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

On 3/21/25 5:33 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.
 

Godel didn't prove that Mathematics wasn't consistent. He proved that it couldn't be proved to BE consistant within itself.
He showed that it couldn't be COMPLETE (able to prove everything that it makes true).
To my knowledge, every perceived inconstancy has been able to be traced to an error in one of the proofs, or to an ambiguity in some definition, thus splitting the system based on the ways that ambiquity is resolved.