Aristotle's theory of projectiles and the impetus theory

The so-called impetus theory was invented in late antiquity by Philoponus, found proponents among Arab philosophers and was also developed in the fourteenth century by Latin-speaking philosophers in western Europe concerning whom it seems not to be quite clear whether – and if so, to what extent – they could draw on Arab and antique sources.Footnote ¹ It replaced Aristotle's theory of unnatural locomotion of simple bodies, which he develops in Physics VIII referring to someone who throws something heavy – say, a stone – upward.Footnote ² According to Aristotle's cosmology, such a movement is for the stone unnatural inasmuch as, being by its nature heavy, a stone moves naturally downward, toward the centre of the earth and the cosmos. Four axioms are characteristic of Aristotle's theory of movement.Footnote ³ First, everything in motion is moved by something, by a mover;Footnote ⁴ second, the movement and the actual moving of the mover are temporally simultaneous;Footnote ⁵ and third, the mover and the thing moved must be either continuous or contiguous, in spatial contact with each other.Footnote ⁶ Finally, the mover of an unnatural movement is outside the moved body.Footnote ⁷ As to the stone, Aristotle assumes that it is initially moved by the thrower and her hand. Now, after the moment in which it leaves the hand the stone is no longer in spatial contact with the hand, and in the same moment the thrower seems to stop moving and might even perish. Hence after leaving the hand the stone could not move if the hand were the only mover of the stone.

Aristotle therefore assumes a further mover external to the stone, namely the air, the medium through which the stone moves. The hand moves not only the stone but also the layer of air with which it is in spatial contact, and this layer does the same to the stone and to the next layer.Footnote ⁸ Thus at each point of its upward movement the stone is moved by something with which it is in spatial contact, and so is each layer. As to the temporal aspect, Aristotle argues that, if a layer of air acted as mover only as long as it was moved by the hand or by the preceding layer, the movement of the stone would last only as long as the thrower moves. Therefore a layer of air must move the stone and the next layer longer than it itself has been moved by the preceding mover.Footnote ⁹ He seems to infer from this condition that a layer of air cannot act as mover simply because it itself has been moved, that there is in addition a force, a capacity to move (dunamis tou kinein Footnote ¹⁰), involved. Most medieval and most modern interpreters maintain that Aristotle assumes that the hand gives to the first layer of air a moving force that is transmitted from one layer of air to the next (and decreases along the way). In this respect, according to these interpreters, Aristotle himself already uses the key feature of the impetus theory – namely the transmission of a force from one body to another one – though he confines this transfer to the thrower and the different layers of the air and excludes the projectile.Footnote ¹¹ Classic mechanics rejects the first of Aristotle's axioms and, by implication, all the other ones. The impetus theory, however, shares with him the first three axioms and rejects only the fourth, for, according to its proponents, the thrower endows the stone with a moving force, the impetus, that moves the stone from within after the stone has left the hand. Franciscus de Marchia, in his lectures on the Sentences in 1319–1320, and, a few years later, John Buridan seem to have been the first to work out this theory in greater detail and with arguments for and against Aristotle's solution.Footnote ¹²

Inasmuch as the adherents of the impetus theory assume that there is a ‘moving force which passes from a moving cause to a movable object and acts on it’,Footnote ¹³ the notion of causality in the impetus theory is often called ‘transmission causality’,Footnote ¹⁴ as opposed to Aristotle's principle of ‘contact causality’.Footnote ¹⁵ Wolff claims that the ‘principle of transmission causality … is not Aristotelian … and could not have emerged out of an internal logic of Aristotelianism’.Footnote ¹⁶ I would like to suggest the opposite, namely that the impetus theory with its principle of transmission causality is essentially Aristotelian, and that it was probably developed by applying motifs of Aristotle's biology onto the issue of the projectiles. In the following section, I present the theories of Aristotle and Aquinas on action of bodies and movement, on the male semen in sexual reproduction and on resemblance between offspring and parents. It is the function of the male semen to transmit a moving force from the male parent into the menses. In the third section, I turn to the problem of the mover of the natural movements of the elements (fire, air, water and earth) and other simple bodies and to its history from Aquinas to William of Ockham. The impetus theory presupposes that simple bodies can have an internal mover. Aquinas denied this presupposition. Duns Scotus, however, affirmed this possibility. In this sense, Duns Scotus made it possible to invent the impetus theory. In addition, the impetus theory could be used to protect Aristotle's theory of movement against the threat of being dismantled and replaced with non-Aristotelian alternatives in consequence of Aquinas's and Ockham's suggestions regarding the movements of simple bodies. Thus I propose in the fourth section that, after Duns Scotus, the theory of the male semen could be applied to projectiles to invent the impetus theory. In addition, Franciscus de Marchia used Aristotle's theory of family resemblance to formulate his version of the impetus theory. In the fifth section, I compare objections to the impetus theory with the advantages of the impetus theory over Aristotle's theory of projectiles. In the final section, I comment on other suggestions regarding the genesis of the impetus theory in the Latin West. In an Appendix, I adduce some aspects that have been neglected in the secondary literature so far.

