[FOM] How much of math is logic?

[Robbie Lindauer]

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."