Existing for all times is still puzzling

Let’s assume causal finitism is false, and that the past can be infinite.

If an object pops into existence ex nihilo at a specific time t, that feels objectionably arbitrary, since we want to know why did it pop into existence then rather than earlier or later (or if it couldn’t have done that, for essentiality of origins reasons, why didn’t something just like it do that).

But if the object has existed for infinite time, that does not feel arbitrary, and some people have the intuition that the object does not call out for an explanation even if it is metaphysically contingent.

This failure to be puzzled is I think based on a mistake. For even if the object existed for an infinite time, we can ask why it didn’t exist for a longer infinite time. That question makes sense. After all, if the object existed on days ...,  − 3,  − 2,  − 1, 0, where 0 is today, then we can ask why before all those days it didn’t exist on an earlier day, one which we might denote  − ω, where ω is the first infinite ordinal.

One might answer: “Well, it didn’t exist on day  − ω, because time does not include day  − ω.” But that doesn’t solve the puzzle. After all, imagine that on day  − 18 an object popped into existence, and when we are puzzled by this, we are told: “Well, day  − 18 is the first day of time. The object couldn’t have existed on day  − 19 because there was no such day.” But now we want to know: Why did time itself begin on day  − 18 rather than on day  − 19 or day $-10^{94}? And similarly, we should want to know why time extends only to the dates ...,  − 3,  − 2,  − 1, 0 and not to day  − ω, or day  − ω − 1, or day  − 2^ω₉₄.

In fact, there is a sense in which the first of the following questions might be less puzzling than the second:

• Why did time begin on day  − 18 rather than day  − 10⁹⁴?

• Why did time extend only to days ...,  − 3,  − 2,  − 1, 0 rather than beginning with day  − ω, inclusive?

For if time is relational, then there might be no real metaphysical difference between time beginning on day  − 18 and time beginning on day  − 10⁹⁴, but even so there is a metaphysical difference between time extending only to days ...,  − 3,  − 2,  − 1, 0 and its starting on  − ω. If time extends only to days ...,  − 3,  − 2,  − 1, 0, then it has no first day, but if it starts on day  − ω, then it has a first day, namely  − ω.

In fact, there are infinities of different possible temporal orders, all of them linear (i.e., reflexive, transitive and total). Why is time one of these rather than another? If times are representable as real numbers (as classical physics assumes), why? Why not merely as rational numbers? Or, more expansively, why not as hyperreals? Or why not as an order that looks like the real numbers with zero removed?

Whatever is the time sequence occupied by an object, even if the object fills the time sequence, it calls out for an explanation why the time sequence that it fills is this one rather than another one.