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Paradox of existence

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Paradox of existence

7
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Posted 05/05/08 - 01:17 AM:	#51
Here is a further point. It it's true that given an infinity of time, every possible event will occur, then for every possible event, there is a finite amount of time such that it will occur within that period of time.

reincarnated
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Posted 05/06/08 - 01:48 AM:	#52
7 wrote: I don't agree with that argument. The probability that some event will happen might be x (where x is non-zero) relative to some set of circumstances, and it might be true that if those circumstances held for an infinite period of time, then the event would inevitably occur. But why can't they hold only for a finite interval? Who says that when the interval ends, that the world will align the same way again later? That is to say, take an event e and assign it the non-zero probability x given conditions abc and 0 otherwise. Say that conditions abc obtain only for a finite amount of time. Why are we justified in assuming that given enough time, those conditions will obtain for another period sometime later? That seems to me like thinking that because 1=1 and the natural numbers are infinite, if we only go on long enough, some other number n will = 1. If probabilistic event E requires a set of circumstances abc as you suggest, then we have to go up one level and ask what is the probability of these conditions abc occuring? If the probability of abc is non-zero then there will be an infinite number of occurences of abc within any infinite timeline (infinity times any non-zero number = infinity), hence there will be an infinite number of opportunities for E to occur. 7 wrote: Maybe a concrete example will help to illustrate my point. The probability that I will grow to a height of 7 feet is non-zero. I could develop a glandular problem that causes radical growth. But once I am dead, the probability becomes 0, regardless of how far time extends past my death. In an infinite timeline there will be an infinite number of occurences of "you" 7 wrote: Here is a further point. It it's true that given an infinity of time, every possible event will occur, then for every possible event, there is a finite amount of time such that it will occur within that period of time. Incorrect. If the occurence of an event within a timeline is simply probabilistic and non-zero and less than unity, then for any finite timeline there is simply a non-zero and less than unity probability that the event will occur. For example, there is a 1/6 probability of throwing a 6 with a die. The probability that it will NOT come up 6 on any one throw is therefore 5/6. If I throw the die 100 times then the probabilty that it will NOT come up 6 on each and every one of the 100 throws is (5^100)/(6^100), which is a very small but NON-ZERO number. It doesn't matter how many times I throw the die (as long as it is a finite number of times), the probability that it will NEVER come up 6 is still non-zero. Edited by reincarnated on 05/06/08 - 01:58 AM
_____________________ �If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple.� (Stuart Burns)

7
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Posted 05/06/08 - 11:30 PM:	#53
If probabilistic event E requires a set of circumstances abc as you suggest, then we have to go up one level and ask what is the probability of these conditions abc occuring? If the probability of abc is non-zero then there will be an infinite number of occurences of abc within any infinite timeline (infinity times any non-zero number = infinity), hence there will be an infinite number of opportunities for E to occur. Yes, I understand that, but I see no reason why the probability of abc obtaining cannot be zero after a certain time. That is, if the conditions obtain, then after a period of time cease to obtain, why must the probability that they will obtain again be non-zero? That must be justified by a philosophical argument, not a probabilistic one. In an infinite timeline there will be an infinite number of occurences of "you" What reason would there be for thinking that these "occurrences" are the same person? It's not necessary to argue the point, though, because I can rephrase my comment. The probability that I will grow to a height of 7' is non-zero for the current version of my existence, but once I die and end this version, the probability that I will grow to a height of 7' during this version becomes and will remain zero, assuming that time is not circular. This proves that if the probability of an event is non-zero, it need not be true that the event will occur given infinite time. Incorrect. If the occurence of an event within a timeline is simply probabilistic and non-zero and less than unity, then for any finite timeline there is simply a non-zero and less than unity probability that the event will occur. For example, there is a 1/6 probability of throwing a 6 with a die. The probability that it will NOT come up 6 on any one throw is therefore 5/6. If I throw the die 100 times then the probabilty that it will NOT come up 6 on each and every one of the 100 throws is (5^100)/(6^100), which is a very small but NON-ZERO number. It doesn't matter how many times I throw the die (as long as it is a finite number of times), the probability that it will NEVER come up 6 is still non-zero. I agree with your objection. That point arose because I was thinking of temporal infinity in terms of numerical infinity. If you know that for some number x, f(x) = 0, but you don't know what number, you can start systematically running through the numbers one by one until you come upon one that works (call it n), which you're guaranteed to be able to do during a finite period of time. In that case, you could have found n with a bounded procedure, if you'd known what you were looking for. So I thought of searching through time until I came upon a point at which the event occurs, in which case I only needed a finite interval. However, this does not work in a non-deterministic model.

