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

Richard Heathfield <rjh@cpax.org.uk> writes:

On 21/03/2025 08:11, Mikko wrote:
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<snip>
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Another part of human knowledge is that there are fools that try to
argue against proven theorems.

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Well, if it ain't proven it ain't yet a theorem. But is that enough?
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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?
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But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
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And Gödel proved not only that it isn't, but that it can't be.
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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.

My understanding is that Gödel proved that there are statements
that are true but not provable.  It's still not possible for both
X and not-X to be provable.  If proofs exist for both, at least
one of the proofs must be flawed.

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */