From: Brian Holtz [brian@holtz.org] Sent: Saturday, April 13, 2002 8:14 AM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote: > So we must eventually postulate a first infinitude in order to avoid > an infinite regress. OK, what's self-contradictory about an infinite regress? You have IIRC acknowledged that time can be infinite. > > or else be uncaused -- since it seems somewhat counterintuitive > > that a finitude could cause an infinitude. > > they would indeed > have to be uncaused, that is to be existent since eternity, "Uncaused" does not imply "eternally pre-existing". > itīs not only counterintuitive but also impossible that there is an > effective way from finiteness to infinity. By "effective" you presumably mean something like "causal". 1. This doesn't rule out uncaused "ways from" finitude to infinitude, since it is logically possible that infinitude could just spontaneously arise uncaused. 2. Why is finitude causing infinitude "impossible" (and not just counter-intuitive)? If it's logically possible that an infinitude could be uncaused, it's also logically possible that a finitude could (in some bizarre counterintuitive way) cause an infinitude. > Not even the master of > infinity himself, Georg Cantor, considered this logically possible. Are you sure? If so, I presume he was restricting the "way" to certain well-defined mathematical operations. I'm not. > > But there is no obvious reason to think that > > infinitudes of any given cardinality couldn't always have > > existed. > > I have no idea how to correlate totally abstract > cardinalities larger than aleph-1=c (i.e. continuum of > real numbers) with anything real. That's not a demonstration that actual infinitudes of such cardinality are impossible. -- brian@holtz.org http://humanknowledge.net