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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology
 providing situational context.
Date: Fri, 21 Mar 2025 09:33:12 +0000
Organization: Fix this later
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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.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within