Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Re: Sets and numbers
Replies: 8   Last Post: Apr 20, 2003 5:38 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Chris Menzel

Posts: 133
Registered: 12/8/04
Re: Sets and numbers
Posted: Apr 18, 2003 3:03 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.