From: Brian Holtz [brian@holtz.org] Sent: Friday, April 26, 2002 8:05 AM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote: > > If an infinite progress is not self-contradictory, then > > neither is an infinite regress. > > But you cannot count from *-inf* upward to 0. Saying that there has been an infinite regress of time is not the same thing as saying it's possible to "count from negative infinity to zero". > > > By the way, does the principle of commutativity hold good for an > > > infinite series? Is (1+1/2+1/3+ ... )=( ... +1/n+ ... + 1/3+1/2+1) ? > > > > I would assume so. > > "of course, we cannot write the sum in reverse, beginning with > the last term and ending with the first, because there is no > last term." Writing the sum in reverse is exactly what you tried to do above. > > No, I don't have to "explicitly describe" how something is > > physically possible to claim that it is not metaphysically > > impossible. Nor do I have to "explicitly describe" how > > something is metaphysically possible to claim that it is > > not logically impossible. > > Well, some further description would bestow some more plausibility > upon your claim... What needs some plausibility bestowed is your claim of logical impossibility in the absence of a demonstration of logical possibility. :-) My claim of such an absence is 100% plausible. > I need to qualify my claim that logical > possibility per se entails metaphysical possibility because > there are cases where it does so and cases where it doesnīt. I agree they are not the same thing. > > it does *not* "go against the grain of everything > > we know about" logical possibility. > > OK, if thatīs the only thing you want to be granted. Logical possibility (of actual infinitudes) is indeed the issue here. > You donīt seem to be too interested in knowing the way > things actually are. I am very much interested in "the way things actually are" -- i.e. truth. One truth in particular that I find interesting is "actual infinitudes have not been shown to be logically impossible". This statement is very much a description of "the way things actually are". > Sheer logical possibilities appear to rank much higher to you > than any other kind of possibility, let alone actualities. Logical possibility is indeed the most inclusive kind of possibility, but this simple fact does not represent a value judgment of mine. > from staring at sheer logical possibility alone we donīt > learn very much about the world. Did I ever say otherwise? > By the way, as a consequence of our debate and my current study of > relevant texts (especially Cantorīs ones) Iīm prepared to acknowledge > a partial defeat and to qualify my "fundamentalistic" opinion about > "actual infinity" in the following way: > It is not true that there can impossibly be any coherent context > within which the semantic employment of "being actually infinite" is > not automatically - that is per se - rendered self-contradictory. Right; if it were otherwise, this issue would already have been so settled that it would not have occurred to anyone to dispute the logical impossibility of actual infinitudes. > its relative logicality does not imply > that there is anything actual which is possibly actually infinite If you mean "logical possibility does not imply physical possibility" I of course agree. If you mean "logical possibility does not imply actual possibility" then whether I agree or not depends on what you mean by 'actual possibility'. > Iīm still very doubtful about > any concrete possibility of anything actually infinite At the risk of starting a whole new debate, I see no reason to agree that actual infinitude is not physically possible. Indeed, it's AFAIK still an open question as to whether the universe is of infinite size. > What could those sets larger than aleph-1 possibly refer to? See Paul's recent answer. -- brian@holtz.org http://humanknowledge.net