Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology providing situational context.

On 3/21/2025 4:33 AM, Richard Heathfield wrote:

On 21/03/2025 08:11, Mikko wrote:
 <snip>
 

Another part of human knowledge is that there are fools that try to
argue against proven theorems.

 Well, if it ain't proven it ain't yet a theorem. But is that enough?
 The background to the work of Church, Turing, Gödel and the like is Hilbert's second problem: "The compatibility of the arithmetical axioms", and the background to /that/ problem is that in the late 19th century mathematicians were occasionally coming up with proofs of X, only to discover in the literature that not-X had already been proved. The question then was which proof had the bug?
 But what if they were /both/ right? It was an obvious worry, and so arose the great question: is mathematics consistent?
 And Gödel proved not only that it isn't, but that it can't be.
 Fortunately, to date inconsistency has tended to surface only in corner cases like the Halting Problem, but Gödel's Hobgoblin hovers over mathematics to this day.
 

When a formal system begins with the basic facts of human
general knowledge expressed using language and can derive
each element of the set of human general knowledge that can
be expressed using language on the basis of these basic facts
by applying only truth preserving operations then undecidability
and incompleteness are impossible.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer