St Thomas and Newton's Laws

[tacf]

I was wondering if anyone knew of a good derivation of Newton's Laws using Thomistic principles. I understand that some think Newton's Laws are just approximations of quantum mechanics, but I think that the vacuum is not a void and that can explain the variability in effect despite only one known cause. Otherwise, this would violate the principle of the uniformity of nature: The same natural causes under the same adequate set of circumstances always produces the same result (Princ 107 from Summary of Scholastic principles by Wuellner).
Anyways, below is the derivation I would give to someone in an intro to physics class. It does get to the three equations of Newton's 3 laws, which he gave but provided no metaphysical explanation for. This is my derivation after reading St Thomas' works, most especially the Summa and his commentary on Aristotle's physics.

Nature is an intrinsic principle of motion and of rest.
Motion occurs in the genuses of quality, quantity and place.
So there is a natural principle of rest with respect to place; let us call this mass. Mass- principle of rest with respect to place.
But since nature is an intrinsic principle of rest and motion, a body must have at least potentially an active principle of motion with respect to place; let us call this momentum.
Momentum - accidental principle of motion with respect to place.
And this is not contrary to St Thomas, who speaks of a power (virtus) imparted to a body moved by a principal agent, even in the case of violent motion. The violent motion lasts as this power remains. "An instrument is understood to be moved by the principal agent so long as it retains the power (virtus ) communicated to it by the principal agent; thus the arrow is moved by the archer as long as it retains the power wherewith it was shot by him . . . And the mover and the thing moved must be together at the commencement of but not throughout the whole movement, as is evident in the case of projectiles." St. Thomas, De Pot., q. 3, a. 11, ad 5. Cf. /// de Caelo et Mund., lect., 7, n. 6
To further clarify the definition of momentum, we note that a power is a quality; and since it serves as an efficient cause of motion with respect to place, it is an active power. But since a thing does not change essentially whether or not it has this power, it is an accidental power; for a stone is still a stone whether it is thrown or not.
Since inanimate beings have no volition, that which is their act will continue necessarily until it reaches its end or is stopped by another.
Now like begets like; i.e., the end of the thing is the form of the thing generated in another. Thus fire begets heat.
So the active power of motion with respect to place, i.e. momentum, begets such act in that which it contacts, contact being the means of all corporeal motion.
Now qualities are between two extremes; in this case, a power of rest and a power of motion. But the active power of motion and active power of rest with respect to place are from the same principle, both being subsequent to an object's nature with respect to place, and both active, for the same reason. For even accidental forms are such only because the nature of an object is such to allow and support them, noting that the nature of an individual object may support diverse degrees of a certain accidental quality. Still, once a being is in possession of such a certain accidental quality, its continuance is dependent upon the nature of the thing, which in the genus of place is also the principle of rest with respect to place. So, both the principle of rest and the principle of active motion with respect to place, are from the same nature, and are by the definition of nature the same.
Now, a certain motion with respect to place is velocity, v. But this is an operation of the accident of the power of motion with respect to place, i.e. due to its power, so this power can be quantified by quantifying the same motion. So the power is quantified by velocity, v.
But there is also the operation of the accident of the power of rest with respect to place when the object is not in motion, which has been defined as mass. And this too can be quantified, let it be m. But given the arguments above, this must persist when the object is in motion (since it is from its nature). So the true active power of motion with respect to place is given by a function of m and v. And since operation is proportional to power for the operation, we conclude the mathematical relationship representing the power of motion with respect to place to be a direct proportionality function, i.e., momentum = mv.
Now, when two bodies contact, they either have the same rest or motion with respect to place or not. If not, then the first acts as an agent to beget its like and impart its accidental principle to the second object. But because this takes place by means of contact, the second object also acts as an agent to beget its like to the first.
"Then [Aristotle] shows why it happens that a mover is moved. For it does not happen precisely because it is a mover but because it is such by touching; because to move is to act in order to cause something to be moved and what is so acted upon by the mover is moved. But whatever acts does so by touching, for bodies act by touching; hence it follows that what acts is at the same time acted upon, because that which touches is acted upon.." Physics 3, Lecture 4, 299.
Now, given that powers are subsequent to the forms of the two objects, and like begets like, the only results possible are some combination virtually present in the original forms, virtually being defined as "by way of active potency or efficacy, after the manner of a cause" (Dictionary of Schol Philos, by Wuellner). So, for any two objects (1 and 2) which touch and then separate (as objects 3 and 4), m1v1 + m2v2 = m3v3 + m4v4.
Now, a change in momentum is a change in a quality, which necessarily implies an efficient cause. Let us call this a force. Force - an efficient cause which results in a change in momentum. Evaluating the special case where mass is constant, we note that since change is proportional to the power of the efficient cause, which is force, we can conclude that F = m(v2-v1) for a change in velocity from v1 to v2 by the force.
But change in velocity is acceleration, so F = ma.
It is clear that if there is no efficient cause to change the power, the power will persist, so if F = 0, no change in momentum will occur.
Also, if two bodies are in contact but no change in momentum occurs, then the net force on the two bodies is 0. So if the bodies are exerting forces upon each other, F1=-F2.

[Geremia]

derivation of Newton's Laws using Thomistic principles

Have you read Pierre Duhem's letter to Fr. Réginald Garrigou-Lagrange, O.P.: "Note on the Validity of the Principles of Inertia and Conservation of Energy"?

cf. also my question: "Are mathematical suppositions of physical theories determined uniquely?"

[tacf]

I have followed your links and read them. Thanks. I put my thoughts below; hopefully they don't come across as too contrarian. 

