Suppose that a beginningless universe is metaphysical possible. With this assumption in mind, it may still be shown that it is irrational to believe in such a universe.

1. If the universe is beginningless, then its past is infinite. (Premise)

2. An infinite past yields infinitely-many actualities. (Premise)

3. If there are infinitely-many actualities, then it is epistemically impossible to weigh any probability. (Premise)

4. Probability can be epistemically weighed. (Premise)

5. Therefore, it is irrational to believe in an infinite universe. (From 1 - 4)

The logic of the argument as stated is pretty loose, but one can follow the reasoning of the premises to the conclusion fairly naturally, I think. (1) is obviously true, and (2) is almost entirely uncontroversial. (4) must be true in order for probability and induction to survive, and these principles are indispensable toward rationality. This leaves us with (3).

Imagine the lines of evidence both for and against a beginningless universe. Further, imagine that the evidence on both sides is inexhaustible. We can represent the evidence for a beginningless universe with the set of all odd numbers {1, 2, 3, . . . n}, and the evidence against a beginningless universe with the set of all even numbers {2, 4, 6, . . . 2n}. This scenario should be expected, given the existence of infinitely-many actualities.

But if this is the case, how can the probability of either hypothesis be reasonably assessed? For every line of evidence for a beginningless universe, there is an equally strong line of evidence against it. Yet, we all know that the probability of a hypothesis can be reasonably assessed. If this is correct, then it follows that it is inconsistent with probability for there to be infinitely-many actualities to take into account. Because of the epistemic warrant for probability, then, it seems that the rejection of infinitely-many actualities, and therefore a beginningless universe, is preferable.

## Friday, September 16, 2011

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ReplyDelete2. An infinite past yields infinitely-many actualities. (Premise)"I suspect that among those infinitely-many actualities would be an infinity of matter and an infinity of space.

That one of those possibilites be actual, but not the other, does not seem to accord with what we observe (and one of which seems absurd):

1) an infinite volume-measure of matter packed into a finite volume-container of space;

2) an infinite distance-measure of space separating each bit of matter of a finite volume of matter.

That both of those possibilites be actual seems to imply the we should observe BOTH simultaneously:

1) an infinite volume-measure of matter occupying every infinite volume-container of space;

2) an infinite distance-measure of space separating each bit of mater of an infinite volume of matter.

[the WV for that post was "packbox"; can it get any better than that?]

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