Appearances of atemporality

Here’s a way to think about presentism. We have a three-dimensional reality and temporal modal operators, such as Prior’s P, F, H and G (pastly, futurely, always-pastly and always-futurely), with appropriate logical rules.

But now imagine this scenario: Reality consists of an eternally frozen time slice from a complex two-way-deterministic Newtonian world resembling our world—“frozen Newtonian world” for short. There are particles at various positions with various momenta (I assume that q = mdx/dt is a law of nature rather than a definition of momentum, and momentum is fundamental), but they are ever still, unchanging in their Newtonian properties. Now if Q is one of the operators P, F, H and G, define the operator Q′ as follows:

• Q′p if and only if either (a) reality consists of an eternally frozen Newtonian world and in an unfrozen Newtonian world that agrees with reality on its present slice we would have Qp or (b) we have Qp and reality does not consist of an eternally frozen Newtonian world and we have Qp.

Then the primed operators behave logically just like the unprimed ones. But according to the primed operators, “there is change and motion”. For instance, for a typical particle z eternally frozen at location x, it will be the case that P′(z is not at x) and F′(z is not at x), since in an unfrozen Newtonian world whose present slice is just like our world’s, there will be past and future times at which z is not at x.

So what? Well, the presentist’s big intuition is that on a B-theory of time there is no change: there is just a four-dimensional block, where one dimension just happens to be called “time” and things are different at different locations along that dimension, but simply calling a dimension “time” doesn’t make it any different from the spatial ones.

But the B-theorist can respond in kind. On presentism there is no change: there is just a three-dimensional world related to other three-dimensional worlds via certain modal operators that are called “pastly”, etc., but simply calling a modal operator P “pastly” doesn’t make it any different from deviant operators like P′.

The presentist will, presumably, say that it’s not just a matter of calling the operator P “pastly”, but rather the operator is the primitive pastly operator, so that if something pastly is different from how it’s now, it has changed. But now the B-theorist can just respond in the same way. It’s not just a matter of calling one of the four dimensions “time”, but rather the dimension is the primitive time dimension, so that if something is different at a different time from how it is now, it has changed or will change.

(Granted, a B-theorist does not need to think that the distinction between space and time is primitive. I am inclined not to, and hence I cannot make the above response.)

Presumably, even after this dialogue, the B-theorist’s alleged reality will look static to the presentist. But I think the presentist’s alleged reality can look atemporal to the B-theorist—it’s just a three-dimensional world with no time dimension and some modal operators relating it to other three-dimensional worlds.