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Aristotle identified a four-fold classification of causality:

  • Material cause, the material from whence a thing has come or that which persists while it changes, as for example, one's mother or the bronze of a statue (see also substance theory)

  • Formal cause, whereby a thing's dynamic form or static shape determines the thing's properties and function, as a human differs from a statue of a human or as a statue differs from a lump of bronze.

  • Efficient cause, which imparts the first relevant movement, as a human lifts a rock or raises a statue.

  • Final cause, the criterion of completion, or the end; it may refer to an action or to an inanimate process.

How does this work in Newtonian Gravity? Can one say for example the final cause of letting a stone fall is that it is attracted to the Earth? Its efficient cause is letting it go? And that there is no material or formal cause?

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  • Didn't Newton explicitly reject the notion of cause, and say only that his theory was descriptive, not explanatory? That's the famous "I frame no hypotheses" quote. So do you mean Newton himself? Or people who misunderstand his theory and believe that it's supposed to be explanatory? In Newtonian gravity, a stone falls toward the earth according to the laws of physics. No causation is implied, no mechanism is implied. We drop a rock, it falls according to an equation. End of story. This is a key point in the philosophy of Newtonian gravitation.
    – user4894
    Feb 14, 2015 at 2:15
  • Can you please clarify whether you are asking about Aristotle or Newton? If the latter, I'll post a response with source material showing that Newton explicitly rejected the notion of causation in his theory of gravity. But if you're asking about what Aristotle would have thought about Newton ... well, how could he have done that? I'm pretty sure you already know about Hypotheses non fingo, so I'm wondering what is the intent of your question. en.wikipedia.org/wiki/Hypotheses_non_fingo
    – user4894
    Feb 14, 2015 at 3:22
  • @user4894: I'm asking about Newton via Aristotle.
    – Mozibur Ullah
    Feb 14, 2015 at 12:24
  • I'm not asking what Aristotle himself would think about Causality in Gravity; but how the notion of Causality as classified by him stands in relation to Gravity. As for hypothesis non fingo, didn't Hooke actually buttonhole Newton about a proof of the inverse square law between the Earth and Sun . Which kind of makes one suspect it was a general hypothesis/conjecture that was floating around the intellectual sphere at the time.
    – Mozibur Ullah
    Feb 14, 2015 at 12:31
  • I'm not asking what Newton himself thought; but that would be of interest.
    – Mozibur Ullah
    Feb 14, 2015 at 12:34

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The four causes are a direct consequence of Aristotle's explanation of motion as the reduction of one mode of being (potentiality) to another (actuality). Thus, your question amounts to how motion (change) is understood in modern physics.
(Thomas McLaughlin is an expert on Aristotelian vs. modern physics' understanding of motion.)

The question of projectile motion is a good example of metaphysicians grappling with understanding the causality of motion in Newtonian physics. Is projectile motion as treated by modern physics really motion (i.e., the reduction of potentiality to actuality) requiring a cause, or is it really a static state?

For example, E. Meyerson, in his Identité et Réalité (1908), writes (pp. 132, 134):

the principle of inertia demands that we view motion as a state; if motion is a state, it must maintain itself like every state. … The principle of inertia demands that we view speed as a substance. Now this is an entirely paradoxical concept for the immediate understanding

Cf. Stanley L. Jaki's "The Physicist and the Metaphysician" regarding projectile motion, quid quid movetur ab alio movetur ("whatever is moved is moved by another"), and the Principles of Inertia and Conservation of Energy. For more on a metaphysician's perspective on the principles of modern physics, see Garrigou-Lagrange's letters to Pierre Duhem (PDF pp. 14-29).

Modern physics is a "scientia media" ("intermediate science"), halfway between the first (physical) and second (mathematical) degrees of abstraction—i.e., modern physics, like ancient astronomy, has "a closer affinity to mathematics, because in its thinking that which is physical is, as it were, material, whereas that which is mathematical is, as it were, formal." (St. Thomas Aquinas's Division and methods of the sciences q. 5 a. 3 ad 6). Now,

By its very nature motion is not in the category of quantity, but it partakes somewhat of the nature of quantity from another source, namely, according as the division of motion derives from either the division of space or the division of the thing subject to motion. So it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion. Therefore, inasmuch as the principles of quantity are applied to motion, the natural scientist treats of the division and continuity of motion, as is clear in the Physics. And the measurements of motions are studied in the intermediate sciences between mathematics and natural science [physics]: for instance, in the science of the moved sphere and in astronomy.
(ibid. q. 5 a. 3 ad 5)

This gives the reason for Meyerson's quote above. Modern physics is "formally mathematical," and mathematics does not "treat of motion, although mathematical principles can be applied to motion."

Leibniz discussed questions regarding causality and force; he, unlike Newton, was not afraid to give metaphysical reasons for Newtonian concepts. (cf. Pierre Duhem's Evolution of Mechanics pp. 16-19f.)

Further reading (from here):

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