Another weird discrete theory of time

Suppose time is discrete. The usual story then is that we are always at some point of time. But what if, instead, we are always between times? I.e., the times themselves are something like imaginary points—we don’t occupy them on their own. It is only the interval between two successive times that we occupy, and we occupy the interval as a whole. Such an interval is a “now”.

If t_n and t_n + 1 are successive times, then we say that at (t_n,t_n + 1) (think of this as an ordered pair or an interval—your choice of mathematical representation!):

• x is F iff x is F at t_n and at t_n + 1

• x is non-F iff x is non-F at t_n and at t_n + 1

• x exists iff x exists at t_n and at t_n + 1

• x non-exists iff x is does not exist at t_n or at t_n + 1

• x is changing from F to non-F iff x is F at t_n but not at t_n + 1

• x is changing from non-F to F iff x is non-F at t_n and at t_n + 1

• x is coming into existence iff x exists at t_n + 1 but not at t_n

• x is ceasing to exist iff x exists at t_n but not at t_n + 1

• x is coming to be F iff x is F at t_n + 1 and either does not exist at t_n or exists at t_n but is not F then

• x is ceasing to be F iff x is F at t_n and either does not exist at t_n + 1 or exists at t_n + 1 but is not F then.

Here is a plausible thesis:

1. x fails to exist or x is F or x is non-F.

On the theory we are exploring, this is false in a now. Instead:

2. x non-exists or is coming into existence or is ceasing to exist or is F or is non-F or is changing from F to non-F or is changing from non-F to F.

This theory is a variant of one I tried out in an earlier post, minus the possibility of the now being a point.