[FOM] CH and mathematics

Arnon Avron aa at tau.ac.il
Sat Jan 19 06:09:41 EST 2008

In two recent postings asked:
>In his recent entry in Philosophy of Mathematics:5 Questions, Solomon
>Feferman asks: "Is the Continuum Hypothesis a definite mathematical 

> If is not a mathematical problem, what kind of a 
> problem is it?

If you assume apriorily that CH is a * definite problem*, then 
of course it is a definite mathematical problem. 

 For some reason you omitted the crucial word "definite" when you
formulated *your* problem. But this is the main issue.

  Set-theoretical platonists would say that CH is a definite
problem. But non-platonists like me, who have always had a 
problem with the concept of "arbitrary set of natural numbers", 
not understanding in what sense such sets "exist", and who 
doubt that the term "P(N)" has a definite (=absolute) meaning, 
necessarily doubt that CH is a definite proposition, with a definite
truth-value. The fact that CH cannot be decided in the strongest
systems that the overwelming majority of  the mathemaricians 
can claim to have some intuitions about,` casts even stronger
doubts that CH can be said to have a definite truth value.

Arnon Avron 

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