Re: A simple question about integers

From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 09/15/04 

Date: 15 Sep 2004 05:56:59 -0700

erayo@bilkent.edu.tr (Eray Ozkural exa) wrote in message news:<fa69ae35.0409141750.5172522c@posting.google.com>...
> I *know* these simple mathematical facts. A 16-year old can easily
> understand them, I think. The skepticism in the question "Are
> there...?" is simply role playing, to quote a question that was
> brought to me in the course of a discussion.

OK, but you asked for some intuition. I'm trying to convey
mine.

> There are two people. I want to tell these people what I think about
> the continuum hypothesis. I find out that they do not know the
> difference between countable infinity and uncountable infinity, so I
> start telling them about Cantor and how he proved the distinction.

That's a difficult one, but it seems you have an even bigger
hurdle with these people, the explanation for how there can
be no upper bound on the integers, which are all finite.

> Using spoken language, without using any writing, I can't manage to
> tell this to them over a coffee table, because one of them raises
> valid looking philosophical objections.

I'm no philosopher. I enjoyed philosophy classes in college,
but on the internet when I get into discussions with self-
styled "philosophers" I tend to get into the same kind of
banging-head-on-table frustration that you seem to be having.
Reading below, I don't see these arguments as "valid looking".
They are silly semantical games. Semantics is not mathematics,
nor is it philosophy.

> I can't argue past these
> objections without being dogmatic like Robin the "thickhead"

You are in a mathematics forum, talking to mathematicians. It's
really silly to complain that a mathematician discussing
mathematics is being rigorous. That's what mathematics is.

> > Let K be an integer. Is K "unbounded"? No. K has a fixed number of digits.
>
> Maybe you appreciate it, but my friend makes a *philosophical*
> objection to this kind of statement. He said, "look, when you make a
> definition like that you are limiting infinity, a concept which by its
> very nature, cannot be limited.".

That makes no sense to me. A concept which by its very nature
can't be limited? He's saying that the word "infinity" unlike
any other word, can't be assigned a meaning?

Sorry, it describes unlimited things, but the word itself
is not "by it's very nature" vague and fuzzy and impossible
to pin down.

But if he wants to say that "infinity by its very nature"
is undefinable, then it's pretty obvious that something that
has no definition has no properties either. End of
discussion.

Good luck.

            - Randy

Relevant Pages

  • Re: Metaphysics of Potential Infinity
    ... >> My clarification of the distinction does not mean to undermine the ... We are talking about the concept of infinity. ... instance in philosophy of computation, or philosophy of mind, or ... philosophy of mathematics. ...
    (comp.theory)
  • Re: Metaphysics of Potential Infinity
    ... >> My clarification of the distinction does not mean to undermine the ... We are talking about the concept of infinity. ... instance in philosophy of computation, or philosophy of mind, or ... philosophy of mathematics. ...
    (sci.logic)
  • Re: NW vs. infinity
    ... philosophy is due to the requirements placed upon a body of knowledge ... Mathematics used to have no concept of infinity. ... trumpet his ignorance of the facts. ...
    (sci.logic)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... agree with the received view in philosophy of mathematics, ... > idea of size and infinity this seems intuitive. ... > of cardinality has immediate consequences is the fact the cardinality ...
    (comp.theory)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... agree with the received view in philosophy of mathematics, ... > idea of size and infinity this seems intuitive. ... > of cardinality has immediate consequences is the fact the cardinality ...
    (sci.math)