[FOM] How much of math is logic?
Ron Rood
ron.rood at planet.nl
Mon Feb 26 13:04:58 EST 2007
joeshipman at aol.com wrote on sunday, 25 feb 2007 at 22:36
(Europe/Amsterdam):
> I'm willing to entertain a variety of notions of "logic", but what they
> have in common is that there is no need for a "subject matter" -- logic
> is purely conceptual, and logical truth applies to every domain we can
> talk about consistently.
>
Note that Frege had this curious notion of a "logical object." An
example of such a logical object would be a truth value.
Furthermore, setting aside the more technical difficulties that his
original project led to (the Russell paradox etc.), Frege, I believe,
held logicism to mean not only that the theorems of mathematics are
logically derivable from a distinguished set of logical truths--the
axioms. He also held that the concepts constituting those axioms are
logical in nature.
Of course this does not settle Richard Heck's question what the
adjective "logical" means.
Ron
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