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.
I have never seen Aquinas's view of per se ordered series described as it is in the opening paragraph of the OP. A per se ordered series means the primary member of that series of causes is the only member which inherently possesses the causality of that series. That's all.
ReplyDeleteThe second paragraph of the OP seems incorrect as far as the robot series being a per se ordered series.
I tend to agree with Don about the machine example and the OP's definitional problem. If A "programming" a causal behaviour in B that leads later to C being caused bvy B was sufficient to make for a per se causal chain, then the grandfather would be said to cause the conception of his grandson insofar as he passes on to the father the genetic programming that includes reproductive organs, libido etc.
ReplyDeleteBut I think Aquinas' concept of a per se ordered series is a bit richer (at least implicitly) than Don says. And, unlike in the OP, I think Aquinas requires more than a cause passing on a form to an effect that enables and inclines the effect towards causation of a further effect. Programming seems to be operating only on the level of formal cause at the next step of the chain, whereas I think Aquinas saw the dependence on prior causes (those before the immediate preceding cause) as including efficient causality and "simultaneity".
But I will admit this is based on reading Thomists and allies with similar ideas (e.g., Barry Miller, who appeared, in my opinion, not to recognise his "Series IV and V" types of causal series were equivalent to the per se ordered series of Thomists) rather than on exegesis of the Angelic Doctor himself. I have no texts to offer off the top of my head.
Aquinas's standard example of per se causation is something like a man moving a stick moving a rock. It's hard to distinguish moving a stick, from moving a hammer, from moving a dead-blow hammer, from activating a power hammer, from activating a robot. Part of the reason is that our current knowledge of how hammers and sticks work is that they absorb and emit kinetic energy, nonsimultaneously. If ordinary hammering doesn't count as per se causation, on the other hand, then we don't actually have any examples of per se causation to work with.
ReplyDelete"In efficient causes it is impossible to proceed to infinity per se—thus, there cannot be an infinite number of causes that are per se required for a certain effect; for instance, that a stone be moved by a stick, the stick by the hand, and so on to infinity. But it is not impossible to proceed to infinity 'accidentally' as regards efficient causes; for instance, if all the causes thus infinitely multiplied should have the order of only one cause, their multiplication being accidental, as an artificer acts by means of many hammers accidentally, because one after the other may be broken. It is accidental, therefore, that one particular hammer acts after the action of another; and likewise it is accidental to this particular man as generator to be generated by another man; for he generates as a man, and not as the son of another man." ( https://www.newadvent.org/summa/1046.htm )
ReplyDeleteWe get two suggestions here for what makes the series per se. First, that the cause is per se required for the effect. Second, that the intermediate cause causes insofar as it is caused. Both of these seem to be true in the robot case.
The point of the man-stick-rock example is that sticks and rocks don't inherently possess the causality of motion. A per se series involves accidental causation for every member of the series except the prime member. Only the prime mover of the series acts with per se causality (is "per se required").
ReplyDeleteIn the robot series the robots are self-reproducing which is the causality of the series. Thus they possess it inherently, so it's not a per se ordered series.
I'm not sure what the purpose is of the convoluted robot scenario. An accidentally ordered series is only "backwards infinite" *potentially* because (unlike the per se series) it needn't have a prime member/mover. So for each member of the series it's always (theoretically) possible there is a prior member. By contrast, a per se series requires, by definition, a first (per se causality) member.
ReplyDeleteAquinas uses the example to illustrate the concept, so good exegesis requires us to use his understanding of the example, in context, not ours. I think it is right that modern physics has no way of modeling a distinction between per se and per accidens causal series. If I am not mistaken, it also has no way of modeling an unmoved mover.
ReplyDeleteMatthew:
ReplyDeleteExegesis requires Aquinas' understanding, but evaluation of the argument requires the truth. And there one wants SOME example that works, or else the first-mover argument becomes very implausible. If the only case of a per se causal series is the one-step series where the unmoved mover moves everything else, and there are no other examples, it's going to be really difficult.
That said, I think it shouldn't be hard to convince Aquinas of the fact that sticks are compressible--like everyone, he is familiar with the bendiness of wood--and as you push on one end, you are basically charging up a spring. And the difference between that and a spring-driven clockwork wind-up robot is merely quantitative. And surely it doesn't matter if we drive the robot by a battery or by a spring.
Don:
"In the robot series the robots are self-reproducing which is the causality of the series. Thus they possess it inherently, so it's not a per se ordered series."
But the same is true of the stick that's moving the stone. The stick-in-motion has the causal power to move the stone, just as the charged-up-and-programmed robot has the causal power to reproduce.
If God created a universe with an infinite past--which Aquinas thinks is possible, though not actual--then the past surely wouldn't be merely potentially infinite.
Sticks don't possess motion inherently. They aren't self-movers. Alternatively, it is of the "nature" of the robots as given in the scenario to reproduce; so it is a power they possess inherently.
DeleteI don't see how per se series have relevance to the question of whether a beginningless past entails an actual infinite or merely a potential infinite.
When you push one end of the stick, I assume what happens is that you are moving a layer atoms at that end in one direction. These atoms initially move closer to the next layer of atoms, but the repulsive van der Waals then push the next layer, which gets closer to the next layer and push that, and so on. You can visualize it by supposing you have a very weak spring and you press at one end. You can see the spring compress as you press it, and the compression wave then travels down the spring to the other end. In other words, the process of pushing one end of the stick and getting the other to move is merely quantitatively different from what happens when you wind up a spring and let it go. And a robot can (in principle) be powered by wound up springs, so there is not a qualitative difference between a wind-up robot's functioning and pushing one end of the stick to make the other end go.
ReplyDeleteAs I understand it, for Aquinas causality is in reference to substances. But even disregarding that, the stick's atoms don't inherently have the causality which the human is giving them by pushing one end of the stick (otherwise the stick could move itself). Nothing controversial here as far as I can tell.
ReplyDeleteIn regards to the robot: if the causality in question of this most recent robot scenario is "being powered up" then (according to the scenario provided) they do not have that inherently. So, yes, this would involve the same causality relationship as in the man-stick-stone series.
Time cannot proceed to infinity because infinity is just a concept, not a number or a representation of a time sequence of real material processes.
ReplyDeleteTime cannot have come from negative infinity for the same reason time cannot proceed to positive infinity.
Consider counting up by 1 each second. Could you ever count up to infinity, even in the case of being immortal? No, because at any time in the future you would always have counted up to some finite numbers. If you never die and just keep counting on and on and on you can never count up to infinity.
"Indefinitely" and "infinitely" are not at all synonymous.
A material process can continue indefinitely, in principle, that is, without ending.
An indefinite material process can never reach infinity.
There is no such thing as an infinitely progressing material process, even in principle.
Circular causation negates the call for an infinite per se regression of movers.
ReplyDeleteInertial motion negates the call for any regress of movers at all.
Existential inertial negates the call for any regress of existential causes.
Aquinas, like Aristotle, conceived of a linear hierarchical one way causal series.
Real causation is always mutual and multilateral at base, thus fundamentally circular and multidirectional at base.
Inertial motion makes any regress of movers unnecessary, much less an infinite regress of movers. Inertial motion means that the premise of the necessity of all observed motion requiring an external mover in the present moment is false.
Existential inertia makes any regress of existential causes unnecessary, much less an infinite regress of existential causes. Material continues to exist because continued existences is no change in the existential aspect of material. If material were to change from existing to not existing then that would be a case of material changing itself or being changed by an external changer from existing to not existing. A change from existing to not existing would call for a changer, so Aquinas has it back to front.