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" wrote > another non-metaphysical argument against the assumption that > there actually are infinitely many stars and that the universe is > actually infinitely large I don't defend either assumption, and in fact think both are probably false. What I defend is the claim that neither assumption is logically self-contradictory. > Can an infinitely large universe stretch out eternally into ever > larger infinities? Well, I think thatīs blatantly absurd. I'm not sure about "larger infinities", but it hardly seems absurd that an infinitely large universe could nevertheless be observed to be expanding. > you can indeed add new elements to an > infinite set (see Hilbertīs hotel), but that doesnīt change the > cardinality of the infinite set at all: aleph-0+n=aleph-0 ! > Transferring this to the real universe would lead to the absurd > consequence that if our universe were actually infinite, it would > nevertheless expand eternally without ever becoming larger. That depends on your definition of "larger". It certainly would not increase in the cardinality of the set of all its unit volumes, but that doesn't mean it couldn't expand. -- brian@holtz.org http://humanknowledge.net