From: Brian Holtz [brian@holtz.org] Sent: Wednesday, March 13, 2002 8:27 AM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote to Paul Filseth: > An actual infinity would have to be something > that is both complete and incomplete, but nothing actual can possess > contradictory properties. Furthermore, as far as not mathematical but > physical objects are concerned "infinity" mustnīt be regarded as > denoting a real quantity You seem to be regarding it as precisely that, because you seem to take it as a requirement for an actually infinite set that a count of its members must end with the quantity "infinity". More precisely, 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. > regardless of how large the universe may actually be > its size is nevertheless finite This may be a correct a posteriori statement of empirical cosmology, but it is not a correct a priori statement of metaphysics. > You can measure yourself to death and still wonīt detect an infinity. > There is no possible measuring instrument with a unit scale "1u,2u,3u, > ..., infinite u" !!! 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. "Paul Holbach" wrote to Torkel: > > for every natural number n, there are at least n > > stars in the universe. > > Iīve put "infinite" in brackets since it > certainly is no number at all. Right; infinity is not one of the "natural numbers" that he envisions ever being the value of n. > I still deny > that mathematical sets are Platonically real I agree. > or that "actually infinitely many" is factually meaningful. It's not verifiable, but it's meaningful (because it's falsifiable). > i.e. infinite mathematical sets are "just a > useful but ontologically noncommittal turn of phrase", > to adopt an expression by Quine Quine probably just meant that discussion of mathematical infinities does not commit one to the existence (or even possible existence) of actual infinities. I don't read his statement to assert that actual infinities are impossible. -- brian@holtz.org http://humanknowledge.net