Some philosophers think that the past is necessary. But if these philosopher think the past is necessary in just the same way that *two and two being four* is necessary, this cannot be right.

Let’s suppose that any fact about the past is necessarily true in just the same way *two and two is four *is necessary, that is necessary *simpliciter*. We might formalize this thesis as

(PN) For any p, if p is true and about the past, then p is necessarily true.

Now consider some fact about the past, that

(1) Two plus two equals four.

Since (1) was true yesterday, the conjunction of (PN) and (1) entail

(2) Necessarily, “two plus two is four”

as well as (2)’s *de re* rendering, that

(2’) Two plus two is necessarily four.

Well, here things seem fine, at least by way of (2) and (2’). Even if someone might be suspicious of (PN), she shouldn’t be suspicious of it because (2) and (2’) are among (PN)’s consequences.

But now let’s consider another fact about the past, that

(3) Atra was on the mat.

Since (3) picks out a fact about yesterday, the conjunction of (PN) and (1) entail

(4) Necessarily, “Atra was on the mat”

as well as (4)’s *de re* rendering:

(4’) Atra was necessarily on the mat.

But this cannot be right. If we’re supposing that the “necessity” in (4) and (4’) is to be understood as necessary *simpliciter*, then the truth of (4) entail each of the following:

(4’’) There is no possible world where Atra was not on the mat.

(4’’’) It is impossible that “Atra was not on the mat.”

And since what is necessary and what is impossible exclude what is contingent, the truth of (4) entails that

(4’’’’) It was not a contingent fact that “Atra was on the mat.”

And perhaps most damningly, (4) entails that

(4’^{x5}) Atra could *not* have not been on the mat.

But (4) through (4’^{x5}) are all false: Despite the fact that Atra was on the mat yesterday, Atra could have* not *been on the mat; it’s a contingent fact that Atra was on the mat; It was possible for Atra to not be on the mat; and there is at least one possible world where Atra is not on the mat. And hence (PN) is false, or at least it needs a lot of work.

I think this shows that for any truth that is not necessary *simpliciter*, the following principle

(*) p → ~◊~p

is false.

And if (*) is false, then for any truth that is not necessary* simpliciter*, the following principle

(~*) p ^ ◊~p

is true.

This seems to suggest that any non-determinist is committed to synchronic possibility.

Labels: modality