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Author  Topic: Big Bang or Big Dud? A study of Cosmology and Cosmogony  Origins  
forgiven Inactive Member 
quote: this is interesting, i have to read more about it... but tell me, how does it jive with the 'actual infinite vs. potential infinite' problem? iow, without using magical numbers how is it we find ourselves here and now if an infinite sequence of past events can be traversed?


forgiven Inactive Member 
quote: ok, let's assume time began (as you say above) with bb... from that very moment, time began... each subsequent moment resulted in an event... using just our history, for example, we know the gettysburg address was written in a certain time, magna carta an earlier time, etc, etc now we can see a sequence of past events, correct? and theoretically, given your statement that time 'began to exist', we should be able to traverse these past events (after all, if you can cross them coming forward you can do the same going backwards) *but*.. if the universe (which includes this very time of which we speak) is infinite, it's impossible to traverse the series of past events unless we use make believe numbers... and if we can't traverse a series of events going backwards, they can't be traversed coming forward... that means we'd never have reached this present event, the one we're obviously at so my comment was meant to show that an infinite universe can't exist (without those imaginary numbers)


forgiven Inactive Member 
quote: whew!! joz objects to imaginary numbers, preferring make believe, you object to make believe, preferring imaginary... sheesh... yes, the use of i as the square root of 1 has applications, i don't deny that... but in the actually existing universe, the one in which we find ourselves, we'd never be here if that universe is *actually* infinite, and it can be shown that it is actually infinite only by using make believe time resulting from make believe numbers... substitute imaginary if you want, that's fine with me


forgiven Inactive Member 
quote: i'm not sure it is a possibility... but by so assuming you seem to be saying that you can increase the number of infinite things by subsequent addition... if a set of "things" can be increased by addition, the set is potentially infinite but not actually so... see the difference? also i'm not quite clear on how a set can be infinite in one direction only, maybe you can explain this to me take an infinite number of boxes containing playing cards... each box contains, in order, 52 cards containing all 4 suits, 52 spades, 52 hearts, 52 diamonds, 52 clubs... now let's continue this series and keep the boxes in the same relative order... if the sum total of those boxes is actually infinite, each containing hearts only would equal each containing clubs which in turn equal the sum total of ALL of the boxes...
quote: i think one of the best examples i've seen concerns an infinite set of dominoes, one of which has a big red 'X' painted on it... all are standing on end... some cause (dare we call it a first cause?) started the dominoes falling... if the set is actually infinite, there would never be a time when the one with the 'X' would be struck... in the same vein, if the universe is actually infinite, we would never be here.. *this* point in space/time would not have been traversed
quote: i grant its usefulness, even its validity, ok? all i'm arguing against is using imaginary numbers to form imaginary time, because there's no basis in reality for assuming it solves any of the problems inherent in an actual infinite


forgiven Inactive Member 
quote: right... potentially but not actually infinite... no, i've followed your posts and i know you don't play semantical games... neither do i, 'least not on purpose... as actual infinite would be something that has always existed, unbounded by space and time, and uncaused (not contingent) by definition... as to whether or such a thing can exist, we're looking at that now in 'one step at a time' thread
quote: ok, a set containing an infinite number of these boxes
quote: the point i was trying to make is, with a set of actually infinite "things," one in which both the individual things and the set itself are infinite, nothing can be added to or taken away... so the total of all individual things within the set would be the same as the total of all things collectively in the set... just an attempt to show that an actually infinite can't exist in space/time else no one event would be traversed
quote: actually it isn't easy to see how that point was reached, or that it's even reachable... the moment we begin counting "1, 2, 3..." we're attempting to add to an infinite set, and such a point can't be reached by either subsequent addition or subtraction.. your examples are ones of potential infinities, and that exists in real time
quote: lol who can? the man's a certifiable genius, so his concepts can't be dismissed out of hand by anyone, least of all me


forgiven Inactive Member 
quote: the reason is, there's an infinite number preceding 'Y' just as there is between 'Y' and 'X'... if any one domino (or deck of cards or universes or whatever) can't be reached, none can... an infinite number precede 'Y', an infinite number precede 'X'... imagine alternating numbers '1' and '2' painted on the side of each... the total number of the dominoes with '1' on the side is exactly the same as the total number with '2' on the side... not only that, the total number of those with '1' on the side is *also* the total number of the ones with both '1' AND '2' on their sides... hey, i just thought of this... do a search for 'hilbert's hotel' when you have time... shows the problem when dealing with an actual infinite better than i can


forgiven Inactive Member 
quote: yes, impossible since we're here and now and we've obviously traversed time events by subsequent addition... i guess i'm saying that using imaginary numbers to create imaginary time to show an actual infinite isn't an application of the use of such numbers that has any merit in the real world, since we end up in the same quandry we began with... that being, we're still in a universe in which a potential, but not actual, infinite exists all it does is push everything away from that point in nontime when bb occurred by making all preceding nontimes into actual infinites, yet at some point we magically cross over from imaginary time into real time... at this point, we leave infinity and are able to traverse time events by subsequent addition... so no matter how we do it, at some point in the chain we're in an actual infinite from which we should never even reach bb, much less now


