From: Brian Holtz [brian@holtz.org]
Sent: Friday, March 15, 2002 6:41 PM
To: alt.atheism.moderated
Subject: Re: finite number of sentences


"Paul Holbach" <heir-of-holbach@freenet.de> wrote

> > you seem to assume that for any actual set,
> > a count of its members must be able to end.  This assumption
> > begs the question of whether an actual infinity is possible.
> [..]
> "infinity" is no possible number and no possible unit of
> measurement.

Nobody is saying it is.

> actuality indeed presupposes theoretical countability

Ah, so you *do* assume that for any actual set, a count of its
members must be able to end.  This is not an argument, but
rather a restatement of your premise.  Can you give an
argument to support it?

> If Iīm right and the whole notion of an actual infinity is
> self-contradictory

That's what I'm disputing.

> nothing illogical is real

Agreed.

> Only if there were an explicit,
> non-self-contradictory definition of "actually infinite"

Example: space or time is "actually infinite" if and only if
it has no end.

> > There are other ways to be led to the conclusion that something
> > is infinite (i.e. has no end) other than the (logically impossible!)
> > method of measuring all the way to its end.
>
> there are no ways of
> showing that something is actually infinite.

There is probably no way to verify an actual infinitude as such,
but its designation as such quite obviously can be falsified, and
thus is meaningful.

> > > > Torkel wrote:
> > > > for every natural number n, there are at least n
> > > > stars in the universe.
>
> Do you have any clue how to interpret Torkelīs sentence above with
> regard to our debate on "actual infinities"?

I interpret him as saying that there is no last star, and
thus the process of counting stars cannot end.

> > It's not verifiable, but it's meaningful (because it's falsifiable).
>
> OK, each of the words "actual", "infinite" and "many" has a
> lexicographic meaning,

That's not my point. My point is that falsifiable statements are
necessarily meaningful. Do you disagree?

> but the entire phrase "actually infinitely
> many" doesnīt denote anything logically possible.

This seems merely to be an intuition of yours, which some people
share, but I don't.

--
brian@holtz.org
http://humanknowledge.net