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: > "complete" means "entire", "lacking nothing". Then I don't see how "complete" implies finite. > thereīs a relativistic problem with regard to > astronomical synchronicity due the finite speed of light I agree that problem is not relevant. > By that Iīve meant the "universal here and now", ie the totality of > cosmic presence, not only the place where Iīm sitting right now. > [..] my current toothache is somehow privileged compared with the > memory of the past one I had last year Your toothache last year was privileged last year; your toothache this year is privileged this year. Neither year is privileged over the other. There is no privileged moment or "universal now". Every moment is a "now" to the mental events with which it is concurrent. > I believe youīre incorrect in claiming that past events themselves > are currently exerting an influence on us from the past I didn't claim that. I claim that if one event A is considered to have (in an atemporal tense and not present tense, since we are defining past/present/future here) a direct or indirect influence on another event B, then A is "in the past" of B. > past events themselves - qua being no longer existent - are > no longer causally "active". You again here assume that there is a privileged "universal now" which defines some tiny privileged set of events as "existent" and all others not. The contrary "B-series" analysis of time is that all events are equally "existent", and that past/present/ future have meaning only with respect to particular events. The notion of a "universal now" effectively (and unparsimoniously) assumes some second and separate dimension of time. To say that the year 2002 is happening in the "universal now" (instead of just saying that 2002 happens in 2002) is to assume that the "universal now" indexes along a distinct series of "nows". If the "universal now" just indexes along the usual series of events, then it adds nothing to the picture because that series is already ordered and the notion of "present" can already defined for it, independently of any "universal now". If instead the "universal now" indexes along a distinct series of "nows", then we could never know that the "next" "now" will be 2003 instead of (say) 1965, because any given time will always seem to be its own "universal now" with a past and future defined by causality instead of by next-ness in the series of "nows". > Itīs absolutely misleading to say "that past events > are currently exerting a current influence on us" I didn't say that. When you want to say what I said, type a quote mark, paste in my text, and then type another quote mark. > Identifying past events with their current effects > or consequences is illegitimate! I don't "identify" events with the other events they influence. I simply order events by their potential to influence each other. > In an illogical wonderland where actually infinite things dwell the > illogical has its own logic. Accordingly, an actually infinitely long > wonderland table would, qua being actually infinite, ie having a > beginning an an end, very well be walkable. No, that's a flat contradiction between the notions of "infinitely long" and "walkable" -- i.e. a completable walk. Saying "the illogical has its own logic" cannot change the fact that you are flatly contradicting yourself. > Of course, thatīs an > illustration ad absurdum and thatīs exactly the way I intended it to > be since I wanted to show you that imagining the actually infinite > does indeed lead to nothing but ficticious absurdities. You're the one assuming an infinitely long table is walkable, not me. Your assumption leads to absurdity; none of mine do. > the set S=(all people taller than 6 feet) is complete if > its extension actually comprises all people possessing this property > such that S=(person 1, p 2, ..., p n). The set S=(all natural numbers) > is complete if its extension actually comprises every natural number > such that S=(1,2,3, ...). If you just define "complete" as "comprising all" of the relevant items, then "complete" does not imply finiteness. > > If by "complete" you mean having a definite (i.e. finite) number > > of members or having a last member, then of course this is impossible > > by the definition of "natural number". > > Therefore, there is no actually infinite set! if you define "actual" as "complete", and "complete" as "finite", then you've just defined "actual" as "finite", and are (once again) simply restating your premise instead of demonstrating it. > An incompletable set can > impossibly be a complete whole containing every single possible > natural number as an actual element and so any infinite set itself > canīt be actual either. Since by "incompletable" you obviously mean "not having a last member", you are (once again) simply defining that you are right instead of demonstrating it. > There you have the contradiction again youīve been asking me for so > many times. Sorry, but if you could demonstrate such a contradiction, you'd be famous for having resolved the problem of whether there can be an actual infinity. -- brian@holtz.org http://humanknowledge.net