Monday, November 29, 2021

Simultaneous causation and occasionalism

In an earlier post, I said that an account that insists that all fundamental causation is simultaneous but secures the diachronic aspects of causal series by means of divine conservation is “a close cousin to occasionalism”. For a diachronic causal series on this theory has two kinds of links: creaturely causal links that function instantaneously and divine conservation links that preserve objects “in between” the instants at which creaturely causation acts. This sounds like occasionalism, in that the temporal extension of the series is entirely due to God working alone, without any contribution from creatures.

I now think there is an interesting way to blunt the force of this objection by giving another role to creatures using a probabilistic trick that I used in my previous post. This trick allows created reality to control how long diachronic causal series take, even though all creaturely causation is simultaneous. And if created reality were to control how long diachronic causal series take, a significant aspect of the diachronicity of diachronic causal series would involve creatures, and hence the whole thing would look rather less occasionalist.

Let me explain the trick again. Suppose time is discrete, being divided into lots of equally-spaced moments. Now imagine an event A1 that has a probability 1/2 of producing an event A2 during any instant that A1 exists in, as long as A1 hasn’t already produced A2. Suppose A1 is conserved for as long as it takes to produce A2. Then the probability that it will take n units of time for A2 to be produced is (1/2)n + 1. Consequently, the expected wait time for A2 to happen is:

• (1/2)⋅0 + (1/4)⋅1 + (1/8)⋅2 + (1/16)⋅3 + ... = 1.

We can then similarly set things up so that A2 causes A3 on average in one unit of time, and A3 on causes A4 on average in one unit of time, and so on. If n is large enough, then by the Central Limit Theorem, it is likely that the lag time between A1 and An will be approximately n units of time (plus or minus an error on the order of n1/2 units), and if the units of time are short enough, we can get arbitrarily good precision in the lag time with arbitrarily high precision.

If the probability of each event triggering the next at an instant is made smaller than 1/2, then the expected lag time from A1 to An will be less than n, and if the probaility is bigger than 1/2, the expected lag time will be bigger than n. Thus the creaturely trigger probability parameter, which we can think of as measuring the “strength” of the causal power, controls how long it takes to get to An through the “magic” of probabilistic causation and the Central Limit Theorem. Thus, the diachronic time scale is controlled precisely by creaturely causation—even though divine conservation is responsible for Ai persisting until it can cause Ai + 1. This is a more significant creaturely input than I thought before, and hence it is one that makes for rather less in the way of occasionalism.

This looks like a pretty cool theory to me. I don’t believe it to be true, because I don’t buy the idea of all causation being simultaneous, but I think it gives a really nice.