I am currently in the process of reading Aquinas' commentary on Aristotle's metaphysics. It is really an amazing piece of work and the fruit of much thinking!
I am currently on Book V, Lesson 2, in which the discussion on causation happens.
For those that don't know, there are 4 causal modes in Aristotle's Metaphysics within 2 types of causation.
The 2 types are:
1) Intrinsic Causation - That which is generated from within (will give examples of this in a bit).
2) Extrinsic Causation - That which is generated from without (will, again, give examples of this in a bit).
Within Intrinsic Causation there are 2 modes of this type that can be called causes:
1.a) Material Cause - That which gives the matter for a thing to be. For example, a bronze statue has as its material cause bronze. The bronze does not come from without the bronze, but is part of the statue itself. Therefore it is intrinsic.
1.b) Formal Cause (Sidenote, this cause is both an intrinsic and extrinsic cause). That which gives a thing the form necessary for it to be what it is. For example, the form of a statue is from within. The form is that which gives "definition" to the matter, to make the matter knowable to the intellect.
Within Extrinsic Causation there are 3 mods of this type that can be called causes:
2.a) Formal Cause - When a thing is made in the likeness of another thing and thus receives its form from that thing though it cannot be that thing. This type of formal cause is of the imitative sort. To bring us back to our statue example, though within it it has the form of statue, and, let us say, it is made to resemble John Paul II, it receives the form of "John Paul II" from John Paul II, who is exterior to the statue and thus a cause for it to be a resemblance of him.
2.b) Efficient Cause - That which brings a thing to movement or rest. For example to throw a ball is to be the efficient cause of the ball, for its accidental properties (such as placement and movement) are changing. The catcher of the ball is also an efficient cause because he is again changing the accidental properties of the ball and bringing it to rest. In another sense, Efficient Cause is that which brings a thing into being, which involves motion.
There are 4 types of the type "Efficient Cause" which Aquinas gets from Avicenna; Perfective, Dispositive, Auxiliary, and Advisory. I will not go into that for now, but the distinctions truly blow the mind away!
3.b) Final Cause - That which is the sake for why a thing is done. To bring us back to the example of the ball, the ball is thrown in order for the other person to catch it. Thus, the final cause of the ball in that action is to be caught.
Now, within Final Causation, there are 2 distinctions; ultimate end and intermediary end. This is the reason for why I posted this post. The ultimate cause is the ultimate "raison d'etre" for a thing to act. Aquinas would say that the ultimate final cause of man is to spend eternity in loving communion with God. But intermediary final causes are things that are necessary in order for the final end, the ultimate final cause, to happen.
Now, to bring it back to the ball example, it would seem to me that Aristotle and Aquinas (if I recall correctly) would argue that intermediary final causes are infinite in nature.
Let me give you an example from Math. Let us say we have the numeric distance between 1 and 2. Between that finite set is an infinite possibility of division. One could never move past 1 to 2, for they could continually go further and further down the decimal scale.
The same in our ball example. When someone throws a ball, the ultimate end is for the other to catch it. But in order for that to happen, there must be an infinite set of motions within the finite set of the throw and the catch.
This would seem to make sense since Aristotle argued that the universe is what he calls a potential infinite. It is measurable, yet without any seeming point to measure. If we went within the set of numbers between 1 and 2, we could say the same, as if there were no beginning or end, though there is, but from within the set, it would be impossible.
It is interesting how this seems to logically follow from Aristotle's theory of the 4 causes and how this shows up within his discussions later on in regards to the infinite.
-Harrison
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