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Re: Sets and numbers
Posted:
Apr 18, 2003 3:03 PM
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On 18 Apr 2003 08:54:53 -0700, George Dance <georgedance@hotmail.com> said:
> Chris Menzel) wrote ...
> > On 17 Apr 2003 10:33:19 -0700, George Dance <georgedance@hotmail.com> said:
> > ...
> > > If he writes it down by using a numeral, .. one could say the 'idea'
> > > is there in the numeral as well.
> >
> > One could, if one wanted to sound foolish.
>
> I don't think it's that foolish to say that, if I read the numeral 2
> and then have the concept of 'two,' I got the concept from reading the
> numeral.
Because of representational conventions you learned elsewhere, not
because the number is "in" the numeral in any plausible sense.
> > > What about the natural numbers that no one has ever thought of?
> >
> > They have not been thought of. Just as there are blades of grass in the
> > arctic tundra no one has thought of.
>
> Well, we do know where those blades of grass are (in spatio-temporal
> reality).
Similarly with numbers. They are nowhere.
> > > But where are all those other natural numbers, of which neither of the
> > > above conditions is true? In what sort of non-spatial, non-temporal
> > > reality do you you believe that these numbers exist?
> >
> > The sort appropriate to numbers and other varieties of abstract entities
> > whose existence seems required by our beliefs but which do not have
> > spatio-temporal locations, of course.
>
> It sounds as if you're saying that, if I have a belief that requires
> some object to exist (for the belief to be true), then it must be the
> case that that object exists (and therefore the belief is true).
If I were, I would be saying something profoundly stupid. Mighty
uncharitable of you. I was saying only that certain of our beliefs
involve reference to numbers, and hence that it appears that numbers
must exist if those beliefs are to be considered true.
> That hardly sounds like an 'of course' answer to me.
The "of course" had to do with the sort of existence the numbers must
possess: the sort appropriate to numbers (and other abstracta), of
course.
> Certainly if someone offered that to me as a proof that God exists ("I
> believe that God exists, and if he didn't I wouldn't have that belief;
> therefore God exists") I would say more than 'oh, of course.'
So would I. But of course your observation here has nothing whatever to
do with what I said.
Chris Menzel
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