Re: infinity

In article <MPG.1d8baf718ca536d598a24e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> William Hughes said:
> <snip>
> > > > > No, I never claimed the sum of all finite naturals "exists".
> > > >
> > > > No I suppose you didn't. You have claimed that:
> > > >
> > > > a: the sum of a finite number of finite integers is finite.
> > > >
> > > > b: there are only a finite number of finite naturals.
> > > >

> > I may or may not be interested in why you believe them. This is
> > not relevant. What is relevant is the fact that a and b imply
> > that the sum of all finite numbers exists


> b implies a,

Only in the sense that a false statement implies anything.

It is equally valid to say that b implies 1 + 1 = 5.

What would be invalid, and false, would be to say that 'a' implies 'b'.


> but knowing that a number is finite is not the same as ever being
> able to pin it down.

The issue is existence of sums, not evaluation of them.

> You cannot pin down the largest finite natural,
> but can you deny that, if in concept it existed, that it would be,
> without a doubt, finite?

Yes, I can, and do, deny that such thing as a largest natural exists, or
that the "size" of the set of naturals, is in any reasonable sense,
finite.
.

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