From: Brian Holtz [brian@holtz.org]
Sent: Friday, April 26, 2002 8:05 AM
To: alt.atheism.moderated
Subject: Re: finite number of sentences

"Paul Holbach" <paulholbachSPAMBAN@freenet.de> wrote:

> > If an infinite progress is not self-contradictory, then
> > neither is an infinite regress.
>
> But you cannot count from *-inf* upward to 0.

Saying that there has been an infinite regress of time is
not the same thing as saying it's possible to "count from
negative infinity to zero".

> > > By the way, does the principle of commutativity hold good for an
> > > infinite series? Is (1+1/2+1/3+ ... )=( ... +1/n+ ... + 1/3+1/2+1) ?
> >
> > I would assume so.
>
> "of course, we cannot write the sum in reverse, beginning with
> the last term and ending with the first, because there is no
> last term."

Writing the sum in reverse is exactly what you tried to do above.

> > No, I don't have to "explicitly describe" how something is
> > physically possible to claim that it is not metaphysically
> > impossible. Nor do I have to "explicitly describe" how
> > something is metaphysically possible to claim that it is
> > not logically impossible.
>
> Well, some further description would bestow some more plausibility
> upon your claim...

What needs some plausibility bestowed is your claim of
logical impossibility in the absence of a demonstration of
logical possibility. :-) My claim of such an absence is 100%
plausible.

> I need to qualify my claim that logical
> possibility per se entails metaphysical possibility because
> there are cases where it does so and cases where it doesn愒.

I agree they are not the same thing.

> > it does *not* "go against the grain of everything
> > we know about" logical possibility.
>
> OK, if that愀 the only thing you want to be granted.

Logical possibility (of actual infinitudes) is indeed the issue here.

> You don愒 seem to be too interested in knowing the way
> things actually are.

I am very much interested in "the way things actually are" -- i.e.
truth. One truth in particular that I find interesting is
"actual infinitudes have not been shown to be logically
impossible". This statement is very much a description of
"the way things actually are".

> Sheer logical possibilities appear to rank much higher to you
> than any other kind of possibility, let alone actualities.

Logical possibility is indeed the most inclusive kind of
possibility, but this simple fact does not represent
a value judgment of mine.

> from staring at sheer logical possibility alone we don愒
> learn very much about the world.

Did I ever say otherwise?

> By the way, as a consequence of our debate and my current study of
> relevant texts (especially Cantor愀 ones) I惴 prepared to acknowledge
> a partial defeat and to qualify my "fundamentalistic" opinion about
> "actual infinity" in the following way:
> It is not true that there can impossibly be any coherent context
> within which the semantic employment of "being actually infinite" is
> not automatically - that is per se - rendered self-contradictory.

Right; if it were otherwise, this issue would already have been
so settled that it would not have occurred to anyone to dispute
the logical impossibility of actual infinitudes.

> its relative logicality does not imply
> that there is anything actual which is possibly actually infinite

If you mean "logical possibility does not imply physical possibility"
I of course agree.  If you mean "logical possibility does not
imply actual possibility" then whether I agree or not depends
on what you mean by 'actual possibility'.

> I惴 still very doubtful about
> any concrete possibility of anything actually infinite

At the risk of starting a whole new debate, I see no reason to
agree that actual infinitude is not physically possible.  Indeed,
it's AFAIK still an open question as to whether the universe is
of infinite size.

> What could those sets larger than aleph-1 possibly refer to?

See Paul's recent answer.
--
brian@holtz.org
http://humanknowledge.net