forgiven Inactive Member 
quote: i don't know... also, i'm not sure if proving the existence of the number 3 is the same time as *traversing* it... see what i mean? even if we can prove the existence of the domino with the red 'X' on it, we'd still have the problem of ever reaching it while playing some cosmic game of knock over the dominoes


forgiven Inactive Member 
quote: eventually i hope to reach that, yes... in the other thread i'm trying to show that, given the existence of *something*, some thing has always existed... once that's established or granted or intuited or whatever, i want to move on to whether or not this always existent thing is (or can be) the universe (which includes time as well as space)... so the (at least to my mind) logical impossibility of an actual infinity existing plays a big role to my thinking, it doesn't really matter whether one says the universe has always existed or whether one says an infinite series of inflation/deflation has occurred... the same problems present themselves


forgiven Inactive Member 
quote: no john, you haven't... your arm traversed a potentially infinite number of points but not an actually infinite number... the fact that it arrived at *this* point proves that


forgiven Inactive Member 
quote: ummmm no actually i'm not wrong... your post concerns actual infinity, and to show i'm wrong you have to show how any one point can be traversed in an actual infinity... i take it you understand hilbert's hotel? if you do, where is it in error?


forgiven Inactive Member 
quote: you're pretty much right on p.e. except i wasn't anywhere near anything past (1)... i know and don't argue the conclusion you posted (God being the cause) for the simple reason that someone *might* say "well i agree with everything but i think instead of God it was a pink unicorn" *grin* the actual infinite is important insofar as it at least stops irrational arguments as to some eternal nature of the universe... however, i'm attempting to show in another thread that *something* is in fact eternal... whether or not that leads to the k.c.a. remains to be seen... it's enough for me, at this time, to have a rational discussion on the things i'm posting, one step at a time as for your objection to #2, you'll have to help me here... when you say 'quantum reality' are you in fact assuming quantum particles "popping" into space/time uncaused and previously nonexistent? if so, i don't see how that alone defeats premiss #2.. it rests on a supposition that's simply unproven (maybe even unproveable)


forgiven Inactive Member 
quote: reading it now john, if i see anything to comment on i'll get back to you... in the meantime, quentin smith is one of my favorite whipping boys


forgiven Inactive Member 
smith, in the link you gave, didn't really touch on craig's argument... here's the relevant quote:
"The collection of past events at r is a proper subset of the collection of past events at 12. Craig feels that the equivalence between an infinite set and a proper subset of that set as applied to real things and events is just not believable (p. 86). It is only unbelievable, however, if one presupposes erroneously that the definition of an infinite set of real things or events is the same as the definition of a finite set of real things or events; namely, that a set necessarily has more things or events belonging to it than any proper subset of itself. if one does not make this false presupposition, then the equivalence in question is perfectly believable." the truth is, craig's argument is not based on the above, but on the impossibility of actually traversing an actual infinite... by offering "...a set necessarily has more things or events belonging to it than any proper subset of itself.." as a definition craig uses in support of his argument, smith misstates the case... craig, in many places and in numerous ways, has said in fact the opposite... in a library containing an actually infinite number of books, any subset of such books (being equally infinite in number), when added together, would equal not only any other subset but also the totality of all books in all subsets if you have an infinite number of science books, of coloring books, of westerns, of mysteries, the sumtotal of each individual "subset" is the same as the sumtotal of all subsets... this is simply the nature of an actually infinite number of things translating that to the argument smith is making re: time, craig and others have put it simply... if the universe is actually infinite, time itself is actually infinite... if time is actually infinite, the set of past events is actually infinite... however, subsequent subtraction of past events is impossible in an actual infinite to go from the signing of the declaration of independence, backwards, traversing every noteworthy occurance in past history, and arriving at the signing of the magna carta, would prove that past events *can* be traversed... if that can be shown, it follows that actual infinity has no place in the real world, else we'd never have arrived at *this* place in *this* time


forgiven Inactive Member 
quote: don't think so john... not only are the members of each subset infinite, the sumtotal of every subset itself is infinite... not only does the sumtotal of all mystery books equal the sumtotal of all cook books, the sumtotal of both those sets equals the sumtotal of all sets... now we can equivocate on the terms, we can say "an infinite number of sets of books exist in which a finite number of cookbooks make up a subset," which is what i think you're doing here... what that would mean is, we find ourselves in a universe of space/time in which a potentially infinte series of past events exist, and this potentially infinite series is itself a subset of an actually infinite etc etc etc... where does potential infinity end and actual begin? our universe is a closed system of space/time in which all past events can be traversed by subsequent subtraction, making it ~actually infinite by definition
quote: smith attempts a similar line, but his arguments have always been unconvincing to me... but imagine you are inside this library with the actually infinite number of books... you happen to be looking for one specific book, probably plantinga's 3 volume set *grin*... you know it's in the philosophy section (subset) of the library... you have an infinite (actually) amount of time to both find and read the books, so you start your journey.... not only would you never reach those books, you'd never reach the subset that contained them, nor would you ever traverse each point inside whatever subset you happen to start... that isn't a really good analogy, hilbert's hotel, aristotle's stadium, and the guy who takes a year to write about each day of his life are better (tho smith attempts to show this one is wrong, his argument has been rebutted in several places)



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