[FOM] How much of math is logic?
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
> 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.
More information about the FOM