FOM: CH and 2nd-order validity
Kanovei
kanovei at wmwap1.math.uni-wuppertal.de
Wed Oct 18 02:54:03 EDT 2000
> Date: Wed, 18 Oct 2000 01:21:41 +0200
> From: Robert Black <Robert.Black at nottingham.ac.uk>
> Subject: Re: FOM: CH and 2nd-order validity
> Personally, I think that every sentence of arithmetic has a truth-value,
> and that CH has a truth-value too. but the problem is to persuade
> non-believers.
The problem is first of all to substantiate the assertion
that begins with "I think", even for sentences of arithmetic,
let alone CH.
Presumably you mean MATHEMATICAL truth value, rather than
something implied by any platonistical/philosophical/theological
arguments.
In other words you seem to "think" that any sentence of arithmetic
(also CH) is either mathematically true or mathematically false.
But this immediately runs into contradiction with the following
observations, that hardly can be questioned:
1) to be mathematically true means to have a mathematically
rigorous proof;
2) the latter means a proof in ZFC
(including "category theory" as a version of ZFC);
3) by Goedel, there are arithmetical sentences unsolvable in ZFC.
V.Kanovei
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