[FOM] AXIOM SCHEMATA

[Donald Stahl]

Assuming that Tennant's questions both refer to the preference (not the 
tendency) I suggest (not on my own behalf) that it might have to do with the 
idea that compositionality is supposed to be the source of novelty and 
unlimitedness---that these are to be worked for, not assumed.  Perhaps it 
has to do with conflating theories with languages, so that the set of axioms 
corresponds to the lexicon. A non-finitely axiomatized theory would then be 
on a par with an unlearnable language.



Best wishes,

Donald E. Stahl 12545 Olive Boulevard
St. Louis, MO 63141-6311 USA






>From: Neil Tennant <neilt at mercutio.cohums.ohio-state.edu>
>To: Matthew Frank <mfrank at math.uchicago.edu>
>CC: fom at cs.nyu.edu, John Corcoran <corcoran at buffalo.edu>
>Subject: Re: [FOM] AXIOM SCHEMATA
>Date: Tue, 13 Jul 2004 19:15:57 -0400 (EDT)
>
>On Mon, 12 Jul 2004, Matthew Frank wrote:
>
> > Given that we generally prefer finitely axiomatized theories to 
>infinitely
> > axiomatized theories, why do we tend to use ZF instead of NBG?  --Matt
>
>Do we, really? And if we don't, why should we?
>
>Neil Tennant
>
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