First Way, Part II: Two Lemmas Make Lemma-aid

TOF's Dilemma

We are now ready to prove two lemmas regarding motion,  hence... dilemma. ROFL. Never mind. We interrupt this pun to stay on focus. Besides, there are a couple of initial propositions.

Those who have been following these maunderings would be well-advised to read

• Background and 
• Part I 

lest they lose themselves in the woods. First, we have to get a word out of our way.

Party log

Definition: Divisible means extended in space. It does not mean that the thing can actually be disassembled physically into discrete parts, although it may. Take a log, which does not appear to be an assembly of discrete components. It still makes sense to talk about "this part of the log" or "that part of the log" when referring to different places on the log. A rectangle is divisible into numerous triangles; but the rectangle is not necessarily composed of a bunch of triangles attached to one another. If we regard the Parmenidean-Minkowski 4-space, this would also apply to different parts along the time dimension. For example, the unborn fetus and the elderly retiree are two parts of the same organism.

The opposite of divisible is a dimensionless point. Modern science regards the electron to be a point particle with a point charge and no spatial extent, but this is only true in a restricted sense. Our friend Figulus tells us than in real life, "confining an electron to an infinitesimally small space would require an infinitely large amount of energy. The electron's wave function is governed by Heisenberg's uncertainty principle, just like everything else in quantum mechanics, and so its wave function extends over space, which means it is not a point particle in the relevant sense."

Photons (which have no mass) are "like" electrons ("they are both screwy," said Feynman). But they are extended waves, not particles of absolutely zero size.

Proposition 1: Whatever is changing is divisible. 

1. If the whole is in potency with respect to X, then it is not changing with respect to X. 
2. If the whole is in act with respect to X, then again it is not changing with respect to X. 
3. Therefore, whatever is changing must be in potency and act.
4. But it is impossible for a thing to be in potency with respect to X and in act with respect to X.
5. Since the whole cannot be both, then a thing-that-is-changing must be changing in one part and not (yet) changing in another.
6. Therefore, everything that changes must be divisible in parts. (Aristotle, The Physics, VI.4)

Proposition 2. All material things are divisible.

1. Suppose a length is not divisible; then it is made up of a finite number of discrete indivisibles (i.e. dimensionless points)
2. Either the points in such a series are separated or they are not.

3. If they are not separated, then they coincide in a single point, which has no length, a contradiction.

4. If they are separated, there are distances between them.
5. If there are distances between them, points can be marked in these distances; and so on as above to infinity.
6. Therefore, the length is infinitely divisible.

[Augros, Appendix 1]

"The first man was Atom!"

The atomists believed in indivisible particles which, happily enough, they called atoms. This was believed by many as an article of faith long before Dalton used the same name for his own elementary particles. He got push-back from the traditional atomists because his "atoms" were not like Democritus' atoms. As it turned out, Dalton's atoms not only were divisible, but some in fact have been physically divided.

All material substances are divisible into molecules. These molecules are divisible into atoms. The atoms are divisible into protons, neutrons, and electrons. Protons are supposedly divisible into quarks. Quarks in turn are of distinct types: up, down, top, bottom, etc., differing by "color", "flavor", etc. and are therefore in principle also divisible. Even electrons seem to be divisible in Aristotle's sense, which surprised TOF no end.

Ready? Let's go.

Lemma 1. Whatever is changing is being changed by another.

1. No divisible being can change itself as a whole.  [Prop. 1]
2. All material beings are divisible. [Prop. 2]
3. Therefore, no material being can change itself as a whole.

When we recall that Aristotelian change is akin to acceleration, this is simply a restatement of Newton's first law. A body in equilibrium will remain in equilibrium unless disturbed by an outside force. And as we have seen in the previous Part, unchanged motion is simply another form of Aristotelian "rest."

Examples:

• An atom emitting an alpha particle is being impacted by a neutron. 
• A species that is adapting is being changed by natural selection (actually, by specific environmental conditions of one sort or another).
• A cat approaching a saucer of milk is being moved by its legs. That is, it is not moving "as a whole" but, being divisible, is being moved by its parts.

As an apple reddens on the high bough;
high atop the highest bough
the apple-pickers passed it by...
Sappho, Fragment 116

• Take an apple changing from green to red. At first it seems to be changing itself.

