XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/30/2025 12:57 PM, Richard Damon wrote:   
   > On 12/30/25 11:15 AM, olcott wrote:   
   >> On 12/30/2025 9:14 AM, Richard Damon wrote:   
   >>> On 12/30/25 9:52 AM, olcott wrote:   
   >>>> On 12/30/2025 8:32 AM, Richard Damon wrote:   
   >>>>> On 12/30/25 12:33 AM, olcott wrote:   
   >>>>>> On 12/29/2025 10:50 PM, Richard Damon wrote:   
   >>>>>>> On 12/29/25 11:35 PM, olcott wrote:   
   >>>>>>>> On 12/29/2025 9:51 PM, Richard Damon wrote:   
   >>>>>>>>> On 12/29/25 6:28 PM, olcott wrote:   
   >>>>>>>>>> On 12/29/2025 5:06 PM, Richard Damon wrote:   
   >>>>>>>>>>> On 12/29/25 4:38 PM, olcott wrote:   
   >>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> There exists a sequence of inference steps from   
   >>>>>>>>>>>> the axioms of a formal system that prove that   
   >>>>>>>>>>>> they themselves do not exist.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Right, there is an INFININTE string of inference steps in the   
   >>>>>>>>>>> base theory that shows that no FINITE string of inference   
   >>>>>>>>>>> steps to show it.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> Rene Descartes said: "I think therefore I never existed".   
   >>>>>>>>>>   
   >>>>>>>>>> There is no sequence of inference steps that   
   >>>>>>>>>> prove they themselves do not exist.   
   >>>>>>>>>>   
   >>>>>>>>>> There is no sequence of inference steps that   
   >>>>>>>>>> prove they themselves do not exist.   
   >>>>>>>>>>   
   >>>>>>>>>> There is no sequence of inference steps that   
   >>>>>>>>>> prove they themselves do not exist.   
   >>>>>>>>>>   
   >>>>>>>>>> There is no sequence of inference steps that   
   >>>>>>>>>> prove they themselves do not exist.   
   >>>>>>>>>>   
   >>>>>>>>>> There is no sequence of inference steps that   
   >>>>>>>>>> prove they themselves do not exist.   
   >>>>>>>>>>   
   >>>>>>>>>> That is all that Gödel ever proved.   
   >>>>>>>>>> That is all that Gödel ever proved.   
   >>>>>>>>>> That is all that Gödel ever proved.   
   >>>>>>>>>> That is all that Gödel ever proved.   
   >>>>>>>>>> That is all that Gödel ever proved.   
   >>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>   
   >>>>>>>>> In other words, you are just showing that you don't know what   
   >>>>>>>>> you are talking about and thus going into non-sense,   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> ...We are therefore confronted with a proposition   
   >>>>>>>> which asserts its own unprovability. 15 … (Gödel 1931:40-41)   
   >>>>>>>   
   >>>>>>> Yes, you have said this before, and I have explained it, but   
   >>>>>>> apparently you can't read.   
   >>>>>>>   
   >>>>>>>>   
   >>>>>>>> Correctly paraphrased as:   
   >>>>>>>> a sequence of inference steps from axioms   
   >>>>>>>> that assert that they themselves do not exist.   
   >>>>>>>   
   >>>>>>> Nope, as I have pointed out, you have missed the context, because   
   >>>>>>> you are so stupid.   
   >>>>>>>   
   >>>>>>   
   >>>>>> a proposition which asserts its own unprovability.   
   >>>>>   
   >>>>> a proposition who has a meaning in the meta-system talking about   
   >>>>> its provability in the base system.   
   >>>>>   
   >>>>   
   >>>> This sentence is not true: "This sentence is not true"   
   >>>> the outer sentence is true because the inner sentence   
   >>>> is semantically incoherent.   
   >>>>   
   >>>>   
   >>>>> You just ignore context as that is just to complicated for you.   
   >>>>>   
   >>>>   
   >>>> I focus on the details that everyone else has been   
   >>>> indoctrinated to ignore.   
   >>>>   
   >>>>>>   
   >>>>>> The proof of such an propostion within the same   
   >>>>>> formal system would require a sequence of inference   
   >>>>>> steps that prove that they themselves do not exist.   
   >>>>>   
   >>>>> Which just shows you don't understand the concept of Formal   
   >>>>> Systems, and their meta-systems.   
   >>>>>   
   >>>>   
   >>>> This sentence is not true: "This sentence is not true"   
   >>>> the outer sentence is true because the inner sentence   
   >>>> is semantically incoherent.   
   >>>   
   >>> In other words, you can't talk about the sentence you want to talk   
   >>> about, so you do to soething irrelevent.   
   >>>   
   >>   
   >> Exactly the opposite Incompleteness and Undefinability   
   >> dishonestly dodge the fact the their actual sentences   
   >> are incoherent by using the meta-level.   
   >   
   > And what is incoherent about using a meta-level.   
   >   
   > All a mete-level is, is to build a new Formal System, based on the base   
   > system that knows the basic properties of the base system.   
   >   
   > For instance, the Rational Numbers can be considers a "meta" of the   
   > Integeres.   
   >   
   >>   
   >> This meta-level is correct to state that these sentences   
   >> are not provable and not true.   
   >>   
   >> The meta-level never looks at why they are unprovable   
   >> and untrue. They are unprovable and untrue BECAUSE they   
   >> are semantically incoherent.   
   >   
   > No, the sentence of G was specifically constructed to have a coherent   
   > meaning in the base system, but you just are too stupid to understand that.   
   >   
      
   Why do you lie about this? Does lying give you cheap thrill?   
      
   ...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 statment G, in the base system, as well as in the meta system is the   
   > claim that there exists no natural number g that satisifies a particular   
   > mathematical property expresses as a primative recursive relationship.   
   >   
   > The mathematics of that is fully coherent in the base system, and WILL   
   > have an answer of either yes or no, even if that system might not be   
   > able to compute that answer.   
   >   
   > In the meta-system, because of how the relationship was created, we see   
   > that in adds meaning from the base system into numbers that inherently   
   > only mean themselves. Just like we can form words with meaning from   
   > letters that have no inherent meaning.   
   >   
   > It seems you don't even understand how "meaning" works, so your core is   
   > based on a fundamental misunderstanding of what you talk about.   
   >   
   >>   
   >> The proper treatment is to toss these sentences out as   
   >> incoherent. The proper treatment is not to create a   
   >> meta-level that simply ignores this incoherence.   
   >   
   > But they aren't.   
   >   
   > I guess to you, mathematics is just incoherent, and logic has to be kept   
   > primative.   
   >   
   > In other words, you are just too stupid to be in the field.   
   >   
   >>   
   >> Tarski's metatheory        Tarski's theory   
   >> This sentence is not true: "This sentence is not true" is true   
   >   
   > You just don't understand what Tarski is saying, as his proof build on   
   > the concept that Godel uses, and Tarski shows that if we assume the   
   > existance of a predicate "True" that will return True if its input   
   > sentance is actually True, but False otherwise (either the contradiction   
   > of the sentence is true, so it is false, or the sentence doesn't have a   
      
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