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Posted 05/06/08 - 11:47 PM:	#54
7 wrote: Yes, I understand that, but I see no reason why the probability of abc obtaining cannot be zero after a certain time. Then we must ask what is it that determines the probability of abc obtaining? Is it the rest of the physical world, or is it something magical and mysterious "outside the physical world" which determines this probability? If the former, then why does the probability of abc become zero when the configuration of the rest of the physical world on which it supervenes is repeated an infinite number of times? If the latter then - good luck. 7 wrote: What reason would there be for thinking that these "occurrences" are the same person? What reason would there be for thinking they are not the same person? They would be physically identical in every respect. 7 wrote: The probability that I will grow to a height of 7' is non-zero for the current version of my existence, but once I die and end this version, the probability that I will grow to a height of 7' during this version becomes and will remain zero, assuming that time is not circular. This proves that if the probability of an event is non-zero, it need not be true that the event will occur given infinite time. You are artificially restricting the timeline to a finite time, by putting in an arbitrary cutoff at the "end" of this version. It's like saying "what is the probability of finding the integer 123 in the infinite list of integers, if I restrict myself to looking at just the first 10 integers on the list"?
_____________________ �If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple.� (Stuart Burns)

7
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Posted 05/07/08 - 12:14 AM:	#55
Then we must ask what is it that determines the probability of abc obtaining? Is it the rest of the physical world, or is it something magical and mysterious "outside the physical world" which determines this probability? If the former, then why does the probability of abc become zero when the configuration of the rest of the physical world on which it supervenes is repeated an infinite number of times? If the latter then - good luck. You're shifting the argument on me. You made a positive assertion. Your claim is that if conditions abc obtain, then cease to obtain, the probability that they will obtain again is non-zero, so they will obtain again given infinite time. I should not be required to tell you why you're wrong, since you haven't said why you're right. Why is it that if circumstances obtain, the probability that they will obtain again is non-zero? You are artificially restricting the timeline to a finite time, by putting in an arbitrary cutoff at the "end" of this version. It's like saying "what is the probability of finding the integer 123 in the infinite list of integers, if I restrict myself to looking at just the first 10 integers on the list"? That example does not clarify what is wrong with my argument. We often talk about the likelihood of events happening over a limited interval of time. For example, we might talk about the probability that a particular region of the earth will receive precipitation on the date z. This is less artificial, but it is merely a further illustration of my point. The probability of precipitation is non-zero on date z, but once date z ends, that's it. It will never be date z again. Edited by 7 on 05/07/08 - 12:22 AM

reincarnated
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Posted 05/07/08 - 12:38 AM:	#56
7 wrote: You're shifting the argument on me. You made a positive assertion. Your claim is that if conditions abc obtain, then cease to obtain, the probability that they will obtain again is non-zero, so they will obtain again given infinite time. I should not be required to tell you why you're wrong, since you haven't said why you're right. Why is it that if circumstances obtain, the probability that they will obtain again is non-zero? Its not "shifting the argument", it's called examining the logical consequences of your premises. Your premise is that the probability of abc obtaining is non-zero at some point in time, but this then becomes zero for the rest of (infinite) time some unexplained reason. I am asking you to examine the coherency of this premise. What determines the non-zero probability of abc obtaining? If this probability supervenes on the physical then in an infinite timeline the physical is repeated an infinite number of times, hence the probability that abc is non-zero is repeated an infinite number of times (that is what supervenience means). If on the other hand you say that the probability does NOT supervene on the physical then you must be advocating some form of dualism, whereby the probability of abc obtaining is determined by something magical and mysterious which is outside of the physical domain. As I said earlier, if this latter is the case then I wish you good luck. Which option would you like to choose? Does the probability of abc obtaining supervene on the physical, or does it not? 7 wrote: That example does not clarify what is wrong with my argument. We often talk about the likelihood of events happening over a limited interval of time. For example, we might talk about the probability that a particular region of the earth will receive precipitation on the date z. This is less artificial, but it is merely a further illustration of my point. The probability of precipitation is non-zero on date z, but once date z ends, that's it. It will never be date z again. Yes, it's ok to talk about the likelihood of events happening over a limited period of time, but then don't mix this up with assumptions about infinite timescales. For the purpose of your argument you must assume either an infinite timescale, or a limited timescale - you cannot assume both at the same time - which is it to be?
_____________________ �If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple.� (Stuart Burns)

