| | Jon,
First of all, please forgive me for addressing you as "John." I'm getting old and senile, and names are the first thing to go. :)
You write, We can be sure that only a finite number of motions, events, may occur given a finite number of entities and a finite duration. We do not have to surrender to ‘there is no answer’ just because motion is relative to a frame of reference. From the assumption that the number of entities is finite, we know that a finite number of observers exist and therefore a finite number of frames of reference. Different observers will record fewer or more motions, but we can still be sure that if we add up all their reports, we will get a finite number. The problem is, you're trying to say that within a finite period of time, there is a specific number of events in the universe, and you can't say that. Since motion is relative to a frame of reference, the best you can do is to say that within a finite time and from a particular frame of reference, there is a specific number of events. But you can't add the numbers from different frames of reference, because you'd be adding incommensurables. That which is in motion from one frame of reference is not in motion from another, so you couldn't add the two motions or events, unless both were considered to be events from a third frame of reference. Accordingly, in order for there to be a specific number of events in the entire universe, they would have to be events relative to a frame of reference outside the universe, and there is none, since nothing exists outside the universe. Now that all the dust has cleared, I would have to say that I haven’t changed my views on infinity at all. Okay. Then please explain to me how there can be an infinite number of events in the universe, if there is no such thing as a number that is actually infinite.
- Bill
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