Aristotle and Aquinas on action of bodies and sexual reproduction

Whenever Aquinas addresses the question of the capacity of bodies to act – i.e. to act as efficient causes – it is against the backdrop of Avicebron's thesis, in Fons vitae, that they do not have such a power; rather, what seem to be the actions of the bodies are those of a certain divine power that pervades all the bodies.Footnote ¹⁷ Against this view, Aquinas lays out the basics of Aristotle's ontology. Every existing body consists of matter, an essential form and various accidental forms. It has all these forms in actuality and in virtue of several of them it can act on something else. The latter must fulfil two conditions in order for an action to occur. It must not have in actuality the form in virtue of which the agent acts but it must be able to have it. Because of these two qualifications it is labelled matter, and matter is said to potentially be, or have, the form: since one cannot, for example, build a house out of air, air is not potentially a house. In the case of an accidental change, the matter is a body, as, for instance, Socrates when he learns the art of architecture. In the case of the genesis of a body, it is some stuff, as, for instance, clay as the matter of a bowl or the menses as the matter of an animal. At the end of the action, the matter has a form just like the one in virtue of which the agent has acted onto it. Thus a transient action of a body is the propagation of the form in virtue of which the body acts, and which is after the action not only in the acting body but also in the matter that was acted upon.Footnote ¹⁸

In the literature, this propagation of a form from one subject to a different one is often called its ‘transmission’. As Wolff says, the ‘revolutionary’ feature of the impetus theory is a ‘new notion of causality’; prior to the impetus theory,

Wolff defines here both Aristotelianism and the impetus theory through transmission causality, and the difference is only that in Aristotelianism bodies do not transmit immaterial forces. He is, of course, completely right in that in Aristotelianism bodies do the same thing as they do according to the impetus theory, namely transmit entities, i.e. bring about that a different subject has a form like the one that the transmitting body has, and in virtue of which it acts. They transmit not only motion and velocity but many other forms that bodies can have. As a matter of fact, they transmit in the first place forms, and use (transient) motion as a means to transmit forms.Footnote ²⁰ Male animals transmit, that is to say reproduce, their essential forms in the menses; physicians, architects and other technicians reproduce the forms they have in their mind in patients, stones and so on; and all these technicians also reproduce the habit of their art through teaching – the cultural equivalent to sexual reproduction – in students of their arts so that the respective habits can continue to be active in different individuals.Footnote ²¹ This common ground of transmission of entities is of course the reason why, regarding projectiles, the way from Aristotle to the impetus theory was not that long. Still, several distinctions have to be observed.

The most important one is certainly that the propagation of a form does not mean that one and the same entity would move, or expand itself, from one body to the next. As Aquinas says,

In addition, most of these forms and bodies do not act immediately onto matter but only through, as Aquinas says, instruments. The hand and knife of a sculptor act as efficient causes onto a piece of wood so that the wood becomes, say, a sculpture of Socrates. Neither the hand qua hand nor the knife qua knife has the form of Socrates. Still, each of them acts as (instrumental) efficient cause of the appearance of this form in the wood inasmuch as both of them are applied as instruments by an artist who has the form of Socrates in his mind.Footnote ²⁴ Thus an instrument acts in virtue of a form of a substance, and this is the reason why an instrument can produce things that are different from, and ontologically more than, that which the instrument itself is, namely, say, this particular part of a body or this particularly shaped piece of metal.Footnote ²⁵ Natural bodies act through the so-called active qualities as instruments. Aquinas distinguishes two general cases:

An example of the first kind would be the heat of a fire that lights a candle. Such natural actions and most, if not all, technical productions have in common that each instrument in a series of instruments must be in spatial contact with its mover as well as with the body (another instrument or an instance of matter) that it moves, and that each instrument moves the adjacent body only as long as the primary mover exists and, in many cases, also moves the first instrument (once the sculptor, moved by her soul, stops moving the hand the knife will no longer move the wood). In addition, there is nothing that passes from one subject to a different one; no part of the primary mover or of any of the instruments moves over to the next subject, none of their forms or movements and no part of their matters. The movement in the candle is produced by the heat of the fire and the movement in the wood by the knife and its movements. However, these are in each case two different movements in two different subjects, and it is not the case that any form, matter or movement has moved as one and the same numerically one entity from the fire into the candle or from the knife into the wood.

According to Aquinas, things are different regarding the second kind of instrument, natural heat in sexual reproduction. Male semen certainly plays a role in it, and it does so after its ejection, and even if the male has passed away in the moment of the ejection. But what precisely is that role, and how does the semen fulfil it? According to Aristotle, both males and females are causes of procreation but in different ways. The contribution of the female, the menses, functions as the matter of the offspring while the male, via his semen, provides the source of motion, the mover.Footnote ²⁷ Male semen consists of some material and a capacity to move – a dunamis tou kinein, a mover – that is the efficient cause of genesis and motion.Footnote ²⁸ The dunamis moves the menses, and it does so according to a specific logos (ratio, ‘score’) that has been imprinted in it by the essential form, the soul, of the male parent. No material part of the semen enters the menses, and the dunamis moves the menses such that the offspring acquires its own internal source of motion, its own internal mover, and finally has in actuality the same kinds of forms and parts that the male parent already has in actuality.Footnote ²⁹ Aristotle does not use many of the distinctions that medieval scholastic philosophers have developed, and he does not use in this context the vocabulary of the different ways of being one that he sometimes employs in ontological contexts. In other words, it might not be wholly impossible to reconstruct the pertinent passages in On Generation of Animals according to Aquinas's concept of the reduction of matter from potency to actuality according to which nothing moves as numerically one and the same entity from the agent into the patient, and which I will call the trigger model of movement.

Aquinas, however, self-evidently assumes that Aristotle means something different. He concludes one of his own discussions of sexual reproduction, in which he refers to On Generation of Animals, as follows:

Or, since the appetitive soul rules only over actual parts of the body, bodily parts that have been cut off do not obey the appetitive soul: ‘by contrast, the semen [a waste product, not a bodily part in the strict sense] is moved by the generative soul, not through commands, but rather through the transfusion [transfusionem] [evidently from the body into the waste product] of a certain force, which remains in the semen even after it has been ejected’.Footnote ³¹ Obviously, Aquinas self-evidently assumes that, according to Aristotle as well as the truth, this force moves as numerically one and the same entity from the male into his semen and from there into the menses, in which it operates as mover in the different stages of the development of the embryo until the embryo has developed its own internal mover, the heart. Thus the different forms and parts of the offspring are numerically different from the respective ones of the male parent, and it is not the case that any of the latter has moved, as numerically one and the same entity, from the male parent into the embryo. However, the force has done so. I will call this model of movement – according to which an agent moves an instance of matter through something that moves, as numerically one and the same entity, from the former into the latter – the migration model.