First, the assertion of principle of inertia: "(1) of itself matter cannot set itself in motion or modify the motion that it has; (2) a body in motion, if no external cause acts upon it, retains a rectilinear uniform motion indefinitely."

This actually allows multiple interpretations. I will just take assertion (2) as it seems more narrowly defined.

Objection: There is no corporeal motion in the void, for motion is from potentiality to act, and the void has no potentiality as it has no matter, the principle of potentiality. Thus corporeal motion is always in corporeal matter. And all motion from a corporeal efficient cause involves touching because all corporeal agents have bodies by definition, and bodies act by touching. And in touching they are touched because they share the same matter (I.e, no fifth element).  All this is in St Thomas' commentary on Aristotle's Physics, with my only extra postulate being there is no fifth element. See Book 3, Lecture 4. So it is impossible for a body in motion to have no external cause acting upon it; so the principle of inertia postulates what happens if an impossibility is true. Well, from a false premise any conclusion can follow.

With this as background, now consider Fr Garrigou-Lagrange's conclusions: "...(1) one motion does not give rise to another except with the invisible concurrence of the First Being, which is the cause of all being as such, of the Prime Mover.... (2) Likewise, from the metaphysical point of view, a local motion cannot be perpetuated in a void, cannot be a perpetual transition from potency to act, without the invisible intervention of the pure Act..." 

(1) is true. (2) is a misunderstanding of a void, motion, and creation. A non-volitional form will act as long as it has a power and a suitable object for that power. The act in local motion is an accidental act in the category of quality, species of power, namely the power for local motion. The suitable object is place. Despite his misuse of the term void, it is true to say that any motion cannot be without the invisible intervention of the pure Act. 

His notes on the conservation of energy opens up a field too broad for me to consider right now.

Duhem starts his letter by saying he is not using the terms physics, axioms, etc in the scholastic sense, but in the technical sense.  So I will try to convey what I think he said, and then comment.

"The fundamental hypotheses of physics are not self-evident truths." 

Objection: That motion exists is self-evident. Once the meaning of the terms of its definition is known, it's existence is immediately assented to by the intellect. But motion's existence is a fundamental principle for the science of physics.  Aristotle and Aquinas go even further, and say the existence of nature is self-evident. Since I think Aristotle and Aquinas were proposing physical theories with fundamental principles, you can see why I have a hard time agreeing with the following Duhem conclusions: (1) We cannot categorically affirm any principle of a physical theory true. (2) We cannot categorically conclude any principle of a physical theory false so long as there has been no observation that disagrees with a deduction of a principle of the theory.

In the end, Fr. Garrigou-Lagrange and Dr. Duhem appear to conclude that it is impossible to know if the principle of inertia is true, and similarly it is impossible to know any truth regarding a principle of nature. But this seems to me absurd. Maybe I misunderstood them.

 

To your other link, "are mathematical suppositions of physical theories determined uniquely according to Aristotle and Plato?"

Depends what you mean by mathematic supposition. A math equation is written word which signifies spoken word which signifies the concept abstracted from the phantasm. Different symbols have a certain meaning by convention, which by definition can vary. Anyways, I would say you could give any meaningful mathematical supposition in words, which in turn would either reflect the concept or not, and in turn that concept would be true or false based on its correspondence with reality. So unless you say mathematical suppositions do not signify concepts, I don't see how you can say multiple suppositions can reflect the one reality, unless you admit that they are actually signifying the same concept. 

Objection mentioned in thread: St Thomas - "Although astronomers tried to reduce the irregularities [of the planets] to a right order by assigning diverse motions to the planets...Yet it is not necessary that the various suppositions which they hit upon be true—for although these suppositions save the appearances, we are nevertheless not obliged to say that these suppositions are true, because perhaps there is some other way men have not yet grasped by which the things which appear as to the stars are saved. Aristotle nevertheless uses suppositions of this kind, in what regards the quality of the motions, as true."

Reply: St Thomas is not saying that if multiple suppositions are found which save the appearances, all are true; only that the appearances can then not be used to disprove the suppositions. He is also speaking of planetary motion, which he considered a doubtful matter; so it seems incongruous to extrapolate from that to say that in general principles of nature do not have true mathematical representation varying only by convention. As he says, "Now the matters to be investigated are difficult, because we can perceive only a little about their causes; and their accidents are further removed from our ken than the bodies themselves are physically distant from us."

[Geremia]

Fr. Garrigou-Lagrange and Dr. Duhem appear to conclude that it is impossible to know if the principle of inertia is true, and similarly it is impossible to know any truth regarding a principle of nature.

Was Duhem's thought too much influenced by Pascalian skepticism? Similar to what Duhem wrote ("We shall never have the right to affirm categorically of any one of the principles of the mechanical and physical theory, that it is true."), St. Thomas wrote, In II De cælo lect. 17 n. 451:

it is not necessary that the various suppositions which they hit upon be true — for although these suppositions save the appearances, we are nevertheless not obliged to say that these suppositions are true, because perhaps theme is some other way men have not yet grasped by which the things which appear as to the stars are saved

To your other link, "are mathematical suppositions of physical theories determined uniquely according to Aristotle and Plato?"

[...] I don't see how you can say multiple suppositions can reflect the one reality, unless you admit that they are actually signifying the same concept.

Two or more different signs can signify the same thing.

[Geremia]

"The fundamental hypotheses of physics are not self-evident truths." 

Objection: That motion exists is self-evident.

Physics studies ens mobile. It doesn't formulate hypotheses about motion or being; that belongs to metascience (metaphysics).