Suárez on propinquity and the efficient cause
In the Principles, Descartes declares that of the four Aristotelian causes, he will retain only one: the efficient. Though some natural philosophers argued on behalf of the final cause and others held that form could be rehabilitated, the efficient cause was in fact the only one of the four to flourish in the new natural philosophy of the mechanists. Descartes’ claim would lead one to believe that he preserved the efficient cause—that here at least we find continuity with the Aristotelian tradition. But it is reasonable to wonder whether, when from a fourfold classification three members are removed, the fourth can remain unaltered. 
The theory of the efficient cause in late Aristotelianism is a kind of bundle. Among its components are a group of what I will call “formal characters”. These are features of efficient causation that are relatively independent both of what is said to be the essence of the efficient cause and of the hylomorphic principles of Aristotelian natural philosophy, or so I will argue.
There are three sorts of question on efficient causes in the textbooks and commentaries: questions on the nature of the efficient cause, and on the causal relation or the “causality” of the efficient cause; and questions on various features or conditions under which efficient causes operate; and finally questions on freedom of the will.
Leaving out the last topic, which does not pertain to natural philosophy, if one looks backward from Hume one sees that by Hume’s time the concept of efficient causation seemed to include only some of the features or conditions attributed to it in late Scholasticism. After Malebranche no-one knew what a “necessary connexion” was supposed to be. The nature, as opposed to the formal characters, of the causal relation became a mystery, which was in need perhaps not of resolution but of dissolution. Post-Humean accounts clearly reflect this. In the twentieth century, for example, Hempel’s theory of explanation, insofar as it was meant to treat causal claims, and Suppes’ probabilistic causation are studied attempts to reduce the causal relation to other relations, which is to say that they presuppose that the causal relation has no “nature” of its own. 
In the modern conception, then, a theory of efficient causation becomes a theory that argues for or against such claims as: 
causes precede their effects in time;
no agent acts except on what is “propinquitous” to it;
the intensity of the effect is proportionate to the strength of the (total) cause;
and given the cause, the effect must follow (this is generally construed in terms of logical relations between propositions).
A theory of efficient causation becomes, in other words, a theory of what I am calling the formal features of causation. Such a theory lays out conditions that cause and effect, or the causal relation, must satisfy, without inquiring into the nature of that relation. 
The looseness of the bundle of formal characters attributed to the efficient cause by the Scholastics made it possible for its various strands to be unraveled. The suggestion I make here—a suggestion that evidently requires more than one instance for its proof—is that the formal characters can be retained even as the principles of natural philosophy are transformed because they are independent of efficient causality's putative nature. Indeed by the time of Hume, it seems to me, there was so little agreement on the nature of the efficient cause that the core of the theory of efficient causation, which had consisted in saying what its nature consists in, comes to concern its formal characters alone. 
Suárez’s Metaphysical Disputations included a thorough treatment of the four causes, starting with questions on cause in general and proceeding through the material, formal, efficient, and final causes. The central disputations on the efficient cause (DM 17-19) treat its definition, the varieties of efficient cause, certain of its formal characters (as I have called them), and the necessity with which efficient causes operate. A later disputation on the comparison of causes with their effects adds questions on temporal priority and the relative nobility of cause and effect.
In this paper I will examine the arguments contained in the sections on propinquity, DM 18.8. The first section concerns whether propinquity of cause and effect is a necessary condition for efficient causality. The second concerns whether cause and effect must be “proportionate,” i.e. similar or dissimilar in the first instance, and whether those causes that admit quantification must be proportionate insofar as a greater quantity in the cause must yield a greater quantity in the effect, regardless of whether they are intensive or extensive quantities. These considerations include, of course, a judgment on the possibility of action at a distance. Suárez, in agreement with Thomas and his followers, and contrary to Scotus and his followers, held that action at a distance was impossible. The interest in his discussion lies in not so much in the position he took as in his account of how causes act on things remote from them—that is, of how causes act through media. The influence of created agents, such as the sun, may extend almost indefinitely, even though it is always limited to a finite sphere of activity; but for this to occur a medium is required. Transmission of influence through media is peculiar to the efficient cause. Once it is shown that there is no action at a distance, which as it turns out is not too difficult, the issue simply becomes one of accurately describing how efficient causes act through media. 