Another theory in On Generation of Animals turned out to be important for the development of the impetus theory, namely Aristotle's explanation of family resemblance.Footnote ³² He assumes a factor in the menses due to which the menses resists the moving force of the male semen. The male semen acts as mover through its heat while the menses is cold: the semen has to heat the menses, has to cook it up. The sex and the other features of the offspring depend on the degree of resistance of the menses against being cooked, and this degree depends on the quantity of coldness in the menses. One extreme is that the menses does not offer any resistance at all. In that case, the offspring is exactly like the father – his twin or double, as it were – and this case is obviously Aristotle's ideal.Footnote ³³ At the opposite extreme the menses offers so much resistance that the offspring is not even a human being. Normally, the offspring is somewhere between these extremes. The stronger the resistance of the menses the more the offspring is drawn to the side of the mother and will be more similar to her and her ancestors than to the father and his ancestors. As Aristotle says, when the principle, the moving force transmitted through the male semen,

This is the case because, in general, ‘the agent itself is acted upon by that on which it acts; thus that which cuts is blunted by that which is cut by it’.Footnote ³⁵ Or, as a summary: ‘That which is acted upon deviates and is not mastered either through deficiency of power [dunameôs] of the concocting and moving agent or because of the quantity and coldness of that which is concocted and structured’.Footnote ³⁶

As one sees, if the impetus theory is about a force that moves as numerically one and the same entity from one subject to a different one, Aristotle and Aquinas's theory of the male semen can have served as a paradigm. The male parent is the model for the thrower, the semen for the hand, and the menses for the projectile. In both cases, a primary mover (male parent, thrower) imparts via an instrument (semen, hand) to another body (menses, stone) a moving force that moves the latter from within, without spatial contact between the moved body and the primary mover, without any further action of the primary mover and even if the primary mover has passed away in the meantime. In addition, in both cases the moved body acquires a state (forms and parts of the foetus, final location of the projectile) that is already present in the primary mover (as the parts of the male parent, as an idea in the mind of the thrower). In other words, in both cases there is a moving force that passes as numerically one and the same entity from one subject to a different one, that acts in spatial separation from the primary mover, and that does so even if the primary mover has passed away. In fact, in sexual reproduction matters are even more complex than in the impetus theory. As in contrast to the hand, the semen itself already operates like a projectile, i.e. in spatial and temporal separation from the primary mover and its moving; a projectile, in addition, that transmits the force which it has received to a further subject. Furthermore, since already the semen operates as a projectile there is, in contrast to the case of the thrower and the projectile, no need for initial spatial contact between male parent and menses. As I show in the next section, Aquinas himself could not yet apply Aristotle's theory of the male semen onto the projectile because, for him, it was impossible that a simple body could have an internal mover. However, Duns Scotus removed this obstacle.

The natural movements of the elements

The light elements (fire and air) move by nature upward and the heavy ones (earth and water) and mixed bodies, such as stones, downward. What is the mover of these movements, i.e. of their natural movements? An author of the fifteenth century, Nicoletto Vernias, deemed this question the ‘most difficult’ problem in natural philosophy.Footnote ³⁷ Since these bodies have these movements as their natural ones, the respective mover should be within them; yet, since they do not have a soul and are homogeneous, it seems impossible to distinguish within them moving parts and moved ones.

Aquinas speaks sometimes of an impetus that was given to a projectile by the thrower. A ‘particularly interesting’ passage occurs in Aquinas's commentary on Aristotle's Physics,Footnote ³⁸ in his interpretation of Aristotle's very discussion of the ‘most difficult’ problem in Physics VIII, 4. Aristotle talks several times of hindrances (e.g. a stone on a wineskin or a pillar on which a stone is lying) and those who remove them, and he says that such removers are not per se but only accidentally the movers (of the water gushing out of the wineskin or of the stone falling down) as a wall from which a ball is rebounding is only accidentally the mover of the ball whose per se mover is rather the thrower.Footnote ³⁹ According to Aquinas, these characterizations are appropriate, since

The generator of the element is also the mover of its natural movement, and this generator uses the essential form that it has given to the element as an instrument through which it moves the element.Footnote ⁴¹

The essential form of the element is not the mover since it is not a ‘principle capable of moving or an active principle’ (principium motivum aut activum) but only a ‘passive principle’ (principium passivum).Footnote ⁴² As Aquinas says in his commentary on On the Heavens, Averroes is right in maintaining that the generator is the mover of the element but he is wrong in maintaining that the immediate mover is the essential form of the element and not the generator.Footnote ⁴³ In other words, regarding its natural movements, an element does indeed have a principle of motion in itself but this principle is not, as Averroes has it, an active principle, a mover; rather, it is a passive principle, a ‘capacity through which something is naturally susceptive to the movement exerted by something else’,Footnote ⁴⁴ a capacity of being moved in a specific way (e.g. earth or a stone downward and air upward) by a mover that is different from the essential form, the entity that functions as the passive principle. In the same context, Aquinas says that, regarding an unnatural movement (e.g. a stone thrown upward), the moved body has no internal principle, neither an active nor a passive one. While the generator of an element does indeed impress into the element a (passive) principle of its natural movement, a violent mover impresses into the stone only movement and no principle of movement, for otherwise the violent movement would result from an internal principle, which contradicts the notion of violent movement; in addition, a stone would, simply by being violently moved in space, undergo a qualitative change, which contradicts the empirical evidence.Footnote ⁴⁵ Referring to this passage and similar ones, Maier concludes that, in the passages with an impetus, Aquinas does not, as some interpreters claim, propose the impetus theory but uses comparisons in a popular idiom without theoretical relevance.Footnote ⁴⁶

