Famously, Aquinas thinks that an accidentally ordered infinite causes
is possible, but a per se ordered one is not. The difference is
that in a per se ordered series ..., A−2, A−1, A0,
item An − 1 (for
n < − 1) is not only the
cause of An, but is the
cause of An’s causing of
An + 1.
But in an accidentally ordered series, An − 1 is not
the cause of An’s causing of
An + 1.
Aquinas illustrates the distinction with a sequence of an infinite
sequence of fathers and sons, since a grandfather is not the cause of
the father’s conceiving of a son.
Now suppose we replace the people in Aquinas’s example with
self-reproducing robots (von Neumann machines), each programmed by its
predecessor to reproduce. Then we have a per se ordered
series.
The following seems to me to be very plausible:
- If a backwards infinite reproductive series of humans is possible, a
backwards infinite reproductive series of robots is also possible.
Yet this seems to be something that Aquinas is committed to by his
example of the accidentally ordered series.
Suppose one bites the bullet and denies (1). What is the relevant
difference between the humans and the robots? It is presumably the
determinism in the robots. Very well, then let’s suppose that each of
the robots has a little hidden switch whose position is permanently set
at the time of manufacturing. When the switch is in the D position, the
robot is determined to reproduce at specific points in its life; when it
is in the N position, at those points in its life, the robot performs an
internal indeterministic quantum coin flip, reproducing on heads but not
on tails.
It seems absurd to suppose that one could have a backwards infinite
reproductive series of robots with the switches in the N position, but
not in the D position. Yet that implausible conclusion seems to be what
Aquinas’s position commits him to.
Here a suggestion for what Aquinas could do.
Aquinas thinks there is a very good metaphysical argument for
rejecting backwards infinite per se ordered series. Suppose
that argument is sound. Then Aquinas could say that this argument does
not apply to the accidentally ordered case. But nonetheless there is a
good argument based on a rearrangement principle or a principle of modal
uniformity that:
If a backwards infinite series of robots with the switch in the N
position is possible, so is a backwards infinite series of robots with
the switch in the D position.
If a backwards infinite series of humans is possible, a backwards
infinite series of robots with the switch in the N position is
possible.
Given the impossibiliy of the series with the switch in the D
position, it follows that the the backwards infinite sequence of humans
is impossible. Aquinas can then simply say that he was wrong about his
example (something that he is willing to concede anyway, due to an
argument from al Ghazali specifically against an backwards infinite
sequence of humans). But nothing in Aquinas’s theory commits
him to the claim that every describable accidentally ordered
backwards infinite sequence is possible. (An accidentally ordered
backwards infinite sequence of square circles is not possible.)
At this point, Aquinas can do one of three things. First, he can say
that while the backwards infinite sequence of humans or N-robots is
impossible, we should remain agnostic whethere there are some backwards
infinite accidentally ordered sequences are possible.
Second, he can give a plausibilistic argument that if the backwards
infinite sequence of N-robots is impossible, probably all accidentally
ordered backwards infinite sequences are impossible as well. (One might
think this would require Aquinas to reject the possibility of an
infinite past. This is not clear. He might still hold that an infinite
past is possible as long as it doesn’t generate a backwards infinite
causal sequence—imagine that every day in the past God creates a rock so
far apart from all the other rocks that the rocks never interact).
Third, Aquinas could try to construct a new example of a backwards
infinite accidentally ordered series that is possible. My intuition is
that the best bet for trying to do this would be to construct a
backwards infinite sequence where each item gets only a very slight
causal contribution from its predecessor, and most of the explanation of
the item’s existence involves God or some other single timeless
being.
I myself like the second option.