This issue is of historical and philosophical interest not only in its own right but also because it can be seen to have had a role in Descartes’ insistence that bodies interact only by collisions. In collision mechanics there are no media; there is only the immediate contiguity of one body with another. If all change is reduced to the collision of bodies, then there is no need for a model of distant causation. Thus the conceptual apparatus employed by Suárez was no longer of use. The notion, for example, of a sphere of influence (in natural philosophy if not among the angels) has no application when the “sphere” of every body is simply its surface. Descartes may have seemed to have retained the notion of a medium in his optics, but in fact a Cartesian medium is only a causal chain, a sequence of collisions. Cartesian physics has no media in the Aristotelian sense.
In what follows I will first present Suárez’s formulation of his position and the arguments on its behalf. I will then turn to puzzles raised in arguments on behalf of immediate distant causation.
	1.	The question
An agent can be distant from a patient only if the two are distinct. So only in transeunt causation does the possibility of action at a distance even arise. In Physics 7c2, Aristotle wrote that the Prime Mover must be “together” with what it moves, which is to say that nothing is interposed between them; this, he added, is common to all movers and things moved. Thomas followed Aristotle, arguing that God is present everywhere and writing that “of no agent, however powerful, does any action proceed to anything distant, unless insofar as the agent acts on it through a medium”. This was the received Thomist position from which Scotus and others dissented. 
The question, then, is this:
When the proximate and immediate cause acts by a power it possesses by itself, and not from another, from which that power flows, must it immediately be in contact [contingere], by its quantity or its presence, with the thing on which it acts; or can it act on that thing immediately, even if it is spatially distant from it?
Suárez conjoined with this a second question: how do agents act on distant things if they do not act on them immediately? Whether any agent can act immediately on a thing spatially distant from it is a question relatively easy to answer: the answer is no. But if agents act immediately only on nearby things, then in order to act on distant things – as they obviously do – they must somehow act on them by way of nearby things. But how? This question is not so easy and the greater part of Suárez’s discussion is devoted to answering it.
Nearness (propinquitas, also indistantia) is for material agents a matter of contact or the adjacency of the quantities of their matter. For spiritual agents it is a matter of “presence,” substantially or by power. In this paper I will concern myself mostly with material agents for whom the distantia between an agent and patient consists in there being “either a part of a body or a space” between them, as Suárez put it. In the ordinary course of nature there can be no void for an Aristotelain, but it is conceivable that two bodies should not be touching even though there is no other body between them. The case of action across empty space, though unnatural, turns out to be a fundamental thought-experiment for Suárez.
	2.	Suárez’s position
Suárez’s resolution of the second, harder question consisted in laying out in four assertiones a model of distant causation. But preceding those assertions is an explication of what he called modi distantiæ et indistantiæ agentis ad passum. These “modes of distance” describe the possible ways agents and patients can be separated from one another.
	2.1.	Modes of distance
The first and most notorious way of being distant is (1) to be separated by a void. All other ways presuppose a plenum. A patient may be distant from an agent because a spatial medium, not empty but entirely full of bodies, is interposed between them. (2) That medium may be entirely indifferent to the action of the agent, or (3) of any agent; or (4) it may be that the agent acts on the medium by a different power than the power by which it acts on the patient; or, finally, (5) the agent may act on both the medium and the patient by the same power (§8¶13, 654. 
Though Suárez called these alternatives modi distantiæ et indistantiæ agentis ad passum, it seems to me that only the distinction between a purely spatial separation and a separation by interposed bodies really deserves that name. The rest of his discussion, no less interesting for all that, is in effect an analysis of the ways in which an agent might act on a patient through a medium. 
Even when an agent acts on both the medium and the patient by the same power there are various ways it can do so. It can act on the patient by impressing a quality on the medium by which the patient is affected. In such a case the agent acts only remotely on the patient. Or it can also act simultaneously on the medium and the patient in such a way that both actions are required in order for the patient to be affected. 
Finally the agent’s action may of necessity spread from near to far, not because affecting the medium is necessary to affecting the patient, but “by necessity of order alone (so to speak)”, for example, if the agent’s influence is always transmitted along a straight line. In other words, The underlying theory upon which the claim of necessity is based is what would now be called the theory of partial and total orders, or in brief, orders. Suárez takes it that if the points of a line ABC are arranged in what we would now call a total order, and if a cause at the endpoint A must act along that line to affect an object at the endpoint, and if in doing so it must affect all intervening points in order, then if the point B is between the points A and C, C being the most distant from the cause, then necessarily the cause must affect B if it affects C.
