[FOM] extramathematical notions and the CH
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Tue Feb 5 19:11:07 EST 2013
Quoting joeshipman at aol.com:
> Any constant which can be approximated arbitrarily closely by an
> algorithm is by definition arithmetical.
Sure. But let me be even more explicit about the hypothetical
scenario I have in mind. Suppose we have a physical theory that
predicts that, say, the mass of a particle is equal to 0 if there are
non-measurable sets of reals and 1 otherwise. It then follows that if
we manage to measure the mass of the relevant particle, and find it to
be 1, we're faced with the decision of either rejecting the physical
theory or the axiom of choice. As you say, this situation can't arise
in case of the sort of physical theories we currently consider even
remotely plausible (or conceivable). But it can't be ruled out solely
on basis of considerations involving "non-absolute" and "absolute"
mathematical notions and principles. Any such conclusion must be based
on an examination of actual physical ideas, theories, principles, e.g.
the holographic principle, the Bekenstein bound, quantum information
theory, philosophical musings about physics and measurement, the
logical and mathematical properties shared by mathematical
formulations of physical theories so far proposed, and so on, and
inescapably must involve non-logical and mathematical ingredients. It
appears we in fact entirely agree on this, so please consider my
harping on it just a somewhat pointless reminder it's a good idea to
be clear on what is based on purely logical considerations and what on
observations about and of physics as we currently know it.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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