Suppose:

- The past has to be finite.
- The future has to be infinite.
- The A-theory of time is true.

*N*be the number of days since the beginning of time, rounded down. Surely no one day is more likely to be objectively present than another, so

*N*is the outcome of a fair lottery with tickets numbered 0,1,2,.... But such lotteries are well known to lead to many paradoxes (e..g, see chapter 4 of Infinity, Causation and Paradox). Thus, one shouldn't hold all of (1)-(3).

Not every A-theorist has this problem: only those who accept (1) and (2) as well.

## 7 comments:

Can you please explain the statement "surely no one day is more likely to be objectively present than another"? My understanding of most A-theories is that today is the ONLY ontologically real day, and so there are no past days or future days to choose from. It can only be today.

No natural number n is more likely than another to be the current number of days from the beginning of time.

I've heard questions like this before, and I genuinely don't understand them.... It seems to me an incoherent question. If you are asking the question at 13.8 billion years after the beginning, then there is only one possible answer. It is a necessary truth that, at the point of your asking, it has been exactly that many years since the beginning. That is not contingent; it's practically tautalogous.

If the universe is objectively getting older, as the A-theory claims, then there is a contingent truth about how old it is.

Necessary truths hold always.

It is always true that the Universe is as old as it is, right? So, whenever you ask the question, it has to be exactly that old (as long as it takes to get to the point where you asked the question). So all that's left to determine is why did you ask the question then instead of earlier, and there is an obvious way to answer that in terms of a chain of causes going all the way back to the beginning, such that you could only be asking the question now.

If the universe has to be 13.8 billion years old, then it never gets older, which is absurd (and which makes the A-theory into a static theory!).

The Universe only has to be 13.8 billion years old every time you ask the question 13.8 billion years after the beginning. It has to be 14 billion years old when you ask the question again 200 million years from now.

My point is that you are only asking the question at a particular point. And the answer is always, "because you didn't ask until now". If you ask "then why did I ask now?" the answer is obviously a chain of causes (including, perhaps, Libertarian choices along the way), which is non-problematic.

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