A problem with the B theory is explaining temporal asymmetry. Time moves in one direction, or agents in time can only move in one direction- from the past towards the future. As Peter van Inwagen said in Metaphysics: Second Edition, we express different attitudes towards the past and the future, in that we are relieved when a painful dentist visit is over. Yet the same appointment with a dentist is anticipated with fear when it lies in the future direction.
B theorists do distinguish between earlier times and later times, but the relations between these are static, and any notion of moving through time towards the future is absent from their theory. The difficulty is in explaining why one time earlier than another time? Given the spatial analogue of B positions to spatial positions, why couldn’t the same time also be later than a future time? Take the times t1, t2, and t3, with t1 being earlier than t2 and t3. Why couldn’t the timeline be flipped, like a ruler, with t3 being earlier than t2 and t1?
B theorists explain change in terms of similarity and dissimilarity at different times. So a person has short hair at t1, and long hair at t2. The change is really the dissimilarity of this person’s hair length at the different times. We would say that the hair grew long between t1 and t2. Yet given the absence of A positions, why couldn’t we also say that the hair shrank from t2 to t1, with t2 being earlier than t1? Causal conditions could be invoked, that long hair requires the existence of short hair attached to the scalp of a living body to grow into long hair. Yet these causal conditions are based on the experience of hair at earlier times growing into long hair at later times, the same earlier and later than positions that are being called into doubt. In this case, the A theory has a less counter-intuitive explanation. Temporal asymmetry occurs because the present moves in the future direction.
Ursula Coope has shown in Time for Aristotle that a similar difficulty may be faced by Aristotelian theories of time, including Thomas Aquinas’s. Aquinas’s theory of time needs a non-temporal basis for the ‘before’ and ‘after’ found in motion, as time is consequent of motion. Can a ‘before’ and ‘after’ in change be given that doesn’t presuppose a temporal order? Prima facie, a non-temporal ‘before’ and ‘after’ is found in motion and also in magnitude, which motion is consequent of. Within Aquinas’s account of time, time is consequent of motion, as time is formally found in the intellect and materially found in motion. Further, local motion, which is the primary basis for time, is consequent of magnitude. While asymmetry in time and motion is fairly easy to grasp, asymmetry in magnitude has difficulties.
Take the line AB. In line AB, there is a ‘before’ and ‘after’ relation with p1 being before p2. As p1 is before p2, being at p1 is also before being at p2. Further, the time t1 in which something is being at p1 is also before the time t2 in which the same thing is being at p2. The problem is, the before and after on the magnitude is only relative to an origin, and the origin in a magnitude is arbitrary. If the line AB were to be flipped, so that it is now BA, then p2 would be before p1. Relative to origin A, p1 is before p2, while relative to origin B, p2 is before p1. This is analogous to the static ‘before’ and ‘after’ or temporal positions in the B theory. Why should t1 be earlier than t2, except relative to an origin? For example, t1 is before t2 relative to the Big Bang, while t2 is before t1 relative to the Big Crunch.
There are two solutions to this difficulty. The first, presented by Coope, assumes that the way the ‘before’ and ‘after’ of place is related to the ‘before’ and ‘after’ of motion is different from the way the ‘before’ and ‘after’ of motion is related to the ‘before’ and ‘after’ of time. In other words, there is an analogous relationship between place and motion on the one hand, and motion and time on the other. The differences can be understood as follows. Motion is dynamic while a magnitude is static. If a racer runs on a race course, the race course remains the same while the runner is constantly changing positions. Further, time, like motion is dynamic, but time has a different kind of reality than motion, in that time is a logical-real being, while motion has a mind-independent kind of reality. Coope further explains, that with respect to Aristotle, magnitude is invoked as an analogy to help explain the before and after of motion. In other words, magnitude serves as an aid in understanding motion.
Another way to approach this problem is to examine the nature of motion. The motion time is consequent of is not limited to local motion, even though local motion is what is best known. Motion is ultimately the act of that which is in potency insofar as it is as such. This would include qualitative, quantitative, generation, and corruption. Presuposed in all these kinds of motions is further the notion of the natures of things in motion. A child is prior to an adult, as a child is in potency to becoming an adult. An acorn is prior to a tree, as an acorn is in potency to becoming a tree. Given these two ways of approaching the problem of asymmetry in time for Aquinas, there are two solutions at Aquinas’s disposal that remove the difficulties.
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