[FOM] How much of math is logic?
Robbie Lindauer
rlindauer at gmail.com
Wed Feb 28 02:31:36 EST 2007
What Frege thought and when is irrelevant to our current discussion
and was not intended as the content of my message. It is sufficient
to assert that at one point Frege thought that V deserved the title
"law of logic" one way or another. Perhaps not "indisputable law of
logic" but then what is an "indisputable law of logic"?
The point was that in order to make logic BE(come) mathematics, both
Frege and Russell saw the need to extend what was called logic, and a
development of that effort is what we have in ZFC, (some) extensions
to Logic to make it sufficient to perform mathematics.
In modern terms, we can see that propositional calculus, predicate
calculus, FOL, FOL+PA, SOL, ..., ZF, ZFC, ZFC
+LargeCardinalAxiomDuJour, etc. have very different strengths and an
attempt to blur the distinctions in strength with a slogan "logic is
math and vice versa" is what is really misleading. This (among other
reasons) is why the logicist programme has ultimately failed.
Robbie Lindauer
robblin at thetip.org
On Feb 27, 2007, at 6:34 PM, Max Weiss wrote:
> "A dispute can arise, so far as I
> can see, only with regard to my Basic Law concerning courses-of-
> values (V).... I hold that it is a law of pure logic. In any event
> the place is pointed out where the decision must be made."
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