XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/29/2025 3:24 PM, Alan Mackenzie wrote:   
   > dart200  wrote:   
   >> On 11/29/25 12:00 PM, Alan Mackenzie wrote:   
   >>> dart200  wrote:   
   >>>> On 11/28/25 1:08 PM, Alan Mackenzie wrote:   
   >>>>> dart200  wrote:   
   >>>>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:   
   >>>>>>> dart200  wrote:   
   >>>>>>>> does the logical construction:   
   >   
   >>>>>>>> "this sentence is false"   
   >   
   >>>>>>>> place a hard limit on our ability to understand truth:   
   >   
   >>>>>>>> yes/no???   
   >   
   >>>>>>> No, not at all.  Anybody beyond early childhood will recognise it as a   
   >>>>>>> mere frivolous distraction from any seeking after the truth.   
   >   
   >>>>>> so why does anyone think such a construct places a meaningful limit in a   
   >>>>>> formal system then?   
   >   
   >>>>> People, in general, don't, apart from one or two exceptions.   
   >   
   >>>>>> "this sentence has no proof"   
   >   
   >>>>> That is a world apart from "This sentence is false.".  It's the kernel   
   >>>>> of Gödel's proof (as you know, of course).  "This sentence has no proof"   
   >>>>> turns out to be true and unprovable (for a precisely defined meaning of   
   >>>>> "unprovable").   
   >   
   >>>>>> "this program loops forever iff it's decided that it halts"   
   >   
   >>>>> As you also know, this is the contradiction reached in one of the proofs   
   >>>>> of the Halting Theorem.  This is also not the same as "This sentence is   
   >>>>> false.", though it is inspired by that nonsense.   
   >   
   >>>>> None of these sentences/nonsenses limit our ability to understand truth.   
   >>>>> They are part of the truth that we understand.  They delineate   
   >>>>> fundamental boundaries of what can be known and proven, in particular   
   >>>>> that truth is more subtle than provability.   
   >   
   >>>>> This opens the possibility that some mathematical conjectures may be   
   >>>>> true but unprovable.  That's just part of existence.   
   >   
   >>>> or mathmaticians bought into a nutzo over-generalization in regards to a   
   >>>> weird but highly limited artifact of self-referential logic   
   >   
   >>> I'm not sure exactly what you mean by that paragraph, but it sounds   
   >>> pejorative.   
   >   
   >>> Would you call 2 + 2 = 4 an "over-generalisation"?  If so, why not?  If   
   >>> not, what is different about Gödel's Incompleteness Theorem?  It is based   
   >>> on the same fundamentals as 2 + 2 = 4.   
   >   
   >> godel's proof does not prove anything about any other premise than one   
   >> particular sentence that is essentially "this truth has no proof" ...   
   >   
   > That's a misunderstanding.  That proof proves that there is such an   
   > unprovable sentence in any logical system bar the simplest.  Since   
   > neither the sentence nor its negation can be proven, you can extend the   
   > system by adopting that sentence or its negation as a new axiom.  The new   
   > system you've just created will likewise have an unprovable sentence.   
   >   
      
   If it is a logic sentence and it cannot be proven or refuted   
   because its proof or refutation requires an infinite number   
   of steps then it is not an element of the body of knowledge.   
   https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)   
      
   > Olcott is (I think) asserting that his system of definitions will not   
   > have any unprovable statements.  Thus his system will either be   
   > inconsistent or be simple in the extreme, to the point of not being able   
   > to do arithmetic.   
   >   
   >>> You seems to be a member of that category of non-mathematicians who   
   >>> reject proven results because they don't like those results.  Peter   
   >>> Olcott is most assuredly such a person.   
   >   
   >> yeah, i am a burnt-out software engineer who's disgusted at the utter   
   >> ridiculousness of using this as some absurd fucking excuse to not fully   
   >> prove the semantics of the software we deploy to production.   
   >   
   > As a retired software engineer, I feel your pain too.  But it may be that   
   > no such proof is possible, I can't say for sure.  And even if it is   
   > possible, it may be that no customer is prepared to pay what it would   
   > cost.  But that's no excuse for the truly dreadful apologies for software   
   > which currently come out some of the "leading" software producers.  I see   
   > no excuse for not fully testing software before its release, like we used   
   > to do.   
   >   
   >> i'm stuck in a fucking looney bin, to be frank...   
   >   
   >> but at least i realize where i am stuck at, unlike most twats reading   
   >> this post   
   >   
   > The world is steadily becoming less sensible, and more brutal and   
   > callous.  Quite frankly, I'm glad I'm not of a younger generation.   
   >   
   >> --   
   >> a burnt out swe investigating into why our tooling doesn't involve   
   >> basic semantic proofs like halting analysis   
   >   
   >> please excuse my pseudo-pyscript,   
   >   
   >> ~ nick   
   >   
      
      
   --   
   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)