From: Brian Holtz [brian@holtz.org] Sent: Wednesday, March 20, 2002 11:01 PM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote > So what is an "infinite quantity", eg an "infinite mass" then?! An infinite mass would be one that any attempt to measure (by comparison to increasingly larger finite masses) would never end. > I think I have already given sufficient argumentational support in > favour of my claim that actuality entails finiteness. That actuality entails finiteness is your premise. Your argument seems to consist in restating your premise. > any finite number of things must be at least theoretically > countable from thing 1 to thing n. Who here is saying that a "finite number of things" is not "theoretically countable from thing 1 to thing n"? > > > Only if there were an explicit, > > > non-self-contradictory definition of "actually infinite" > > > > Example: space or time is "actually infinite" if and only if > > it has no end. > > Thatīs a non-contradictory but fairly tautological pseudo-definition Every definition is a tautology -- by definition. > since the Latin word "infinitus" means exactly "having no end". So we > have "Something has no end if it has no end." Yes, and you seem to be asserting that "to have no end" is is obviously self-contradictory for existent things. I disagree. > Furthermore endlessness can well be assigned to potential (!) > infinity, i.e. the endless and eternal possibility of reiterating an > operation over and over again, but whenever applied to actual/real > quantities it leads astray, for quantitative concepts imply > finiteness. "Quantitative concepts imply finiteness" is a restatement of your premise. Why should we agree? > An infinite length, for instance, is no length at all > because something actually infinitely long would possess all lengths > and no length! It would possess no finite length, and would be longer than any finite length. But to assume that the only lengths are finite lengths is just to assume your premise. > Infinite dimensions are unreal! Another restatement of your premise. (Maybe type your premise in all-caps, and then we'll all finally recognize that you're right. :-) > If there were actually infinitely long things, there could eg > be two different sorts of infinitely long tables: > The first one has no beginning and no end and yet the carpenter has > fixed two legs at precisely each end. If you define a "table" as having two "ends", then an "infinitely long table" has an infinite distance between the two "ends", and it is an illicit appeal to inapplicable intuition to speak of "the carpenter" who can go from one "end" to the other in a completable journey. > The second one has a recognizable beginning and thatīs exactly where > the carpenter has fixed two legs. He then walks all along the > infinitely long table and fixes the other two legs on the other end so > that his work is eventually finished. Again, it's contrary to the definition of an infinitely long table to assume that the carpenter can finish a walk from the beginning of the table to the end. > Does this make any sense to you...?! Infinity is nowhere and you canīt > even get closer to "something" that is nowhere. This last sentence makes no sense to me. > as there is no end, where > the other two legs can be fixed, the table must remain a two-legged > cripple and, therefore, can never stand. Congratulations, you've just proved that a carpenter cannot walk far enough to put the final two legs on an infinitely long table. :-) Now, how does this rule out the possibility of an infinitely long tabletop? Or of an infinitely long table whose legs were affixed by two different carpenters? > Isnīt it crystal-clear to you that the concept of an actual infinity > is inevitably flawed and cannot be transferred to reality? No, the correctness of your premise is not crystal-clear to me, no matter how many times you restate it. :-) > Iīm expecting nothing else but a yes since youīve at least agreed with me > that nothing illogical can be real! You haven't shown that an actual infinity is illogical. Also, if this could be shown, don't you think that fact would be noted in reference works discussing infinity? It isn't. > Iīve been asking for an acceptable definition > of "actual infinity" and not of "potential infinity"! I would define an "actual infinity" as an existent infinity. Depending on your definition of "complete", including "complete" in the definition of "actual infinity" either begs the question (and thus demonstrates nothing) or leaves the question open (which is how I contend it is). > it is absolutely pointless to say that a thing is infinitely > heavy if the process of measuring its heaviness cannot end. No, that the measuring process cannot end is in fact what qualifies the thing as "infinitely heavy". > quantitative infinities are literally immeasurable in principle so > that you canīt even start the process of measuring them. You can certainly start; you just can't end. > > My point is that falsifiable statements are > > necessarily meaningful. Do you disagree? > > itīs a mistake to suppose that two or more combined lexems > always constitute a logically consistent phrase. I nowhere suppose that, and defy you to quote me otherwise. Again, your earlier denial that "'actually infinitely many' is factually meaningful" runs afoul of the principle that falsifiable statements are necessarily meaningful. "This table is actually infinitely long" is falsifiable, and thus factually meaningful. > > This seems merely to be an intuition of yours, which some people > > share, but I don't. > > Itīs not "merely" a foggy intuition Iīve experienced during a state of > mystical contemplation Strawman. I said nothing about fogginess or mystical contemplation. Intuition is a perfectly valid form of evidence in philosophical debate -- unless the intution is not shared by the person you're debating. > In fact there are some many people who reject the notion of "actual > infinity", the most prominent of whom is our old buddy Aristotle. Argument from authority. If such impresses you, then shouldn't you be devastated by the fact there doesn't seem to be a single philosophy reference work that asserts that an actual infinity is logically impossible? -- brian@holtz.org http://humanknowledge.net