Thoughts on CH

[Joe Shipman]

CH is about subsets of the real numbers. That’s much more concrete than AC which I’d a statement about arbitrarily large and abstract sets.

Sent from my iPhone

> On Jan 25, 2020, at 9:50 PM, Annatala Wolf <a.lupine at gmail.com> wrote:
> 
> 
>> 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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