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Posted 05/07/08 - 12:54 AM:	#57
Its not "shifting the argument", it's called examining the logical consequences of your premises. Your premise is that the probability of abc obtaining is non-zero at some point in time, but this then becomes zero for the rest of (infinite) time some unexplained reason. I am asking you to examine the coherency of this premise. What determines the non-zero probability of abc obtaining? If this probability supervenes on the physical then in an infinite timeline the physical is repeated an infinite number of times, hence the probability that abc is non-zero is repeated an infinite number of times (that is what supervenience means). If on the other hand you say that the probability does NOT supervene on the physical then you must be advocating some form of dualism, whereby the probability of abc obtaining is determined by something magical and mysterious which is outside of the physical domain. As I said earlier, if this latter is the case then I wish you good luck. Which option would you like to choose? Does the probability of abc obtaining supervene on the physical, or does it not? These circumstances, and their probabilities, always supervene on the physical, broadly construed. However, depending upon the specific set of circumstances, there could be a temporal component, as in my examples. Yes, it's ok to talk about the likelihood of events happening over a limited period of time, but then don't mix this up with assumptions about infinite timescales. For the purpose of your argument you must assume either an infinite timescale, or a limited timescale - you cannot assume both at the same time - which is it to be? I am not mixing them up. I am supposing that time is infinite, but that there are finite subsets of time (or limited intervals of time). Then I index the probability of an event e to a set of circumstances, including a temporal element. Then I observe that if e's probability of occurring between the times x and y is non-zero, it hardly follows that given an infinity of time, e will happen. Event e is time-indexed, hence, after the upper bound (y) passes, e will never have another opportunity to happen. Edited by 7 on 05/07/08 - 01:02 AM

reincarnated
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Posted 05/07/08 - 01:12 AM:	#58
7 wrote: I am not mixing them up. I am supposing that time is infinite, but that there are finite subsets of time (or limited intervals of time). Then I index the probability of an event e to a set of circumstances, including a temporal element. Then I observe that if e's probability of occurring between the times x and y is non-zero, it hardly follows that given an infinity of time, e will happen. Event e is time-indexed, hence, after the upper bound (y) passes, e will never have another opportunity to happen. OK, I think we are going round in circles (is a circle an endless loop, or a finite loop?). This suggested "time-indexing" is just another way of saying "we will consider only a finite subset of time from the infinite set of time". Just as in my earlier example of the probability finding the integer 123, we need to dsecide whether we will look for this integer in the infinite set of integers, or in a finite subset of that infinite set. The answer we get obviously depends on what set we choose. If we choose to look only in a finite subset, then the question whether the complete larger set is infinite or not is irrelevant. What you are suggesting is looking in a finite subset. I am not sure there is anything more to discuss?
_____________________ �If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple.� (Stuart Burns)

7
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Posted 05/07/08 - 01:42 PM:	#59
If we choose to look only in a finite subset, then the question whether the complete larger set is infinite or not is irrelevant. Indeed, that is my point. If I talk about probabilities indexed to a finite period, then it does not matter whether time is infinite or not. After the finite period is over, no amount of time will allow it to reoccur. It is a counterexample because I've given an example of an event such that: 1) at some point, the probability of the event is non-zero and 2) the event need not happen given infinite time. I believe it's a good argument, as far as it goes. The next question is, if the set of circumstances relative to which an event has a non-zero probability does not include a temporal constraint, is it possible that the event still might fail to occur given infinite time (because the circumstances fail to obtain ever again)? It is not so easy for me to formulate a counterexample for that one. In fact, I am inclined to believe that there can be no such counterexample, but no argument is apparent to me that could establish this.

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