the necessity of the past redux.

Let PAST be the conjunction of every true proposition about the past. The necessity of the past thesis says that the past is necessary. In other symbols:

(NP) PAST.

Since the necessity operator ‘’ is equivalent to ‘~◊~’ (i.e., it is not possible that not), the truth of NP is equivalent to

(NP’) ~◊~PAST.

If NP’ is true, it follows that there are no contingent truths about the past, since for P to be contingent, P must be both not necessary and not impossible. But surely there is at least one contingent truth about the past. For example, though it’s true that

(P) Atra was on the mat,

P could have been false. In other symbols:

(PC) P ∧ ◊~P.

If (PC) is true, then (NP’) is false, for (~◊~P ∧ ◊~P) is a formal contradiction. Ergo, etc.