[FOM] Godel numbers, use, and mention

[Richard Heck]

> > M.J.Murphy:
> The point is,
> > (A) It is improbable that Bacon wrote Macbeth
> > (B) It is probable that Shakespeare wrote Macbeth
> > does not imply
> > (C) Shakespeare <> Bacon
> > whereas by Leibniz it should.  That's all.  It may make you happier to put
> > "there is strong/weak evidence that" or  "everyone dis/believes that"
> > instead of  "It is im/probable that".
> Perhaps I still miss the point.  I'm not sure how  "it is probable"
> is gives us an opaque context.  How could it be possible to hold A) and B)
> and not C)?

It seems to me that one might hold (A) and (B), but still be agnostic as
regards (C). (I do not think one could regard (C) as false, but as
always agnosticism is the crucial case.) If one thought it very probable
that Shakespeare wrote Macbeth, but very improbable that Bacon did, then
one should presumably regard it as very improbable that Shakespeare is
Bacon. But it does not seem to follow that Shakespeare is not Bacon. 

These remarks only hold if the relevant notion of probability is
subjective probability, as it obviously must be, since no sense is to be
made of its being *objectively* probable or improbable that Shakespeare
is Bacon. Either he is or he isn't. And if it is objective probability
that is in question, in some particular case, then Leibniz's Law seems
to hold. If, because of his previous exposure to Kryptonite, it is
likely that Superman will develop some form of cancer, then it is also
likely that Clark Kent will develop some form of cancer, because Clark
is Superman.

Richard Heck