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   sci.logic      Logic -- math, philosophy & computationa      262,912 messages   

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   Message 261,946 of 262,912   
   olcott to Tristan Wibberley   
   Re: on mathematical ghosts (3/3)   
   15 Dec 25 09:56:24   
   
   [continued from previous message]   
      
   >>> i hang out there tho, i have my own reasons for posting this there   
   >>>   
   >>   
   >> Theory of computation issues are disrespectful   
   >> spam to that group that violate Buddhist compassion.   
   >>   
   >> I was a long time poster to alt.zen. I still   
   >> have 8969 messages posted there since 2005.   
   >>   
   >> Also my great grand uncle Henry Steel Olcott   
   >> was a very famous Buddhist.   
   >>   
   >>>>   
   >>>> int sum(int x, int y){return x + y;}   
   >>>> sum(3,2) should return 5 and it is incorrect   
   >>>> to require sum(3,2) to return the sum of 5+6.   
   >>>>   
   >>>   
   >>> u can argue about what computing machines actually exist all u want,   
   >>> and whether anything actually computes the halting *function*, i'm not   
   >>> going to argue over what the halting *function* itself is   
   >>>   
   >>   
   >> Then you get the wrong answer.   
   >>   
   >> In computability theory and computational complexity   
   >> theory, a decision problem is a computational problem   
   >> that can be posed as a yes–no question on a set of   
   >> input values. https://en.wikipedia.org/wiki/Decision_problem   
   >>   
   >> Most people have no idea that there is such a thing   
   >> as an incorrect question. Because of this they misclassify   
   >> incorrect yes/no questions as undecidable decision problem   
   >> instances.   
   >   
   > Yes, I think so to.   
   >   
   > I'm pretty sure it's an extension of a domain error once it itself is   
   > extended to an untyped system.   
   >   
      
   *This is the foundation of most of my work*   
   Kurt Gödel in his 1944 Russell's mathematical   
   logic gave the following definition of the   
   "theory of simple types" in a footnote:   
      
       By the theory of simple types I mean the   
       doctrine which says that the objects of   
       thought (or, in another interpretation,   
       the symbolic expressions) are divided into   
       types, namely: individuals, properties of   
       individuals,relations between individuals,   
       properties of such relations, etc. (with   
       a similar hierarchy for extensions), and   
       that sentences of the form: " a has the   
       property φ ", " b bears the relation R to   
       c ", etc. are meaningless, if a, b, c, R, φ   
       are not of types fitting together.   
      
   Without a system of types when the notion of   
   a dead cat is fed to a decider to see if the   
   "dead cat" has a square root value of 5   
   conventional thinking will call this undecidable.   
      
   > Just as the identity function from even numbers to even numbers   
   > converted naively to an untyped system doesn't terminate when you apply   
   > it to an odd number, a nullary function (errrr... terminology   
   > carelessness) doesn't terminate when it's specification constrains it   
   > such that there's no valid value (errr... terminology carelessness again).   
   >   
   > When we lift a function into a partiality monad we may extend its domain   
   > and I think there is one or more extension functions (not a standard   
   > terminology, just descriptive) to the extended domain (allowing for the   
   > identity extension function when lifting total functions).   
   >   
      
      
   --   
   Copyright 2025 Olcott

              My 28 year goal has been to make
       "true on the basis of meaning expressed in language"
       reliably computable.

              This required establishing a new foundation
              --- SoupGate-Win32 v1.05        * Origin: you cannot sedate... all the things you hate (1:229/2)   

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