"WM" <email@example.com> wrote in message news:firstname.lastname@example.org... > > The fact that some discrete items might lack a determinate number, > this being connected with the possibility of them being given as a > complete whole, was, of course, the traditional, Aristotelian point of > view, which Intuitionists, more recently, have still held to. But many > others now doubt this fact. Is there any way to show that Aristotle > was right? I believe there is.
> > For when discrete items do clearly collect into a further individual, > and we have a finite set, then we determine the number in that set by > counting. But what process will determine what the number is, in any > other case?
by counting, or not counting, which do you think ?
> The newly revealed independence of the Continuum > Hypothesis shows there is no way to determine the number in certain > well known infinite sets. [...]
if it was infinite, than you could not determine the number, right ?
>The key question therefore is: if > there is a determinate number of natural numbers, then by what process > is it determined?
you have cart before horse.
> Replacing 'the number of natural numbers' with > 'Aleph zero' does not make its reference any more determinate.
no, Aleph wont like that.
> The > natural numbers can be put into one-one correspondence with the even > numbers, it is well known, but does that settle that they have the > same number?