In his interpretation of Physics VIII, 4, Aquinas considers, like Aristotle himself, the case of something heavy – e.g. water – that is heated by something already warm – e.g. a fire – and thus turns into air, which then moves upward. Hence there are two successive movements – the first the transformation of water into air and the second the upward movement of this air – and the mover of the first movement is definitely outside the water for it is a different body, the fire, that heats the water (and, in doing so, is the generator of the air). Now, according to Aquinas, Aristotle says in lines 254b33–254a18 that, in contrast to animals, the elements cannot have an internal mover of their natural movements, and he concludes that also the mover of the second movement is outside the element and is the same mover as the one of the first movement, namely the generator, the fire that has transformed the water into air. It seems unavoidable that this explanation violates the second and the third axioms of Aristotle's theory of movement. Duns Scotus, at any rate, interpreted it that way, for he objects that the generator cannot be the mover of the second movement because the movement continues even if the generator has passed away right after the end of the first movement, and if one says that the generator is present as a force in the instrument, this force must be an actual mover, which something like a passive principle is not.Footnote ⁴⁷

Duns Scotus maintains – in his view, following Aristotle – that the mover of the second movement is the essential form of the moved body (in the examples, the essential form of the air and the one of the stone).Footnote ⁴⁸ William of Ockham adopts this solution,Footnote ⁴⁹ and applies the two directions that Aquinas's solution of the ‘most difficult’ problem might take to the issue of the projectiles. Unless Aquinas adds (which he never seems to do) that the generator moves also the medium, the generator cannot but move the second movement through an action at a distance (i.e. acting on things with which the agent is not in spatial contact and such that the bodies in between do not act as instruments) and thus violate the third axiom of Aristotle's theory of movement. What is more, if one takes into account Duns Scotus's objection, it might be unavoidable to say that the element moves without any mover (and thus violates even the first axiom). Ockham rejected Aristotle's theory of projectiles (since it contradicts the empirical evidence) and argued that some agents – for example, the Sun, magnets, throwers of projectiles – could act at a distance.Footnote ⁵⁰ He recognized later that, in contrast to magnetism and the Sun, the existence of the thrower is necessary only for the beginning of the movement. Thus he declared that, after the separation of projectile and thrower, the mover was the moved thing itself and therefore mover and moved thing were wholly indistinguishable.Footnote ⁵¹ This statement amounts to the claim that the movement of the projectile does not have a mover, especially if one keeps in mind his general theory of locomotion, namely that locomotion is not a thing different from the thing in motion.Footnote ⁵²

The step from Aquinas to Duns Scotus is for two reasons not very difficult. First, since Aquinas himself speaks of the essential form of an element as an internal principle and instrument, one just has to shift the emphasis from the generator to this form to recognize it as the internal mover. Second, the identification of the form as the internal mover of an element assimilates the case of the elements to the general model of causation and action that I presented in the second section, and according to which a body reproduces one of its own forms in a different individual in which this form acts as mover independently of the reproducing body (as when a physician teaches medicine to students who then can act as physicians independently of their teacher). By the same token, one has simplified the theory of natural movements for, now, all natural movements – those of animated beings as well as those of simple bodies – have an internal mover, while, according to Aquinas, the latter have only a passive principle.Footnote ⁵³ If the generator can give to the stone an internal mover, why should the thrower not do so as well? Franciscus de Marchia and Buridan adopt Duns Scotus's solution of the ‘most difficult’ problem,Footnote ⁵⁴ and in the first draft of his commentary on the Physics Buridan recommends the impetus theory by pointing out that, after all, it is the heaviness that moves, as an internal mover, the stone in its natural movement.Footnote ⁵⁵ He seems to want to indicate with this remark that Duns Scotus's solution of the ‘most difficult’ problem has taken the decisive hurdle after which one can try to further streamline the theory of movement by assimilating not only the natural but also the unnatural movements of the elements to the general model of causation and action. In the printed version of his commentary, Buridan offers, besides empirical arguments, only one reason for the impetus theory, namely that if one assumes that a moving force can be impressed by the thrower into the air, ‘we can say, and have to say’,Footnote ⁵⁶ that such force can be impressed into the stone. Aquinas still accepted Aristotle's explanation of the projectile,Footnote ⁵⁷ and could not yet take advantage of the fact that already Aristotle himself used the decisive feature of the impetus theory since Aquinas could not even in the case of the natural movements of the elements recognize an internal mover. However, Duns Scotus paved the way to turn a feature of Aristotle's theory of projectiles against this theory itself and further streamline the theory of movement.

In fact, Duns Scotus's solution of the ‘most difficult’ problem not only enabled the Latin philosophers to develop the impetus theory, it also forced them to do so if they wanted to keep the movement of the projectile within Aristotelian parameters. As I pointed out, Aquinas's solution of the ‘most difficult’ problem and Ockham's two suggestions concerning projectiles violated one or more of the axioms of Aristotle's theory of movement. Regarding the natural movements of the elements one can shift from Aquinas to Duns Scotus in order to safeguard this case against the threat of dismantling Aristotle's theory of movement. Thereafter, however, an Aristotelian would no longer take Aristotle's theory of projectiles for granted. The prospect of further streamlining Aristotle's general theory has opened up, and at the latest after Ockham's critique the validity of Aristotle's theory of projectiles is at stake. Turning, after Duns Scotus's solution of the ‘most difficult’ problem, back to Aristotle's theory of projectiles, one can no longer ignore the fact that it is in no way a particularly elegant theory,Footnote ⁵⁸ and one realizes that it is, most probably, just false.Footnote ⁵⁹ However, an Aristotelian will adopt none of Ockham's proposals either. They will simply be beyond the imagination of an Aristotelian, or she will believe that she has good reasons to defend the Aristotelian theory against such alternatives. In this situation, the best move is to apply Aristotle's general theory of movement and causation not only to the natural movements of simple bodies but also to their unnatural ones and develop the impetus theory. In this way one achieves an elegant theory that is confirmed by the phenomena,Footnote ⁶⁰ and which streamlines Aristotle's theory of movement, and one further protects Aristotle's theory against the threat of being dismantled.

