[FOM] Godel numbers, use, and mention

[mjmurphy]

Dean Buckner wrote:


> Most of us would agree
>
>     (A) It is improbable that Bacon wrote Macbeth
>
> (though some people including Cantor, as it happens - see
>
> http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html)
>
> would differ.)  And we all agree that
>
>     (B) It is probable that Shakepeare wrote Macbeth
>
> But if Shakespeare = Bacon, then, by Leibniz and from (B),
>
>     (C) It is probable that Bacon wrote Macbeth
>
> which contradicts (A).  From which (if we agree (A) and (B)), we agree
that
> Shakespeare <> Bacon.
>
> This could revolutionise our approach to criminal detection!  It's certain
> that Jack the Ripper committed all the Whitechapel murders.  But it's
> uncertain whether any of the "usual suspects" committed them.  So, by
> Leibniz, we can rule them all out.
-------

I sometimes wonder about these arguments surrounding use/mention,
referential opacity.  Most of us agree with A) because we do not agree with
Shakespeare = Bacon.  If we agreed with Shakespeare= Bacon, presumably most
of us would not agree with A.  And then C would follow nicely.

The same with Frege's puzzle.

1) John believes p.
2) p=q
3) John believes q.

Many times, 3 is perfectly valid.  So I'm not sure what you are trying to
show.

Cheers,

M.J.Murphy