[FOM] CH and mathematics
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.
More information about the FOM