Buridan discusses the question whether the impetus is the movement itself or something different. The first alternative means that the movement is its own cause, or, for Ockham at any rate, that it has no cause. As one sees, the question is whether one accepts an explanation that ultimately violates all the axioms of the Aristotelian theory of movement, or whether one avoids this prospect by adopting Buridan's impetus theory. As to the first alternative, Buridan does not mention the second possibility but argues that the impetus is not the movement itself because nothing can produce itself and, furthermore, there would be an infinite regress of movers.Footnote ⁶¹ In addition, he adduces some who say – according to him, jokingly – that a movement can cause itself inasmuch as, after its beginning, one phase of it produces the next one. However, he rejects this assumption since it violates the necessary temporal simultaneity of movement and mover.Footnote ⁶² Thus if the movement cannot be its own cause it has no cause. To avoid this road the mover must be different from the movement.Footnote ⁶³ In other words, for Buridan the first and the second axioms of the Aristotelian theory of movement are self-evident – so much so that, in his response to the challenge to their validity, he just reaffirms them. He can easily do so since it is precisely the impetus theory that enables him to save Aristotle's theory of movement against the threat of being dismantled.

Aristotle's biology as the paradigm of the impetus theory

Even though for Aquinas the impetus theory was out of the question, he has provided the road map for its development. As I quoted, he assumes that the active force in semen and embryo stems from the father and acts in virtue of his soul. In Quaestio disputata de potentia, he is confronted with the objection that this is impossible since, in that case, the force in the semen would act as an instrument of the father, but an instrument moves only as long as it itself is moved by a mover, and mover and moved thing have to be conjoined, which is not the case with the force in the semen and the soul of the father.Footnote ⁶⁴ In his response, Aquinas advances the general thesis that ‘an instrument is considered to be moved by the principal agent as long as it retains the force that has been impressed in it by the principal agent’,Footnote ⁶⁵ and he illustrates this thesis with all of the three kinds of case that I have discussed so far:

Wolff refers to this passage to claim that the notion of semen as an instrument of the father is alien to Aristotelianism, and that therefore, historically, the impetus theory of projectiles preceded the theory of semen as an instrument.Footnote ⁶⁷ However, this notion of the semen – as an instrument that can operate when spatially separated from the male parent and even if he has passed away in the moment of the ejection – is crucial in Aristotle's On Generation of Animals.Footnote ⁶⁸ As I pointed out, Aquinas adopted this theory, used it always in his frequent discussions of the issue and obviously never challenged it. By contrast, in his commentary on Physics VIII, 10, he explains Aristotle's theory of projectiles without in any way challenging it,Footnote ⁶⁹ in his interpretation of the natural movements of simple bodies he explicitly denies that a simple body can have an internal mover of its movements, and in his commentary on On the Heavens he says that a simple body cannot even receive a passive principle of its unnatural movements.

In addition, only if one maintains, as Wolff does, that the ‘spirit’ of the impetus theory is not Aristotelian will one assume that the Latin philosophers found the impetus theory in Greek or Arab sources or invented it in an act of non-Aristotelian imagination. However, this assumption is in no way necessary. When one assesses a theory, it is useful, or even unavoidable, to try to consider alternatives. Now, according to most medieval philosophers, in his theory of projectiles Aristotle himself talks of a force that is transmitted from one subject to different ones. Therefore, even if one does not know Aristotle's theory of the semen, but particularly if one does, one will not have many difficulties in formulating an impetus theory (and then, if one wishes, rejecting it on the ground that Aquinas adduces, or, if one accepts Duns Scotus's solution of the ‘most difficult’ problem, adopting it).Footnote ⁷⁰ Furthermore, any answer to a question or an objection has to take into account the intellectual state of the questioner, and the participant who raised the objection against Aristotle's theory of the semen obviously did not know this theory. For this reason, the order of the examples in Aquinas's answer most probably does not say anything about the historical order of the acquisition and development of different theories by Aquinas and others but only about Aquinas's opinion of how to lead in the best way possible the participant to an understanding of Aristotle's theory of the semen.

In addition, the participant had a notion of instrument that was so narrow that it even excluded the impetus theory. If one wanted to familiarize such a person with Aristotle's theory of the semen, it was certainly a convenient way to adduce the impetus theory as a model, for here one had the same relations in a simpler version which, in addition, could be demonstrated to the eye. If the person then objected, one would lay out the differences that cause the model not to work in the case of the projectile but to work in the case of the semen. To use a model in this way, it is not necessary to regard all of its possible applications as true. As a matter of fact, if Aquinas really thought of the impetus theory, he would have to mean in the second example also an active principle, for otherwise the bridge to the case in question, the semen, would break down. However, as was mentioned, he himself regards the essential form of an element to be only a passive principle, and he seems never to have challenged this assumption. Thus he means in the second example either an active principle or a passive one. In the first case, he does not regard this example to be true and there is therefore no need to assume that he subscribes to the impetus theory. In the second case, he cannot mean in the first example the impetus theory.

