Re: Sorry Godel - All Truths are Provable


Charlie-Boo wrote:
Rupert wrote:

We know that Goedel's sentence G is true but not provable.

No you don't. You have to assume the system is sound and then
you've just assumed practically what you conclude.


I think that belittles Goedel's achievement somewhat. Anyway, tell me
what metatheory you want to work in and what object theory you want to
talk about and I'll restrict myself to saying things that can be proved
in that metatheory. (My metatheory was ZFC and my object theory was
PA). Presumably it has to be a metatheory where the notion of truth is
available, so it has to be reasonably strong.

And that still doesn't say where logic fails us.

What logic? I don't understand your reasons for thinking the
truth-value of a statement has to coincide with its provability-value.

Why won't the car
start? The existence of a bad wff or bad experience trying to start a
car doesn't tell us where the instrument is failing.

And given
any provable sentence P, G&P is true but not provable.

Better make that any true sentence P.


Yes, you're right.

C-B

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