An Ultrafinite Set Theory
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From: MoeBlee on 3 Mar 2010 11:34 On Mar 2, 11:11 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Of course, if MoeBlee doesn't even consider PA to be > adequate for the sciences, what chance does RE (or anyone > else) have in convincing him that a _weaker_ theory, such > as an ultrafinitist theory, is adequate for science? As far as I know, first order PA is not adequate. (I'm open to being convinced otherwise, though.) MoeBlee
From: Aatu Koskensilta on 3 Mar 2010 11:37 MoeBlee <jazzmobe(a)hotmail.com> writes: > As far as I know, first order PA is not adequate. (I'm open to being > convinced otherwise, though.) Sink your teeth into the mumblings of Feferman on predicativism, ACA_0, proof-theoretic reductions, what not, then! -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: MoeBlee on 3 Mar 2010 11:41 On Mar 3, 10:37 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > MoeBlee <jazzm...(a)hotmail.com> writes: > > As far as I know, first order PA is not adequate. (I'm open to being > > convinced otherwise, though.) > > Sink your teeth into the mumblings of Feferman on predicativism, ACA_0, > proof-theoretic reductions, what not, then! But isn't ACA_0 a theory not compatible in strength with PA rather than a theory weaker or equal to PA? MoeBlee
From: MoeBlee on 3 Mar 2010 11:41 On Mar 3, 10:41 am, MoeBlee <jazzm...(a)hotmail.com> wrote: > compatible I meant 'comparable'. MoeBlee
From: Aatu Koskensilta on 3 Mar 2010 11:42
MoeBlee <jazzmobe(a)hotmail.com> writes: > But isn't ACA_0 a theory not compatible in strength with PA rather > than a theory weaker or equal to PA? Nope. ACA_0 aka elementary analysis is a conservative extension of PA. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |