Thoughts on CH

[Annatala Wolf]

On Sat, Jan 25, 2020 at 1:02 AM Joe Shipman <joeshipman at aol.com> wrote:

> I don’t understand why so few mathematicians are willing to say “of course
> CH is either true or false..."
>


With regard to independence from ZF, it might help to take a step back and
look at the same question about AC. Certainly, not all mathematicians would
agree "of course AC is either true or false", even among those who accept
the excluded middle. It is a philosophical position to claim there are
meaningful truths (mathematical or otherwise) outside what we can examine
and prove. Finitists and ultrafinitists don't even accept the existence of
the set of natural numbers, despite obvious proofs that natural numbers are
limitless.

Personally, I'm something of a Platonist, so I feel that the naturals
exist, and AC and CH do have answers. It seems like hubris (to me) to
assume that just because humans with our finite limitations lack the
ability to prove something, that must mean the thing doesn't exist. But
mathematics is largely about proving results, and when we've proven that a
proposition is unknowable, in the eyes of many this places it outside the
bounds of mathematical truth.

-- 
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enum E{A;System s;String t="/* Annatala Wolf, Lecturer%n * Department of
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