The 12th century birth of the notion of mass which advised modern mechanics

(... and void and movement in the void)

Pp369-377 Duhem; Le Systeme du monde

Conclusion of Tempier, Averroes (Ibn Rushd), Ibn Bajja (Avempace)..

"And there came to be some Scholastics who believed, as Ibn Bajja did, that the true natural movement of a weight — its essential and simple movement — is the movement it has in a vacuum, and that the movement observed in a resistant medium is a complex movement consisting of the simple movement and the retardation introduced by the resistance of the medium. These scholastics were the precursors of Galileo, Descartes, and Beeckman, who developed the theory successfully. And by following the trail of Avempace, because of the discussion of Averroes, they would know that they were substituting a new dynamics for Aristotle’s dynamics."

(See also debates about the Impossibility of Void and Scholasticism before 1277: Ibn Bajja’s Argument; St Thomas Aquinas and the Concept of Mass.)

Robert Grosseteste fully supported the Aristotelian denial thus: "In nature the plenum behaves in such a way that it cannot not be; therefore the void cannot be …One can have only an indirect science of the void (per accidens); one can in no way have a direct science of it (per se). The void does not have a real definition, a definition of species. It admits only of a definition in name; it does not result that it is a being from its definition except as a manner of speaking (nisi secundum vocem tantum).

Refer to p 377 to 378 on.

In spite of the unanimity of 13th cent. Scholastics toward the rejection of the possibility of void, Ibn Bajja’s objection against one of Aristotle’s reason’s did not cease to preoccupy some of them. Although Franciscans like Roger Bacon, who often referred to the impossibility of void in his various writings, did not even allude to what Avempace had written, the Dominicans showed themselves to be more attentive toward this restatement of Joannes Philoponus’s arguments. Albertus Magnus gives a detailed exposition and an equally detailed refutation of the objection he attributed to Avicenna, and to Avempace (Although Averroes had affirmed the priority of the latter with respect to the objection). What Albertus asserts is only a paraphrase of the Commentator’s discussion in any case; no new conclusion emerges from his prolix paraphrase.

Albertus Magnus’ teaching was long retained by the Dominicans; we can recognize its reflection in what Ulric of Strasbourg asserted about movement in the void. After having demonstrated that weight would fall instantaneously in a vacuum as Aristotle, he relates, though some what obscurely, the objection he attributes to Avicenna and Avempace (as did his teacher). He rejects this objection because in his opinion it contradicts the rule that "Aristotle had formulated in books VII and VIII of the Physics: if a motor moves something, for some distance, during some time, the motor would move half of it the same distance, during half the time. [If Avicenna and Avempace are correct] the motor would be able to move the half more than the whole; it would be able to move half of it the same distance in less than half the time."

No reason is given for this assertion. Instead of retaining Albertus Magnus’ lecture, Ulric would have done better to have studied what St Thomas Aquinas wrote about the movement of a weight in a vacuum. Thomas Aquinas gives a concise analysis, both exact and penetrating, of Averroes’s reasonings; specifically he takes up the exposition of the fundamental principles of Peripatetic dynamics (as did the Commentator –Averroes), whose essential statement is as follows:

"But in regard to heavy and light bodies, when we subtract that which the mobile body has from the mover (meaning the form, which is a principle of movement and which the generator or mover gives), then nothing remains except matter, in regard to which no resistance to the mover can be considered. Hence it follows that in such things the only resistance is from the medium."

But Thomas Aquinas rejects Ibn Rushd’s reasons and judges them severely: "Sed haec omnia videntur esse frivola."

"When the form, which the generator imparts, is removed from heavy and light things, a body with magnitude remains only in the understanding. But a body has resistance to a mover because it has magnitude and exists in an opposite site [opposite to where movement would lead it]. No other resistance of celestial bodies to their movers can be understood."

Thomas thinks that this division between motor and moved thing that Peripatetic philosophy had declared impossible can be accomplished, at least, in thought; thought distinguishes, on the one hand, a form, the motive force or gravity, and, on the other hand, prime matter given determined dimensions, not prime matter bare and simple, but a quantified body occupying a certain location and resisting the force attempting to bring it somewhere else. Even though this division of a weight into gravity and a body of determined magnitude can only be accomplished in thought, it suffices in order for us to be able to assimilate the movement of heavy or light bodies with the movement of celestial bodies; it also suffices to render inoperative one of Aristotle’s objections against the possibility of void.

Thomas’s assertion is extremely brief; let us not allow its brevity to make us misunderstand its importance. For the first time we have seen human reason distinguish two elements in a heavy body: the motive force, that is, in modern terms, the weight; and the moved thing, the corpus quantum, or as we say today, the mass. For the fist time we have seen the notion of mass being introduced in mechanics, and being introduced as equivalent to what remains in a body when one has suppressed all forms in order to leave only the prime matter quantified by its determined dimensions.

St Thomas Aquinas’s analysis, completing Ibn Bajja’s, came to distinguish three notions in a falling body: the weight, the mass, and the resistance of the medium, about which physics will reason in the modern era."