[FOM] CH and mathematics
James.Hirschorn at univie.ac.at
Fri Jan 25 21:48:40 EST 2008
On Wednesday 23 January 2008 15:03, Arnon Avron wrote:
> Let me add that in general I cannot understand an argument
> that something is true because things will look bad if it is not.
> What a kind of a *mathematical* argument is this?? (and
> if productivity is the issue rather than meaninmgfulness and
> truth, than why not accept as true V=L, which is a very
> fruitful axiom?).
Productivity cannot be the sole criterion for truth because two incompatible
statements can both be productive, e.g. V=L and MM (Martin's Maximum).
The axiom V=L seems particularly easy for a Platonist to refute. I should
think that any reasonable Platonist believes that the concept of infinity, as
being beyond the finite, has a reality independent of any formalization. Then
from Cantor they know that some infinities are larger than others. Along
these lines, of not putting an artificial "ceiling" on infinities, I suspect
they believe that large cardinal axioms are true provided that they are
consistent (at least for the currently known LC axioms). However, even the
existence of a measurable cardinal negates V=L.
There are surely also other very convincing Platonistic arguments against V=L.
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