Finally, for the reasons mentioned it is of course possible that, in the quotation at the beginning of my third section, Aquinas thinks of the impetus theory, and that he could do so without the help of non-Latin sources or a non-Aristotelian imagination. However, it is not even necessary that Aquinas has the impetus theory in mind for he uses in the quote the word ‘impetus’ also for the essential form of an element, in his view a passive principle. Similarly, it is in no way necessary that, in the quote at the beginning of this section, he talks about the impetus theory. As to the second and the third examples, he says explicitly that the force is in the generated element and in the semen, regarding the first example, however, only ‘as long as the force … lasts’. Thus in the light of the question of his seriousness about the examples, it is not only possible but even highly probable that, in the first example, he is talking about Aristotle's theory of projectiles. He has two points here. The first is that all the three cases have in common that there is a force involved that operates in spatial separation from its giver, and regarding this point it does not matter whether the force is in the moved thing or in a medium. The second point is the theory of the semen, and here Aquinas would offer one of those series of intensification and completion that are a hallmark of his philosophizing: in the case of projectiles the respective force is active but outside the moved body (namely in the air), in the case of the natural movement of simple bodies inside but passive, and only in the semen (and embryo) both inside and active. Aquinas is well aware of the differences between Aristotle's (and his own) theory of projectiles and Aristotle's (and his own) theory of the semen. In a further discussion of procreation, in Quaestio disputata de anima, he is confronted with the thesis that nourishing and other activities in the embryo are caused not, as he himself assumes, by a force in the embryo that comes from the male parent, but rather by the soul of the embryo, for

Aquinas answers that

In the light of all these considerations, it is much more likely that, historically, the development did not, as Wolff assumes, begin with the impetus theory, but rather led, as I suggested in the preceding sections, from the Aristotelian theory of the semen via the ‘most difficult’ problem to the invention of the impetus theory.Footnote ⁷³ Aquinas's analogy between semen, element and arrow showed the way – not for those whose notion of instrument was so narrow as to exclude all three kinds of case, but for those who already knew Aristotle's theory of the semen, a biological specification of his general theory of action and causation or even, given the primacy of animals in Aristotle's natural philosophy, its heart. Duns Scotus pushed Aquinas's analogy of the semen and the natural movements of the elements a step further than Aquinas himself had done in the quote in this section, and filled the gap that Aquinas had left between the natural movements of the elements and the general theory – the absence of an active principle in an element. Thereafter, Franciscus de Marchia and Buridan removed the difference between the projectile in Aristotle's understanding on the one hand and his theory of the semen and the general theory of action on the other and attributed an internal mover not only to the menses and the natural movement of an element but also to the projectile.Footnote ⁷⁴

In sum, Aristotle's theory of the male semen could provide for the impetus theory the paradigm of a force that moves, as numerically one and the same entity, from one subject to a different one. As to the way in which the force is received in the projectile, Franciscus de Marchia used Aristotle's theory of family resemblance, which I summarized above in my second section. From the viewpoint of Aristotle's ideal case – the doubling of the father – the shortest summary of this theory is that a force with a certain amount of heat will realize itself in the menses the better the smaller the quantity of coldness in the menses is; that is to say, the less cold, the less opposite to the semen, the menses is (or the closer to each other semen and menses are). Before adducing other evidence, Franciscus de Marchia presents three arguments which Maier does not discuss since they are, in her opinion, ‘distinctively speculative and hardly intuitive’,Footnote ⁷⁵ and taken ‘from the most abstract ontological sphere and not from experience’.Footnote ⁷⁶ This assessment is certainly wrong for at least the first of these arguments is an application of Aristotle's theory of family resemblance.

Franciscus de Marchia shows that the impetus is received also by the medium, the air, but much better by the projectile, say a stone. The first premise of the first proof is that, in contrast to lightness and heaviness as parts of the essential forms of the elements and as movers of the elements in their natural movements, the impetus does not have an opposite.Footnote ⁷⁷ As one can also see in his proof of the second premise, with this thesis he obviously locates the impetus in the middle between the two mutual opposites and extremes, heaviness and lightness. The second premise is that every moving force that has no opposite and can be received by the air can also be received by any mixed body and much more so by the latter than by the air.Footnote ⁷⁸ He proves this sentence in the following way: a form that has no opposite is much more capable of being received by a subject that has no opposite than by a subject that has an opposite.Footnote ⁷⁹ Now, the forms of mixed bodies are more removed from the extremes of an opposition than are the forms of elements (since the latter are these extremes themselves); to put it differently, the forms of mixed bodies (and these bodies themselves) are somewhere in between the middle and the extremes, namely the essential forms of the elements (and these elements themselves).Footnote ⁸⁰ In other words, since the impetus is in the middle, the opposition, or distance, between the impetus and mixed bodies is smaller than that between the impetus and the elements. Thus the impetus is more easily received by a stone or any other mixed body than by an element.Footnote ⁸¹ (It is received best by the mixed body that is precisely in the middle between the extremes.) In brief, the impetus is in the middle and is better received by something closer to the middle than by something more remote from the middle. In other words, it is as in Aristotle's theory of reproduction: the less opposite to the moving force the subject is the better this subject receives the force.

Since Franciscus de Marchia compares aspects of the impetus three times with the heat produced by a fire in a body of water,Footnote ⁸² one might think that he applies here assumptions about such phenomena to projectiles. After all, if two bodies of different temperatures are brought in contact with each other, the cooler body gets warmer and the warmer one cooler. However, these processes differ from insemination and impetus in one crucial aspect. The larger the temperature difference between the two bodies is the more action occurs, and if they are of equal warmth – i.e. if there is no opposition between them – nothing happens; no heat, no coldness is transmitted from one body to the other. In other words, the temperature difference and the quantity of action are proportional to each other. It is the same with any qualitative change, for the closer to the final state a subject already is the less action and movement have to take place, and if something already fully has a form in virtue of which an agent can act, there will be no action and movement at all. In the case of semen and menses, however, the temperature difference and the quantity of action are inversely proportional to each other inasmuch as the moving force of the semen is received by the menses the better the less opposite to, or the more like, the moving force the temperature of the menses is, and the moving force realizes itself within the menses to the highest degree possible if there is no opposition between the moving force and the menses. By analogy, according to Franciscus de Marchia the stone receives the impetus better than the air does, and it is moved by the impetus more than the air is, because it is less opposite to the impetus than the air is. Thus it cannot have been the mentioned phenomena but only Aristotle's theory of sexual reproduction that enabled Franciscus de Marchia to develop his first argument,Footnote ⁸³ and he looks upon the issue from the same perspective as Aristotle does in his ideal case of sexual reproduction, the doubling of the male parent. At a later point, Franciscus de Marchia summarizes his first three arguments thus: ‘the more appropriate to a mover a mobile thing is and the less it resists the mover the more it is able to receive the mover and the more it does receive it’.Footnote ⁸⁴ This statement is, in this context at any rate, nothing but an abbreviation of Aristotle's theory of family resemblance in On Generation of Animals.