However, its color is being changed by sunlight in the 3,600 to 4,500 Å range. This light activates the anthocyanin in the apple's skin to absorb the near-ultraviolet, violet, blue and green regions of the spectrum, thus reflecting red. 

The redness of apples

So sunlight changes the anthocyanin, which is a part of the apple-skin.  In the common course of nature, red is that-toward-which the apple is determined.  In a less common course, i.e., in the absence of light, yellow is the end of the process.

Corollary 1: The changer must be actual with respect to the potency being actualized. 

1. That which is merely in potency does not actually exist.
2. Whatever does not actually exist cannot do diddly-squat.
3. Therefore, that which reduces a thing's potency to actuality must itself be actual.

Basically, a thing cannot give what it does not have, either formally or eminently. The match that sets the log ablaze possesses fire in a formal sense.  Sometimes an actualizer possesses the quality in an eminent sense: the match is actualized from being potentially alight to being actually alight by means of the phosphorus in the matchhead, which contains fire "eminently" and is actualized by friction.

Now there are often objections made to this by folks who (glancing ahead toward the telos of the syllogisms) feel compelled to deny the freaking obvious.

Objection A: What about inertia, hunh?

Inertia is not a principle of motion, but a resistance to change in whatever motion the body already has. As such, it bears a striking similarity to the principle of life in living bodies. As such, inertia is the very reason why a change in motion requires an outside force! A body in inertial motion is not changing its motion. It is changing its location, and the cause of that change is whatever imparted the original momentum in the first place. [Feser, 2012] 

The inertia concept does not seem to apply to other forms of motion: change of quantity or quality, as in generation/destruction, increase/diminution, and alteration. An apple moving from green to red does not keep going by inertia out into the infrared; a cat approaching a saucer of milk does not continue walking past it.

Objection B: What about quantum effects, hunh?

There ought to be a rule that says the first person to invoke quantum mechanics loses the debate.

Newtonian mechanics cannot predict
which apple will fall or when.
Are falling apples uncaused?

This objection often takes the form of a claim that radioactive decay is uncaused. But what is really meant is that an individual decay event is unpredictable. But the same is true in thermodynamics and life insurance: we lack  information on all the individual elements and so we must content ourselves with statistical pattern predictions rather than predictions of actual individual units. (cf. von Hayek, "The Pretence of Knowledge.") But even if an individual death event is typically unpredictable, no one claims that there is not a cause of death!

In fact, radioactive emissions do seem to have causes. If they did not, we would be unable to create them at will in nuclear piles. Bombardment with neutrons seems to work quite well.

The cause of the decay of an atom, says Figulus, is quantum mechanical tunneling, and it is governed by the time evolution of the atom's wave function. Over time the undecayed atom evolves into a superposition of decayed and undecayed states. According to the Copenhagen interpretation, the decay (or non-decay) of the atom is then caused by an observer looking at it. There are, of course, other interpretations beside Copenhagen who can give different causes, but they all give causes.

Now just as we may be unable to determine a cause of death, we may be unable to determined the cause of any one particular radioactive emission. (One supposes a multitude of potential causes available in either case.) But to claim that "we don't know what caused X" is not equivalent to "Nothing caused X."

We've only been noodling over the quanta for about a hundred years or so, so it's not beyond reason that we don't know everything yet. That quantum mechanics works out statistically means little. It's what von Hayek called the "pretence of knowledge." Besides, look how long Ptolemaic mathematics worked without being physically true!  There is a nice little overview by Richard Hassing of the differences between Aristotelian, classical, and quantum physics here.

Objection C: You haven't shown that every change even requires a changer! Hunh?

This is a denial that motion even requires an explanation at all. It's not that X is moved by another, by itself, or whatever; it's that it is not moved by anything. This one causes jaws to drop. Motion JUST IS! It is inexplicable. That sound you hear is the entire Scientific Revolution crashing and burning.

If TOF were to add up all the items denied by people trying to dance nimbly around the forthcoming conclusions, they would add up to an incoherent mess of mutually contradictory denials. When Free Will is on the table, sometimes foolishly justified by quantum uncertainty, the denialists will argue the strict determinism of 18th century mechanics. When First Cause is on the table, they will deny causal determinism and deploy quantum uncertainty. It is the denial that matters, not any desire for a coherent worldview.

