How can FOL logic be at the same time complete and only semi-decidable?
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From: Daryl McCullough on 9 Aug 2010 08:09 Aatu Koskensilta says... > >George Greene <greeneg(a)email.unc.edu> writes: > >> Aatu K.'s replies are often abusive. > >They are? Yes. You torture us with the literary techniques of understatement and irony. -- Daryl McCullough Ithaca, NY
From: Aatu Koskensilta on 9 Aug 2010 10:50 Herman Jurjus <hjmotz(a)hetnet.nl> writes: > On 8/7/2010 4:06 PM, Aatu Koskensilta wrote: > >> The observation that a complete theory is decidable is perfectly >> fine. (It's a mystery why it seems to have eluded Hilbert!) > > Huh? The set of all closed sentences that are true in N is a theory, > and it's complete - but it isn't decidable. Right, it's the observation that a complete axiomatizable theory is decidable that's perfectly fine. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechen kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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