Objections to the impetus theory and its advantages

There are two major objections to the impetus theory. First, it is impossible to distinguish in a simple body a moving part and a moved one.Footnote ⁸⁵ Both Buridan and Franciscus de Marchia maintain that the movement cannot be its own cause since this would violate the law of non-contradiction.Footnote ⁸⁶ Still, both leave it at that and make no effort to show how the force can move the body.Footnote ⁸⁷ When Buridan, as I mentioned above, suggests that there is no significant difference between a force in the medium and a force in the stone itself, he ignores that the latter moves the body in which it is while the former moves a different one.

Second, if the stone has an internal mover of its unnatural movement the distinction between natural and unnatural movements seems to collapse. The notion of nature and natural movement in Aristotle has been interpreted differently. Both Aquinas and Duns Scotus assume that, according to Aristotle, as well as to the truth, nature is in the first place a passive principle in the sense that I have already adduced, and that for a movement to be natural it is sufficient that the moved body has such a principle, which is absent in an unnatural movement.Footnote ⁸⁸ Since this distinction is neutral towards the presence or absence of an active principle in the moved body, it allows one without any difficulty to attribute to an unnatural movement an internal mover. Ockham and Buridan, however, regard nature as, according to Aristotle, as well as to the truth, an active principle, a mover.Footnote ⁸⁹ Buridan suggests that the movement of the stone upward is unnatural and violent because

This is certainly a sound way to preserve the difference even under the assumption of nature as a mover. In addition, the impetus theory leaves untouched all the other cases of technical movements, and already Aristotle himself says that a technical movement can accidentally have an internal mover.Footnote ⁹¹

As to the advantages of the impetus theory, the principle of parsimony definitely speaks for it and against Aristotle.Footnote ⁹² In addition, outwardly the movement of the stone upward certainly does not differ from its fall in terms of continuity. The impetus theory can account for this similarity,Footnote ⁹³ while Aristotle, because of his recourse to the different layers of air as movers, has to assume that the movement of a projectile only appears to be continuous without being so.Footnote ⁹⁴ Buridan objects in general to Aristotle and to Averroes that the air normally seems to resist a body in locomotion.Footnote ⁹⁵ A millstone and some children's toys continue revolving for some time after the removal of the hand that has initiated the movement, and they do so also if one has shielded them against the surrounding air.Footnote ⁹⁶ A ship that people on the banks have towed against the current continues for some time to move in the same direction after the ropes have been dropped.Footnote ⁹⁷ The further one wants to jump the longer and speedier one has to run up, having left the ground one is not moved by one's legs or arms, and as to the air one just feels it blowing into one's face.Footnote ⁹⁸ Confronted with these phenomena, Aristotle would probably not have much to say on behalf of his explanation of projectiles. However, for the sake of the argument let it be supposed that he could have defended his explanation, that the impetus theory had severe disadvantages,Footnote ⁹⁹ or that Franciscus de Marchia and Buridan were careless about the difficulties of the impetus theory. These assumptions would just support the point of my paper, for they would simply underscore how naturally, after Duns Scotus, the impetus theory obviously recommended itself to an Aristotelian in order not only to unify the Aristotelian theory of movement but also to prevent it from being dismantled.Footnote ¹⁰⁰

Other ways to the impetus theory in the Latin West

For Maier, the step from Aristotle's explanation to the impetus theory was just a matter of experiment and, so to speak, ‘puzzle solving’ within the ‘normal science’ of Aristotelianism.Footnote ¹⁰¹ Blumenberg sees a fundamental shift of the status of the divine creation that lead to the impetus theory inasmuch as, in the fourteenth century, the world as a whole gained a certain inner substantiality that it had lacked before.Footnote ¹⁰² Wolff interprets the impetus theory as a broad paradigm in which the problems of projectiles and mechanics became prominent only comparatively late;Footnote ¹⁰³ in the Latin West, Peter John Olivi invented it around 1290 as a theory of interest on capital to solve the financial problems of the cities in southern France and Italy.Footnote ¹⁰⁴ For Funkenstein, however, the provocation, for reason, of the sacrament of the Eucharist host led to the impetus theory,Footnote ¹⁰⁵ while Flüeler suggests that its way was paved in the 1270s by commentaries on Aristotle's theory of slavery in his Politics.Footnote ¹⁰⁶ Grün maintains that the impetus theory is a chapter in the history not of mechanics but rather of pantheism, in between the Neoplatonists and Goethe, Schelling and Hegel.Footnote ¹⁰⁷

From my point of view, Maier is basically right. The invention of the impetus theory just required knowledge of Aristotle's biology. Neoplatonic traditions were not necessary. As to Flüeler's thesis, one has to distinguish in the Aristotelian concept of movement two factors, namely the logos – or the ‘score’ – of a movement and its ‘energy’, so to speak. A proximate efficient cause (as opposed to a remote or universal efficient cause, such as the Sun) has to provide the former but not also the latter. The adviser is the efficient cause of the war,Footnote ¹⁰⁸ the architect of the house,Footnote ¹⁰⁹ and the doctor of the knowledge of the students of medicine.Footnote ¹¹⁰ Each of them can act as the principal efficient cause without providing the ‘energy’, and in principle by mere speech. They can do so because each of the instruments that they use (the decision-maker, the soldiers, the workers on the construction site) or of the matters that they work upon (the students) has its own source of ‘energy’ (its soul and vital heat) and just needs the score for its movements, which it can store in its memory. By contrast, the male semen provides not only the score but also the ‘energy’, the heat. Now, Aristotle certainly defines the slave as an instrument.Footnote ¹¹¹ However, a slave has a soul,Footnote ¹¹² and thus just needs the score for the movement while menses and projectiles lack not only the score but also the source of ‘energy’ and the memory. Therefore either each verbal communication with a movement consequent upon it or none of such communications could have prepared the way to the impetus theory.

