The Dynamic B Theory

​The key to a dynamic (Aristotelian) B Theory of time is a notion of relative potentiality. Some things are potential relative to one event or point in time but no potential relative to others. So, for example, my winning the Noble prize in 2020 is potential relative to some point in my life (say 1960) but clearly it is potential relative to the present (Dec. 31, 2020). We can use relative potentiality to define relative actuality: an event E is actual relative to time t if it is absolutely actual and nothing is potential relative to t that is not also potential relative to E.
 
But what can it mean to say that one event is potential relative to a time or another event? Isn't potentiality a simple property and not a binary relation? The right B-Theoretic answer, I think, is to say that 'being' is said in many ways (as Aristotle says in Metaphysics Gamma 2). There are many ways of 'being' potential. These different modes of being correspond to different moments in time.
 
How do substances actualize potentialities? If a substance has an active power at t, and some patient has at all times prior to t the potentiality relative to those times of being changed in the appropriate way, then it is possible for t to be a time at which the agent exercises its power on the patient, actualizes the patient's potentiality. Suppose this involves the patient's becoming A (where A is some contingent accident). The patient's being A at t is absolutely or eternally actual. Nonetheless, it is actual because of the agent's exercise of its active power at t, and because of the patient's potentiality for being A in the preceding interval of time. Thus, some actual facts are causally explained by others, which corresponds to their location in time.
 
Formally, we can model this dynamic B Theory by using a series of trees. Each tree has a trunk (representing the past and present) and a set of branches, representing the potential futures. Each moment of time has its own tree, representing what is potential and what is actual relative to that time. One moment of time is later than another just in case it's tree is smaller, in the sense that the later tree will have a longer trunk and fewer branches. As time passes, branches (representing relative potentialities) fall off the tree (to use Storrs McCall's vivid image). We can then define two kinds of future tense: that which might yet happen (with reference to the present moment's future branches) and that which will actually happen (with reference to future trees).