This last case, as it turns out, is the default case as we might say.
	xlix.1.	 No action across a void
The first of Suárez’s assertions is that “an efficient cause can effect nothing in a distant patient, if an empty space is interposed” between them. It is for that reason that the universal providence of nature endeavors to prevent the occurrence of empty space—the famous horror vacui. Or rather, as Suárez said, we can infer from the horror vacui that a gap in the plenum is to be avoided for the sake of “commodiousness and utility,” even though not ruled out by the nature of corporeal things, and we infer that because no agent can act across a gap, not even God.
Since a void cannot occur naturally, experience provides us no test of action across a gap. But suppose, Suárez wrote, that the space between agent and patient is filled with a body that “interrupts the action of the agent,” so that the space “entirely impedes the action [of the agent] on the distant patient,” even if the patient is within the sphere of action of the agent. A void is effectively just such a body – it doesn’t resist the action of the agent but is incapable of receiving its action, just as an opaque body, rather than resisting the action of light, simply lacks the capacity to be acted on by it and so fails also to transmit the action of light. 
The void so conceived is rather like a Cartesian body, which has no positive power of resisting the movement of other bodies, and its “inertia” consists entirely in its being subject to the laws of motion. Suárez’s argument resembles Descartes’ on the nonexistence of the void. Nothing has no properties, said Descartes, and so if there really is nothing between two bodies, that nothing has no dimensions, no size, etc. (PP 2¤18, AT 8.1:50). Suárez for his part supposed that because a void cannot take on the action of any agent, which would entail its having a property, it is thereby a perfect impediment.
The conclusion to be proved, then, is that if there were empty space between an agent and its would-be patient, no action of the agent could reach the patient because an empty space “interrupts” all actions. But—you might say—the term ‘interrupt’ already presumes that some sort of continuity is required when an agent and its action are not in the same place, because the patient is distant and because the action or motus effected by the agent is in the patient. Nothing, it would seem, precludes the action of this fire on that tree over there, for example, unless you presuppose that something spatially between them must connect the fire to its action. Commonsense favors, it would seem, this view, so Suárez has his work cut out for him.
	0.1.	Whatever an agent can effect at a distance, it can effect in the medium
Suárez’s second assertion is that an agent can act on a patient which is distant from it only if it can act on the medium that occupies the space between them. If the previous assertion is accepted, this one follows readily. “If the medium were not necessary to sustaining and as it were conveying the action of the agent,” Suárez wrote, the relation of the medium to the action would be per accidens, and it wouldn’t matter whether the medium was real or not (¤8¦16, 656). But we have already seen that no agent can act across a void. So it’s not incidental that something real, something receptive to the agent’s action, has to be interposed between the agent and the patient. 
	0.1.	Whichever power of the agent acts on distant objects must also act on the medium
Suárez’s third assertion is that the action of the agent on a distant object and its action on the medium (whereby it acts on the patient) must arise from the same power:
In order that the agent should affect a distant patient, it is not enough that it should by another entirely distinct power or action act in the medium; rather it is necessary that by the same power by which it acts on the distant patient, or by a subordinate power, it should begin to act on the medium near to it, and spread its action or influence throughout the medium out to the distant patient (§8¶17, 656).
The argument is that if the agent acted on the medium by one of its powers, and on the distant patient by another power, then “formally there are two agents, even though materially they happen to be one by virtue of being of one suppositum or subject” (ibid.). The formally distinct agent that was acting on the distant patient would effectively be acting on it at a distance. So, for example, if a candle, which has the power both to heat and to dry, dried the air around it while simultaneously heating a distant object, it would be as if that object were being heated at a distance. Even if the drying of the air paved the way, so to speak, for the action of the heat by disposing the air to cease resisting the heat, still that disposition would be “merely material,” and so it would be irrelevant that it was caused by a power residing in the same agent as the heat for that power could just as well have resided in another agent coincidently operating simultaneously.
Suárez’s second and third assertions depended on his first: if action across a void were possible, then agents wouldn’t need to act on the medium to affect distant objects, nor would the same power of the agent need to affect both medium and object. Causal relations, in other words, depend upon spatial relations and, as we have seen, insofar as it is a good thing for the world to be universally causally connected causal relations in part determine the topology of physical space (as we now call it).
The model, then, of action at a distance includes an agent, a patient which is not near the agent, and a medium. In the standard case the agent acts only on the part of the medium that is near to it, thereby affecting the patient indirectly; its action on the medium and on the patient must be effectively a single continuous action, originating from a single “virtue” in the agent. But that virtue, Suárez told us, need not be a single form. It may be a coalition of active powers. The continuity of the action, moreover, need not be “rigorous and physical.” It suffices for the continuity of the action to be “according to some sort of subordination and causality” (§8¶18, 657). 