As to Funkenstein, close to the end of Latin Scholastic philosophy in the seventeenth century, Francisco Suárez offers a classification of instruments by means of two criteria. An instrument can operate spatially or causally in conjunction with its user or in separation from the user. Spatially, an instrument is in conjunction with its user if there has to be spatial contact (organic union or touch) between the instrument and its user. Causally, an instrument is in conjunction with its user if it can operate only if its user simultaneously exerts a specific force, while it is in separation from its user if the user does not need to do so. Thus there are four kinds of instrument: those with spatial and causal conjunction (e.g. a pencil), those with spatial conjunction but causal separation (e.g. the heat of a fire), those with causal conjunction but spatial separation, and finally those that require neither spatial nor causal conjunction. Suárez adduces the impetus and the male semen as examples of the fourth kind but the sacraments as examples of the third.Footnote ¹¹³ This is not surprising. Instruments of the fourth kind might be the most sophisticated ones,Footnote ¹¹⁴ but to be in need of them is a mark of finite agents. As a matter of fact, the need of any kind of instrument indicates a finite agent. By contrast God is eternal and, regarding his power, omnipresent. He might use instruments but he is not in need of doing so since, in its relation to his power, every finite being cannot but immediately meet the first three axioms of Aristotle's theory of movement.

Funkenstein writes,

According to this analysis, the sacrament would be an instrument of the fourth kind. After the projectile has left the hand, the thrower is spatially separated and causally inactive, and there is in the projectile only one force, namely an instrumental one; the same holds true for the semen, which, in addition, does something that the projectile does not do, namely transmit a force into a different subject, the menses. By analogy, when the sacrament is active, God is spatially distant and causally inactive, and there is in the sacrament only one force, namely an instrumental one, and this force transits into the receiver of the sacrament. This is not the opinion of Aquinas and Franciscus de Marchia. According to Aquinas, there is in the sacrament an instrumental force that has ‘a being that transits from one thing into another one’ (from the sacrament into the receiver of the sacrament),Footnote ¹¹⁶ and which operates in virtue of a principal cause, namely a divine force.Footnote ¹¹⁷ Aquinas adduces in his entire discussion of the issue of force in sacraments in general and in the Eucharist host in particular only instruments of the first kind (hand, axe, stick, hammer),Footnote ¹¹⁸ evidently because he assumes that, when the instrumental force in the sacrament is active, it is moved by the divine force, which is active and in contact with the sacrament if not within the sacrament.Footnote ¹¹⁹

Franciscus de Marchia even denies that there is an instrumental force involved. He discusses the issue of projectiles in the very context of the question of the sacraments, and states right at the beginning that within each sacrament there is the supernatural force that God himself is, and that therefore the question is whether in a sacrament there is only this force or, in addition to it, another one, an instrumental force, produced by God.Footnote ¹²⁰ Since, therefore, an instrument of the first kind would suffice, he adduces as examples the same instruments as Aquinas.Footnote ¹²¹ However, Franciscus de Marchia maintains that the force of God within the sacrament produces the effect immediately, without any instrument.Footnote ¹²² As Maier notes,Footnote ¹²³ even prior to Franciscus de Marchia authors discussed the issue of instruments even if they, like Franciscus de Marchia and most Franciscans, denied the existence of an instrumental force in the sacraments. Thus Franciscus de Marchia could introduce his new theory of projectiles and use it to support his claim that even artificial and natural instruments of the first kind (hammer or hand) operate through an instrumental force,Footnote ¹²⁴ even though his theory of the sacraments could not lead him to his theory of projectiles, and even though the theory of projectiles was irrelevant to the theory of the sacraments. Hence he could not invent the theory of impetus to show that the mode of causality of the sacraments was familiar to human beings. On the contrary, the only moral of the impetus theory in that context could be to underscore the difference between finite beings and God, namely that God does not need any instruments or instrumental forces in order to act, neither things like hands nor projectiles or semen.

Funkenstein could object that Franciscus de Marchia could have got the inspiration for his impetus theory from, say, Aquinas's theory of the sacraments even though he did not accept the latter. This is certainly not impossible. After all, Aquinas's theory of the sacraments amounts to the impetus theory if one looks not only at God and the sacrament but also at the receiver of the sacrament and assumes that, after leaving the sacrament, the instrumental force is active in the receiver without a force in the sacrament or the divine force being active. However, as I have shown, Aquinas could have easily formulated such a theory because it is merely a simplified version of Aristotle's theory of the semen, which Aquinas had used so often in his discussions of the issue of procreation and the production of a soul. Hence Aquinas's theory of the sacraments, or, for that matter, the idea that a sacrament acts like the semen, like an instrument of the fourth kind, would be an offspring of Aristotle's theory of the semen.Footnote ¹²⁵ In addition, as I have shown, the way could easily lead from the theory of the semen via the ‘most difficult’ problem to the impetus theory, without any stopover at the theory of the sacraments. In fact, such a stopover would have been an impasse since God, because of his omnipresence, needs at most instruments of the first kind.Footnote ¹²⁶

As to Wolff, the tradition of the seminal reasons (rationes seminales) on which Olivi draws was a kind of cosmological biology that could absorb many influences. If it had lived without Aristotelian biology, and if Wolff's interpretation of Olivi's short statements is right, Aristotle's biology was not the only way to the impetus theory.