Re: Claude.ai provides reasoning why I may have defeated the conventional HP proof

On 7/15/2025 8:08 AM, Tristan Wibberley wrote:

On 10/07/2025 15:09, olcott wrote:
 

All of logic is a mental abstraction
with no physical existence.

 Copyright Tristan Wibberley. All Rights reserved.
 Nonsense! Logistic formal systems are entirely about symbol manipulation
and avoid admitting mental abstraction, they're wholly physical although
some of them are contingent on the availability of infinitely large
amounts of paper and ink. Try telling me about a theorem with no
symbols, not even in brain structure, neither spread over time nor space!
 The place people get muddled up is thinking that ontological assignments
are part of the system.
 That's why they think systems can be inconsistent instead of merely
indiscriminate. They think one of the objects of the system is logical
negation even when it isn't AND they think that the fact they think it
also makes it so for everyone. Probably because they conceive of a
logistic system via embedding in another system, formal or informal, and
are unable to do it algebraically so they "define" one of the symbols to
be negation instead of inferring it from the symbol's properties.
 The reality is the system they think inconsistent is either informal
(and therefore not logistic) or it merely doesn't contain any
propositions distinct from its theorems.
 

The following requires translating all of the basic
facts of the world into a finite set of finite strings.
These finite strings encode natural language semantic
meanings as something like Montague grammar or Rudolf
Carnap Meaning Postulates.
Consistent and complete logic systems are defined by:
(a) Stipulating a finite set of basic facts that
     are defined to be true.
(b) The only rule of inference is semantic logical
entailment from these basic facts.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer