FOM: CH and 2nd-order validity

Robert Black Robert.Black at
Wed Oct 18 03:34:54 EDT 2000

>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.

Actually, I would deny both (1) and (2). But if you do hold to (1) and (2),
(3) is no longer available, since all you can prove in ZFC is that *if ZFC
is consistent* there are arithmetical sentences undecidable in ZFC. Because
I think it's true (though not provable in ZFC) that ZFC is consistent, *I*
can conclude that there are arithmetical sentences undecidable in ZFC, but
it doesn't seem that *you* can!


Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845

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