Way One Analyzed Logically

Defending Aquinas's First Way: “Whatever is Moved is Moved by Another”

Let's define what I will call the notion of change per se. Intuitively, something changes something else per se if it is the most immediate and proper cause of the change. For instance, my hand pushes a stick which pushes a ball. Here is a somewhat more formal definition of changing per se, which we will call (PS):

(PS) x is changing per se something y with respect to feature P just in case (i) x is changing y with respect to feature P, (ii) x's action taken alone is sufficient for changing y with respect to P, and (iii) the action of any proper part of x taken alone is not sufficient for changing y with respect to P. [def.]

This definition can be made somewhat more precise, but the concept should be clear. The idea behind what I've called change per se is that whatever changes something else per se is the thing that changes y in the most immediate sense and a sense more proper than other things. So, for instance, take the following objects: Me, my hand, my hand's atoms, and a stick. When my hand changes the location of the stick, I can be said to change the location of the stick; however, I cannot be said to change its location per se, since, arguably, if somehow my hand persisted in its motion without the rest of my body, it would still be sufficient for the stick's changing with respect to its location (contra iii). On the other hand, arguably, my hand, or at least some part of it, changes the stick's location per se, since clearly it can be said to be changing the stick's location, thus satisfying (i), it arguably satisfies (ii) for the reasons stated, and it satisfies (iii) since if you removed most of the hand but left a few of the atoms in motion it would not be able to bring about the stick's change of location. Now maybe you will disagree with my example and say that given my definition the hand does not change the stick's location per se, but it should be enough to at least illustrate what I'm trying to get at.

(EXT) x is an object external to y just in case x is not y and x is not a part of y.

Now we need the following premises. I will translate them into symbols, and from my translations it should be clear which formulas correspond to which English phrases.

(1) For all x, if x is changed with respect to P by something y then there is some actual thing z which is changing x with respect to P.

Translation 1: ∀x[∃yCxy→∃z(Az∧Cxz)]

(2) For all x and y, if y is actual and x is changed per se with respect to P by y, then y is either an object external to x or y is a proper part of x.

Translation: 2: ∀x∀y[(Ay∧Dxy)→(Eyx∨Pyx)]

(3) For all x, if x is changed with respect to P by something actual y, then there is a z which is actual and changing x per se with respect to P.

Translation 3: ∀x[∃y(Ay∧Cxy)→∃z(Az∧Dxz)]

(4) For all x and y, if y is changing x per se with respect to P, then y is changing x with respect to P

Translation 4: ∀x∀y(Dxy→Cxy)

(5) For all x and y, if x is external to y, then x is not identical to y.

Translation 5: ∀x∀y(Exy→x≠y)

(6) For all x and y, if x is a proper part of y, then x is not identical to y.

Translation 6: ∀x∀y(Pxy→x≠y)

Now, given all the above premises 1-6 we can prove:

(7) For all x, if x is changed with respect to P by some y, then x is changed by some non-identical z.

Translation 7: ∀x(∃yC(xy)→∃z(D(xz)∧x≠z))

I won't explain the proof here; instead, for anyone who doubts me, I have attached a formal proof below. From 7 and 4 of course it follows that whatever is changed with respect to P is changed by some non-identical z: That is to say, whatever is changed is changed by another. I'll leave the relatively simple proof to the reader.

Proof of 7:

For those looking to understand the symbolism if you haven't taken a serious logic class, you can start here. 

However, you don't need to understand the symbols to understand the post. This is not just because the meanings of the expressions are given before each (and you can make up identities to make them make sense, for example x=a dog, y= a cat etc, and then apply them to motion in general) but also because the whole idea can be written in a paragraph summary. (but far less succinctly than a logical sentence) My comments are in blue and emphasis in bold. Aquinas' first proof for God states the following:

[The first and more manifest way is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion [Some debate that, but walking in front of a bus might change their theory…]. Now whatever is in motion [x] is put in motion by another[y], for nothing can be in motion except if it is in potentiality to that towards which it is in motion [everything is goal directed, moving towards a certain end state]; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. [There is always an instigator which makes the potential actualized.] Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. [Wood doesn't become hot by itself.] Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot [it can be potentially hotter, but not potentially hot]; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself. Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again.[An ongoing chain of motion, but not like dominos as we are talking about act and potency…this is an atemporal causal relationship] But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. [In the Aristotelian view, the motion of objects is a single event, which I will speak about below.] Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God.]

The distinction between cause and effect in the modern and classical viewpoints is something which needs to be clarified, as it has not even been done by the preceding article. Unlike the classical view (the view according to which the above was written) the modern view sees cause and effect not one “necessary” event given the nature of those beings that are involved (Aquinas) but rather are coincidental conjunction because of temporal (immediate) relation. (¹⁵ Rosenberg, Alexander. The Atheist's Guide to Reality: Enjoying Life without Illusions. New York: W.W. Norton, 2011. Print. 34. “In our experience, things can only happen in one direction: a match can’t go from being put out to being lit to being struck. But at the basement level of reality, the opposite of any sequence of events can and does happen. Given the present state of the universe, the  basic laws of physics can’t determine in which temporal direction we are headed.”) On this view,  the best way to study reality is to fragment event and identify the most temporally successive but immediate element as cause to some effect. 

This means finding the cause per se, as spoken of above. As a result of the modern world looking to a mechanical explanation of things as sufficient for explanation, the concept of causes outside of the merely mechanical fell to the side. These were (and are) the formal and final causes which are no longer even understood to apply to the above text from Aquinas, as he intended them. Because of this most people when they read the above, the see it as a situation where the last domino fell and so therefore another domino must have hit the penultimate and another before that one and so on back, these people miss the most powerful aspect of this 'proof' and ridicule it as “too simplistic” or dependent on a belief that infinite regress is not possible. However, this is a purely mechanical account of causation, as mentioned. As EA Burt says in his History of Modern Science:

First, the real world in which man lives is no longer regarded as a world of substances possessed of as many ultimate qualities as can be experienced in them, but has become a world of atoms (now electrons), equipped with none but mathematical characteristics and moving according to laws fully statable in mathematical form. Second, explanations in terms of forms and final causes of events, both in this world and in the less independent realm of mind, have been definitely set aside in favor of explanations in terms of their simplest elements, the latter related temporally as efficient causes, and being mechanically treatable motions of bodies wherever it is possible to so regard them. In connexion with this aspect of the change, God ceased to be regarded as a Supreme Final Cause, and, where still believed in, became the First Efficient Cause of the world.

However, to acknowledge that bodies greater than the parts which make them up exist (a human is different than atoms) means that there is a potential in a human being that is not in any combination of atoms. Actually…to even ascribe an identity to an atom is to admit of formal and final causality, as I have harped on before. 

The point of this post is make sure that the first proof of Aquinas' is not read in with a mere 'modern' understanding. Unfortunately the analysis above stops at infinite regress (7) but it makes it does very clearly lay out the idea of a cause per se, which not all effects are the results of. It is a very logical presentation of proof one, but could use a bit more Aristotle.