Re: Godel's Incompleteness theorem

Tonico <Tonicopm@xxxxxxxxx> writes:

If you say "any truthful statement can be derived", you are messing
things up: how can you know whether a statement is truthful if you
haven't yet proved it? It sounds like a tautology: if the statement
can be derived (I understand this as meaning proved), then it is
truthful, and of course the other way around: if it is truthful then
it is so because it can be "derived" (= proved) in the system.

For the first-order language of arithmetic truth is a mathematically
defined property of formal sentences, and it's mathematically provable
that there are many (consistent) formal theories in which falsities
are derivable, and that being true is not equivalent to being formally
derivable in any formal theory.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxx)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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