Friday, June 12, 2020

The A-theory and a countably infinite fair lottery

Let’s suppose that the universe has a beginning and the tensed theory of propositions (which is accepted by most A-theorists) is true. Then consider for each n the proposition dn that n days have elapsed from the beginning of the universe. This proposition is contingent on a tensed theory of propositions. Exactly one of the propositions dn is true. No one of the propositions dn is more likely to be true than any other. So, it seems, we have a countably infinite fair lottery. But such are, arguably, impossible. See Chapter 4 of my infinity book. (E.g., it’s fun to note that on the tensed theory of time we should be incredibly surprised that it’s only 13 billion years since the beginning of the universe.)

Since the universe does have a beginning (and even if it does not, we can still run the argument relative to some other event than the beginning of the universe), it seems we should reject the tensed theory of propositions.

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6 comments:

  1. Walter Van den AckerJune 13, 2020 at 2:53 AM

    Alex

    The universe cannot have a beginning if it is the creation of a timeless being.

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  2. enigManJune 14, 2020 at 3:03 PM

    This comment has been removed by the author.

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  3. enigManJune 14, 2020 at 3:05 PM

    (sorry for the deletion) Assuming only that there was some event in the past, you have to assign equal likelihoods to each counting number of days ago that it was. Those likelihoods cannot be real number valued probabilities, but therefore you seem to have an argument that likelihoods do not have to be probabilities.

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  4. Husain AlshehhiJune 14, 2020 at 9:34 PM

    Unrelated to this post, but do you mind enabling SSL on this site?

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  5. Michael GonzalezJune 17, 2020 at 1:36 PM

    Pruss: What do you mean when you say that no one of d(n) is more likely to be true?? At 13 billion years from the beginning, the d(13bil) is 100% more likely to be true than any other d(n).... Am I missing something? If it is true (truth being in the present tense, just as the sentence is in the present tense) that 13 billion years have passed since the beginning, why on Earth would any other d(n) be even sort-of likely to be true?

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  6. UnknownJune 18, 2020 at 5:18 PM

    Perhaps I'm misunderstanding something but I don't see the tensed theory of time to entail an actual infinite but a potential infinite. This would not lead to any metaphysical absurdities.

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