>>>> about the   
   >>>>>>>>>>>>>>> shape of the Earth.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> The point is that not even a universal consensus equates   
   >>>>>>>>>>>>>> to truth.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> No, but it is a significant aspect of culture. A question   
   >>>>>>>>>>>>> of importance   
   >>>>>>>>>>>>> is not a matter of truth but a matter of opinion.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>> Many poeple also   
   >>>>>>>>>>>>>>>>> find it useful to know that any attempt to construct a   
   >>>>>>>>>>>>>>>>> cmplete theory   
   >>>>>>>>>>>>>>>>> of arithemtic would be a waste of time.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> Yet only when the architecture of the formal system is   
   >>>>>>>>>>>>>>>> screwed up.   
   >>>>>>>>>>>>>>>> If you want to build a formal system that is not   
   >>>>>>>>>>>>>>>> anchored in a   
   >>>>>>>>>>>>>>>> screwed up idea than this is straight forward.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> That 2 + 3 = 5 has practical value even if the theory   
   >>>>>>>>>>>>>>> around it   
   >>>>>>>>>>>>>>> cannot be made complete.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> *Refuting Gödel 1931 Incompleteness*   
   >>>>>>>>>>>>>>>> You begin with a finite list of basic facts and only apply   
   >>>>>>>>>>>>>>>> the truth preserving operation of semantic logical   
   >>>>>>>>>>>>>>>> entailment   
   >>>>>>>>>>>>>>>> to these basic facts.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> It is generally accepted that the set of axioms can be   
   >>>>>>>>>>>>>>> infinite   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> Not when we are representing the finite set of human   
   >>>>>>>>>>>>>> general knowledge.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Once again you try to deceive with a change of topic. There   
   >>>>>>>>>>>>> is no   
   >>>>>>>>>>>>> need to prove the incompletenes of human general knowledge   
   >>>>>>>>>>>>> as that   
   >>>>>>>>>>>>> already is obvious. But Gödel's and Tarski's theorems are   
   >>>>>>>>>>>>> about   
   >>>>>>>>>>>>> natural number arithmetic and its extensions so they need   
   >>>>>>>>>>>>> to cover   
   >>>>>>>>>>>>> the possibility that there are infinitely many axioms.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Tarski admits that he anchor his whole proof on the   
   >>>>>>>>>>>> liar paradox and   
   >>>>>>>>>>>   
   >>>>>>>>>>> He doesn't "anchor" it to the liar paradix. The liar paradox   
   >>>>>>>>>>> has some   
   >>>>>>>>>>> formal similarity to the sentence Tarski constructs but is   
   >>>>>>>>>>> not a part   
   >>>>>>>>>>> of the proof. Consequently anything said about the liar's   
   >>>>>>>>>>> paracos is   
   >>>>>>>>>>> irrelevant to the correctness of the proof.   
   >>>>>>>>>>   
   >>>>>>>>>> Factually incorrect.   
   >>>>>>>>>   
   >>>>>>>>> False. Tarski confirms what I said:   
   >>>>>>>>   
   >>>>>>>> And I prove my point in the paragraph that you skipped.   
   >>>>>>>   
   >>>>>>> Not relevant to Tarski's rerutation of your "Factually incorrect".   
   >>>>>>   
   >>>>>> He anchored his whole proof in that he   
   >>>>>> needed an extra level of logic to do this:   
   >>>>>   
   >>>>> You need metalogic if you want to say anything about logic.   
   >>>>>   
   >>>>>> X is any expression of language that is not   
      
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