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) and I would like this thread to be cleaner. 8)
Don't worry about itHughDP wrote:I turned my nose up at this one for the totally unscientific reason of just not feeling comfortable with it (an infinity within an infinity etc.)
. The concept of infinity is always a difficult one for anyone to get their head around, which is of course the point of Kant's first antimony (as I said before).This is a bit of a fallacy. For example you could say that the set of integers is infinite and includes every possible number (note that each one occurs only once, not an infinite number of times). If I removed every integer which was divisible by 9, the set would still be infinite but no number divisible by 9 has ever occurred.HughDP wrote:So if we accept an infinite past...everything that could possibly happen has already happened an infinite number of times.
I can see that, but I'm not sure how that translates when we apply it to temporally sequenced events. Given an infinite regression of causes in infinite time, restricted only by the laws of physics, I would still suggest that everything that can happen already has happened an infinite amount of times.OccamsRazor wrote:This is a bit of a fallacy. For example you could say that the set of integers is infinite and includes every possible number (note that each one occurs only once, not an infinite number of times). If I removed every integer which was divisible by 9, the set would still be infinite but no number divisible by 9 has ever occurred.HughDP wrote:So if we accept an infinite past...everything that could possibly happen has already happened an infinite number of times.
I believe Vilenkin (et al.) have actually made a similar argument.HughDP wrote:I can see that, but I'm not sure how that translates when we apply it to temporally sequenced events. Given an infinite regression of causes in infinite time, restricted only by the laws of physics, I would still suggest that everything that can happen already has happened an infinite amount of times. Or have I missed something?
HughDP wrote:I can see that, but I'm not sure how that translates when we apply it to temporally sequenced events. Given an infinite regression of causes in infinite time, restricted only by the laws of physics, I would still suggest that everything that can happen already has happened an infinite amount of times.
The hypothesis made by Knobe, Olum & Vilenkin really refers to an infinite number parrallel universes within an infinite multiverse. They refer to the idea of branching off universes based on the different possible outcomes of Quantum events. In this case every possible outcome will have occurred.harvey1 wrote:I believe Vilenkin (et al.) have actually made a similar argument.
Agreed. What I was thinking, though, was that I understand Hugh saying that if the laws of physics did not expressively prevent particular events, then given enough time those patterns would repeat. In the case of your examples, there is a limitation on the degrees of freedom inherent in the construction of the number line, and that's why certain patterns cannot repeat. However, if there were no such restriction (e.g., a situation in the Universe that KO&V proposed), then I don't see any reason why those patterns wouldn't repeat. So, for example, pi might have a pattern of 500 zeroes all in sequence somewhere within the digits of pi, and that pattern of 500 zeroes can and possibly does repeat infinitely many times.OccamsRazor wrote:The hypothesis made by Knobe, Olum & Vilenkin really refers to an infinite number parrallel universes within an infinite multiverse. They refer to the idea of branching off universes based on the different possible outcomes of Quantum events. In this case every possible outcome will have occurred.
What would prevent the 500 zeroes repeating an infinite number of times if the numbers occurred exactly in a random configuration? I guess what I'm getting at is if the probability for 500 zeroes is remote (but not zero) for a short finite sequence, then it would seem to me to become probable for a very long finite sequence (i.e., 1 trillion digits of pi). In that case, the strong probability of a string of 500 zero occurrences would repeat every trillion digits ad infinitum. Hence, wouldn't the probability be very near 1 that the sequence would repeat an infinite number of times...?OccamsRazor wrote:Using your example a stream of 500 zeroes can possibly exist in the digits of pi and possibly can exist an infinite number of times, but likewise 500 zeroes could never exist in the line and still maintain the irrationality of pi.
Absolutely nothing. My point is that it is not a necessity that such a sequence does occur (although you may argue that it is probable).harvey1 wrote:What would prevent the 500 zeroes repeating an infinite number of times if the numbers occurred exactly in a random configuration?
But... I've never claimed that the infinite set of regressive causes must be computable in finite time. I'm afraid I still don't see why this is a requirement.harvey1 wrote:My point, though, is that your analogy of complete infinity of negative integers breaks down since a complete infinite set of causes would need to exist, but it is not possible to compute such a set.
What do you mean by "reference an event" ? I claim that it's possible to reach any specific event from any other specific event in finite time. For example, we could look at any event happening in the present, and trace a causal chain from it to the "past" and "future" events (causality-wise, not necessarily time-wise), of arbitrary length, as long as that length is finite.3) Causes must be actual events that can be referred to as occurring (i.e., if it is logically impossible to reference that event, then it cannot be a cause to an event that you can reference)
Point taken, sorry.Again, I've never claimed this. I've claimed that an infinite set of (regressive) causes cannot exist.