The funny part about this objection is that no examples of uncaused motion are ever put forward. Go figure.

Of course, the more wary may realize that somewhere in our future is precisely something that moves without being moved, so they might want to rethink this objection.

Now there are more potent and technical objections to this first Lemma, such as those raised by Anthony Kenny. "Kenny accuses Aquinas of numerous logical fallacies, equivocations, irrelevancies, and—perhaps the most memorable accusation—of tying his arguments ... to an outdated and discredited Aristotelian/medieval cosmology." But TOF refers all such questions to  Dr. Oderberg, who has written an entire paper on just this Lemma. James Chastek nicely summarizes the matter:

The “moved by another” claim does originally mean... “no whole can be in motion unless it has parts which are moving”. This is clearest in organic wholes: if a hand is going to move, then the muscles need to move the tendons, and the tendons the bones. But this is also true of the inorganic: if some whole stone x is flying through the air and you stop a part of it, then either the whole x will stop altogether, or a part of it will break off and you will no longer have the whole stone. Either way, the relevant whole you were considering stops moving. Considered in this way, the only way one could have something natural in motion without its being moved by another would be if nature were composed of Euclidean points, but this seems impossible both a priori and on the basis of experiment. Nothing in nature is infinitely small.

-- "Moved by another and self-motion in nature" (Oderberg link added)

Now cometh Lemma the second, and to deal with that we must first address a distinction.

Distinction: A sequence of changers can be ordered essentially or accidentally. These are called per se and per accidens sequences.

A sequence is ordered accidentally if each changer in the sequence possesses the power to change another regardless whether any prior changer is still acting. For example: a woman may possess the power to give birth regardless whether her mother is still alive. She possesses the power of birthing in and of her own self.

A sequence is ordered essentially if each changer in the sequence possesses the power to change another only if a preceding changer is acting concurrently upon it. For example, a clarinet does not have the power to play Mozart's Clarinet Concerto in A in and of itself. It will only play if Sharon Kam is playing upon it concurrently.¹ A mover like the clarinet is called an "instrumental" mover, happily so since the clarinet is literally an instrument! In a similar wise, TOF's very own clarinet will not make music by itself. Unfortunately, it does not seem to make music even when TOF is playing it, although he has summoned ducks in this fashion.²

Clarifications:
1. Sharon Kam. Or Benny Goodman, or Mr. Acker Bilk, or et al. C'mon, work with TOF here.
2. TOF was a triple-threat man in concert band: he could wield clarinet, bass clarinet, and oboe with equal ineptitude. The oboe was especially effective for calling ducks. 

However, let us consider another example: that of a golf drive. The golf ball will not change its motion and leap off spontaneously toward the green unless the club strikes it. Certainly, it is moving with the rotating Earth and all that irrelevant crap; but it will not change unless it is struck, and kinesis means more specifically change by actualizing a potential. Similarly, the club possesses no power to move the golf club in and of itself. If the golfer is not swinging the club, the club will not be moving the ball.¹ The club is being moved in turn by the arms and shoulders, which are being moved by the muscles, which are being moved by the nerves, which are being moved by the motor neurons in the brain, which are being moved by chemical reactions at the synapses, which are being moved in turn by the will of the golfer.²

And more to the point of an essentially ordered series, the club will cease swinging if in media res the golfer were caught up in the Rapture™. Similarly, if Sharon Kam were removed, the clarinet would stop playing. Kinesis ceases!³

Stipulated, the club would undoubtedly fly off somewhere because the swing, once started, has given it an impetus that will take time to dissipate to the contrary impetuses of friction or gravity. But it stops changing relative to the act of driving a golf ball, and anything subsequent is accidentally ordered.

Similarly, some echo of the music may linger or there may be some time delay in the propagation of the music to more distant seats in the gallery,where they may hear the music after it has ceased being produced. This is utterly irrelevant. The concurrency of the mover and the mobile takes place at the point where the potential is being actualized. People who raise "objections" like these are no doubt sincere, but they have no idea how anal they sound. They think TOF is discussing a general theory of the physics of motion!