	0.1.	Some complications
Suárez’s fourth assertion, which consists of two complementary claims, further qualifies the model. First, even though the medium on which the agent acts must be nearby it need not always be the case that the intentio of the agent in causing is that it should first act on the medium and then through the medium act on a distant object. The production of visible species in air or water is a case in point. Visible species per se cause only sensations in a visual organ because “the action of the species per se et ex intentione naturæ is wholly ordered to the eye, since only in the eye can the visible species have the effect for which they were instituted” (¤8¦19, 657). In short: sometimes the action of an agent on its medium is, though not merely per accidens, because without a medium the agent cannot act on distant objects, but nevertheless it is incidental to its per se effect on a distant object because only that effect is, so to speak, explicitly comprised in the nature of the cause.
Second, sometimes the agent acts on a distant object not through the medium but as if it were “conjoined” with the medium through which its influence is diffused. The efficient cause in this instance is the mereological sum of agent and medium, a thing to which the object acted upon is near. Thus we would no longer have an instance of distant causation. This second case is approximated in those instances where, as Suárez later wrote, the agent “acts through [a nearby portion of the medium] as through a medium necessary to the continuation of the action, or so that the action occurs without interruption” (§8¶21, 658). The medium, so to speak, enlarges the agent so that it can be near the objects it acts on. (Think here of Descartes’ analogy between light rays and a blind man’s staff, which is in effect just a continuation of his hand.) Thus it is only in relation to some notion of its essential dimensions that the agent could be said still to be distant from the patient.
	0	 Puzzles
The arguments on behalf of immediate distant causation consisted mostly in examples in which an agent or power apparently acts without a medium on something spatially separated from it. But Suárez also presented two systematic arguments against the claim that agents act only on objects not spatially separated from them (§8¶8–9).
	2.2.	Spheres of action 
Suárez’s position was that an agent can act immediately only on what is near it, with the qualifications noted above. Being near at least entails not being spatially separated from the agent, or more precisely, being part of or inhering in a body that is not spatially separated. But strictly speaking only the bounding surface of the bodies surrounding the agent is not spatially separated from it. If an agent acts immediately only on what is near to it in that sense, then it “would act through that surface on immediate[ly near] parts, and through nearer parts on more distant parts, dividing as it were its action by all proportional parts, near and remote.” But this “enumeration” of all the proportional parts of the surrounding medium is “scarcely intelligible,” especially for changes that must occur instantaneously throughout some portion of matter, such as generation (§8¶8, 653). Moreover, since there is no corporeal whole which is near the agent in this strict sense, the subject on which the agent acts is not well-defined.
The difficulty here is that physical change occurs in bodies, which is to say that they occur in things having not just two dimensions but three. On pain then of supposing a volume to consist actually and not just potentially in a collection of surfaces, one cannot confine the action of agents to a surface. But only for the surface surrounding a body does the word ‘near’ have a precise sense. Otherwise there is no obvious way to distinguish nearby from distant objects, especially in the case of a body surrounded by a continuous fluid. One could take the entire medium to be one thing and thus all of it to be near the agent, but it would be difficult then to explain why in some cases the transmission of the agent’s action takes time as well as why an agent acts more intensely on some parts of the medium than on others.
If the subject on which an agent is capable of acting is not well-defined, then neither is its sphere of activity well-defined. The immediately surrounding surface is evidently not that sphere. But if we try to extend the range of an agent’s immediate action beyond that limit, we must do so either arbitrarily or by appeal to extrinsic features (e.g. the resistance of the medium). And what is worse, we will be unable to explain why the action of the agent is not equally intense throughout its sphere of activity, even though experience obviously tells us that the actions of some agents diminish in proportion to the distance of their objects:
since a power is finite, it does not equally overcome [the resistance of] things near and far, and so greater nearness leads to greater perfection in the action; but if the agent acts on remote [things] only through those nearby, it will communicate to remote things all the intensity of quality that it communicates to things nearby, because this quality is similar in activity to that of the agent [illa qualitas est active suæ similis], the remote part is capable of receiving it, and is immediately near to the nearer part (¤8¦9, 653).
There is no reason, in short, for the intensity of a quality to diminish in proportion to distance from the agent. Instead it should be transmitted identically from nearby to distant parts of the medium.
Suárez believed these objections had been answered by his second, third, and fourth assertions. The sphere of action of an agent and the domain of its immediate action (or rather of its immediate action independent of preceding immediate actions) do not in general coincide. It is true that an agent acts immediately primo et per se only on what immediately surrounds it. On the remoter parts of its sphere of activity it acts immediately but only as a continuation of its action on the nearer parts. That followed from the nature of efficient causality. But the limitation of the activity of created agents to a determinate finite sphere “originates from the limitations of its power” (¤8¦47, 668). 
