On 18 Apr 2003 08:54:53 -0700, George Dance <firstname.lastname@example.org> said: > Chris Menzel) wrote ... > > On 17 Apr 2003 10:33:19 -0700, George Dance <email@example.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.