[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 

> 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.


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