During my analytic metaphysics reading group this evening, I was convinced that several ways of speaking of time are reductive and insufficient to capture temporal notions fit for processional accounts. The idea of “time slices” or speaking of “a at time t is F” treats time as a linear dimension, and it does not work for processional models of temporality. The problem is that it treat time as if it were a discrete unit and an event as if it were completely actual. However, time as event cannot be actual else it would be eternal and not temporal. Moreover, time cannot be a discrete unit and be continuous without denying that the past has a constitutive relation to present, which has another constitutive relation to the future.
I have been developing my own Americanist theory of time from studies of Royce, Peirce, Whitehead, Hartshorne, and Cummins. I have a much work ahead of me, and much behind me, and I would like to present a fuller proposal than I have before. See my prior posts: "Emergence, Temporality, and Consciousness," "Thinking Temporality and Process,""Aristotle, Dewey, and Temporality,"and "Individuals in Process Philosophy."
Below is a representation of an actual event as an irreducible unit of time in a process. The model presumes the following parameters. First, an actual event is an irreducible complex of present-past-future. An event is such by virtue of its constitutive relations from the past and to the future. The past is fully actual, the present is the moment of change, and the future is what might be. If we ignore or sever the past, then we get change without ground. If we do the same for the future, we get a present tending towards nothing in particular, which is absolute chaos. It must be limited at least by the laws of nature. Second, the relation of past-to-present is not the same as present-to-future. The actuality of the past limits the possibilities of the present to the potentialities (real or existentially constrained possibilities given a locale) of the past. Hence, the past is fully actual, while potentiality and selectivity is of the present. What is being selected is not what potentialities are extant, which the past determines, but how the potentialities interact so as to come together into new configurations, potentialities, and their realizations. The future is the anticipated realization(s) of potentiality, and differs from the past in that it is real but not fully actual, and from the present in that it anticipates a determinate realization of the selected potentialities of the present. In sum, the past provides the determinate ground of potentiality that limits which potentialities are in play in a locale, whereas the present is the play of potentiality in forming structures, and the future is the possibilities of the present as limited by the tendencies of the past. When this whole event become “past,” that means one determinate configuration of potentialities stabilized to concresce into the next moment.
The diagram presumes many prior discussions, including my articulation of “potentiality.” Potentiality is a triad of 1) capacity, 2) activity, and 3) realization unto actuality, all three of which are concurrent. The realization of any potentiality is an actuality that occurs through its activity. Capacity, however, is not necessarily inherent in some singular actuality, but occurs through transactivity. One admitted weakness of this view is that I am uncertain about questions in invoke a regress and ask what is the ultimate ground of potentiality—is it potentiality all the way down?
Above, I represent an actual event as the irreducible unit of time as part of a process. The only way I can imagine representing a notion of time as dimensional, i.e., as having discrete units, is to actualize it. But this reduces time to a mere unit of measurement, or in terms of my model, as mere determinate pastness. Suddenly, explaining continuity becomes a problem insomuch as one event is constitutive of the next.
For those who are wondering, I do presume that time is a local and relative phenomenon, and this there is no "universal t" such that any schematization of time has universal applicability--no a at t is F unless t is something other than a dimensional unit.
I would greatly welcome comments, especially questions for clarification. This is still years away from seeing prime time.