And that is "concurrent." Anyone caught using "instantaneous" should immediately wash his (or her) mouth out with soap. As Whitehead pointed out in his Principle of Relativity, there are no such things as "instants" or "instantaneous moments." All physical events occur over a span of time.

What it comes down to is this: instrumental (secondary) movers can propagate a change, but cannot originate it.  We are now ready for the second lemma.

Clarifications:
1. is moving. Notice the present progressive tense, which captures the sense better than Latin or Greek.
2. Yeah, will. Deal with it.
3. Kinesis ceases. It rhymes! TOF is tempted to do the entire post in rap.

The gear train cannot proceed without limit. Without a first
gear actually turning, none of the subsequent gears will turn.
This First Gear all men call Motor.

Lemma 2. There cannot be an infinite regress of instrumental changers.

1. An instrumental changer cannot transmit a change unless a primary changer is acting concurrently upon it.
2. An infinite regress has no primary changer.
3. There cannot be an infinite regress of instrumental changers.

A common example is a series of turning gears. Each gear is the series is turned by prior gear is the series. Since none of the gears possess the power of moving itself, the gear train will not move even if it is infinitely long unless there is a something called a motor or a crank or some other such thing.

 

Update: added comments by Figulus in the comm box to the narrative above.

Next Exciting Episode: The Big Kahuna 

Indicium Librorum

1. Aristotle. The Physics, Book VI. Book VIII
2. Augros, Michael. "A ‘Bigger’ Physics," The Institute for the Study of Nature, Jan. 28, 2009 (MIT)
3. Chastek, James. "On Jerry Coyne’s claim to miss no subtleties in St. Thomas’s arguments," (Just Thomism, Sep 8, 2009)
4. Chastek, James. "Moved by another and self-motion in nature," (Just Thomism, Dec 2, 2013)
5. Chastek, James. "Two bases for “everything in motion is moved by another," (Just Thomism, Jan 2, 2014)
6. Chastek, James. "Omne quod movetur as a principle of all physics," (Just Thomism, Jan 27, 2014 )
7. Chastek, James. "Inertia, the life of the inanimate" (Just Thomism, June 10, 2014)
8. Feser, Edward. "Clarke on the stock caricature of First Cause arguments," (Feser blog, Jul 12, 2014)
9. Feser, Edward. "The medieval principle of motion and the modern principle of inertia" in Proceedings of the Society for Medieval Logic and Metaphysics, Vol.10, 2012.
10. Gage, Lawrence. "Aristotle's Atoms" (Real Physics, Feb 6. 2006)
11. Hassing, Richard F. "On Aristotelian, Classical and Quantum Physics." (Lecture, Thomas Aquinas College, Mar. 7, 2003/updated 6/18/08)
12. von Hayek, Friedrich August. "The Pretence of Knowledge," Lecture to the memory of Alfred Nobel, December 11, 1974
13. Oderberg, David S. "Instantaneous Change without Instants," in C. Paterson and M.S. Pugh (eds) Analytical Thomism: Traditions in Dialogue (Aldershot: Ashgate, 2006): 101-18.
14. Oderberg, David S. "‘Whatever is Changing is Being Changed by Something Else’: A Reappraisal of Premise One of the First Way," in J. Cottingham and P. Hacker (eds) Mind, Method and Morality: Essays in Honour of Anthony Kenny (Oxford: Oxford University Press, 2010): 140-64.
15. Sachs, Joe. "Aristotle: Motion and its Place in Nature" (Internet Encyclopedia of Philosophy)
16. Schlappa, J. et al., "Spin–orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3." Nature 485, pp. 82–85 (03 May 2012)
17. Thomas Aquinas. Summa contra gentiles, I.13, (Dominican House of Studies)
18. Thomas Aquinas. Summa theologica, I Q2 art.3, (Dominican House of Studies)
19. Thomas Aquinas. Compendium theologiae, Bk.1 ch.3, (Dominican House of Studies)
20. TOF. In Psearch of Psyche: Some Groundwork. (The TOF Spot, July 11, 2014)
21. TOF. America's Next Top Model, (The TOF Spot, February 4, 2014)
22. Unknown.  Compendium of Theology -- translated into modern English
23. Vieru, Tudor, "Electrons Are Not Indivisible Particles." (Softpedia, April 19th, 2012)