From: Brian Holtz [brian@holtz.org] Sent: Friday, March 29, 2002 9:26 AM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote > I´m still firmly > convinced that "actually infinite" is an illogical and thereby unreal > property as far as multitudes, ie numbers of things and set elements, Yes, but you are only convinced of this because you define 'actual' to mean finite: actual -> complete -> finite. > you have actually managed to make me somewhat uncertain > concerning magnitudes, ie quantitative physical properties > [..] such as density, mass, energy, weight and so forth. Interestingly, my intuition is the opposite. I consider it intuitively crystal-clear that there is nothing illogical about not actually being able to ever finish traveling a distance or counting a multitude. Not being able to ever finish measuring a magnitude seems a little stranger, because finite magnitudes are essentially measured "all at once", whereas any non-trivial finite distance or multitude has to be handled incrementally. > [magnitudes] can be successfully > counterattacked from my finitist point of view This is because of you define actual/complete as "here and now", and are appealing to an illicit intuition derived from the fact that we can only experience a finite local "here and now" (despite your claim to generalize to the "universal here and now"). It's indeed more naively intuitive that an infinite magnitude could be "here and now", but again: these naive intuitions simply aren't accounting for the actual definition of 'infinite' as "having no end" or "being more than any quantity N". > we would never be able to ascertain such a fact empirically by > means of measurement or any other direct or indirect method. We couldn't conclusively verify an actual infinity, but we could take successive measurements that would tend to reinforce our suspicion of the actual infinity, which of course would at all times remain eminently falsifiable. -- brian@holtz.org http://humanknowledge.net