The diminution in intensity proportionate to distance observed in some agents can be explained if we suppose that the effectiveness of their action depends partly on the “concurrence” of the agent, even though the nearer parts of the medium are capable of acting on more distant parts in their own right. The agent does not act on distant parts of the medium merely by way of nearby parts that operate as its instruments. The agent also acts by an “actual influx” into those distant parts,
either because it is not necessary that the patient should be absolutely near to the agent, when from that agent there emanates an action which is continuous and without interruption; or also because from the agent and the power received in the medium there is composed, as it were, one whole agent, which touches upon the distant part, and thus can act on it with all its power (§8¶23, 659).
The influx of the agent is necessary to the action of nearer, already effected parts of the medium on more distant parts, and so its intensity will be determined by the nature of the power with which the agent acts.
	0.1.	Rectilinear transmission
A second general line of argument against the necessity of a medium consists in showing that in some cases an agent acts more intensely on more distant objects than on closer ones. That could occur only if the agent acts immediately on the more distant because the quality it imparts to nearer objects is weakened (remissa) in the medium. Of the many examples brought forward to confirm this conclusion, one has an especial importance both in Suárez’s treatment of distant causation and in the subsequent history of physics. 
We know that the sun’s light and heat proceed from it in straight lines. Suppose that the sun’s luminosity affected remote objects only by way of illuminating nearby objects, which in turn passed the qualities of light on to the more remote. Then those nearer parts would impart the qualities bestowed on them by the sun equally in all directions, as if they were little suns themselves. It would follow that for a part that was on a line L from the center of the sun to that part, not only the succeeding part of the line would be illuminated but equally also the next parts to the left and right of the line—or rather all those in a sphere surrounding that part! But that’s not what actually happens. Hence the greater intensity with which the succeeding part on the line L is owing to the immediate action of the sun alone.
[Insert figure 1 here]
Figure 1. Action of light in the medium.

How is it, then, that the sun and other agents like it (fire, candles, etc.) act more effectively along straight lines? Suárez referred first of all to his claim that sometimes an agent is conjoined with the medium so that the actual cause of change in a remote object is the sum of the two. I’m not sure how that is supposed to apply in the present case however. One might say, for example, that parts of the air illuminated by the sun act by the sun’s power [in virtute solis] as well as by their own in the direction away from the sun’s center but only by their own power in other directions. But that, Suárez noted, is a gratuitous assumption since there is no reason why a part of air acting by the sun’s power should not act equally in all directions (§8¶32, 663). Alternatively one might distinguish the illuminating power given to parts of air by the sun from similar powers given, for example, to objects heated by fire. An object heated by fire has the power to generate fire in its surroundings even if the fire that heated it no longer exists. But the same should not be said of air illuminated by the sun. If the sun were to disappear, the air would cease to have any power of illumination. This difference, however, does not provide any obvious grounds for supposing that the influence of the sun is transmitted along straight lines. Suárez concluded by simply repeating the assumption he earlier called gratuitous. Thus the puzzle remains unsolved.

	0	Conclusion
Suárez concluded from his four assertions that for efficient causes the natural mode of acting is “quasi by the continued line of its action from near to far” (¤8¦20, 658). He recognized that the arguments he has given were not decisive. More significantly from our perspecitve, they are not grounded in the nature of efficient causality. But even if no sufficient reason can be given for their  mode of acting, experience still shows us that this is how efficient causes do act. We do “often judge [É] the natures of things from what we experience, even if we are incapable of giving a deeper reason” for our judgments. 
The object of vision, for example, “multiplies its species along straight lines” while the object of hearing also multiplies its species along oblique lines (thus it is capable of transmitting them through the pores of otherwise solid materials). This we know from experience, and we are justified in concluding that this is the natural way for such causes to act. But whether distant causation occurs turns out to be an empirical question.
 The two puzzles I have mentioned— (a) the difficulty of determining the subject of action, and thus the sphere of action, of material causes and (b) the rectilinear propagation of the influence of light—were not trivial. Nor were they easily resolved by the new science of the seventeenth century. It took the ingenuity of a Huygens, for example, to show why light seems to travel in straight lines. The question of the sphere of activity was eventually replaced in physics by laws determining the force of gravity, the strength of magnetic fields, the intensity of light and so forth, and so, except in politics, the notion of a sphere of activity has ceased to have any use.