Locke on Powers: The Geometrical Model
Locke on Powers: The Geometrical Model
Abstract and Keywords
Locke's ontology of relations and powers points to an alternative to the occasionalists' cognitive model of causality. So far, though, this is all it has done; it remains to be seen just how Locke proposes to account for the tie between cause and effect. Conceptual foundationalism offers the outlines of a story here: while there is no genuine, mind‐independent relation of cause and effect, there is still an objective ground on the basis of which a suitably disposed mind will (and should) think of this relation. What explains this ground is the geometrical model of causation. This chapter shows how the geometrical model fits with Locke's corpuscularianism and his claim that some geometrical propositions are synthetic and a priori. It also recasts Locke's distinction between primary and secondary qualities in such a way as to reconcile a number of seemingly conflicting texts.
Locke's ontology of relations and powers points to an alternative to the occasionalists' cognitive model of causality. So far, though, this is all it has done; it remains to be seen just how Locke proposes to account for the tie between cause and effect. Foundational conceptualism offers the outlines of a story here: while there is no genuine, mind‐independent relation of cause and effect, there is still an objective ground on the basis of which a suitably disposed mind will (and should) think of this relation. I shall call what explains this ground the ‘geometrical model’ of causation.1
Recall Malebranche's ‘argument from elimination’ in Chapter 10. There, Malebranche asked, ‘What would [a] power be? Would it be a substance or a modality? If a substance, then it is not bodies that act but that substance which is in bodies. If the power is a modality, then there will be a modality in bodies which is neither motion nor shape.’ Locke takes Malebranche's first point: a power cannot be a further feature of a body, distinct from its qualities, or else the body cannot itself be said to act. This comes out most clearly in his discussion of the will. Railing against the scholastic tendency to reify faculties, Locke insists that it is minds or persons, not the will, that have the power to act or not to act. ‘Powers are Relations, not Agents’ (Essay, II. xxi. 19: 243). Similarly, it is the body that has the power, not a faculty or homunculus attached to it. Like other defenders of course‐of‐nature mechanism, Locke does not see the problem (p.171) with embracing the second horn of this dilemma. In fact, ‘the different Bulk, Figure, Number, Texture, and Motion of [a body's] insensible Parts’ (II. xxi. 73: 287) are the only cause we can imagine for the ideas bodies produce in us and for the changes they bring about in one another. Given Locke's foundational conceptualism, we can call these properties the supervenience base of the power relation, always keeping in mind that this base is not identical with the relation itself, which requires a contribution from the mind in the form of the activity of comparison.
As is well known, Locke claims that our clearest idea of active power is derived from the mind's reflection on its own operations. Locke has been read as making a concession to Hume when he admits that observing the antics of bodies gives rise in us only to the idea of passive power.2 Having given up on deriving the idea of power from outer experience, so the story goes, Locke stubbornly hangs onto the inner experience of power. Hume then emerges as a consistent empiricist, and Locke as a mere halfway house on the way to a full‐blooded denial of causal realism.
This is quite wrong. For denying that experience of bodies provides us with an idea of active power is hardly tantamount to claiming that it provides no idea of power at all. Power, Locke writes, ‘is twofold, viz., as able to make, or able to receive any change: The one may be called Active, and the other Passive Power’ (II. xxi. 2: 234). In bodies, the power to initiate a change is the power to initiate motion. Bodies, as far as we can tell, simply do not do this; our experience of bodies does not provide us with ‘any Idea of the beginning of Motion’ (II. xxi. 4: 235).3 So all bodies can do is transmit motion that they receive from some other source. This source will have to be a mind, whether finite or divine. But this presents no barrier, in principle, to seeing the physical world as a network of powers. Locke is far from agreeing with Glanvill's claim that ‘causes are so connected that we cannot know any without knowing all.’4 Not having ‘a view of Nature while she lay in her simple Originals,’5 and hence not knowing the ultimate origin of motion, cannot prevent us from knowing what will happen at the next moment. Moreover, a universe structured by passive powers is quite enough to provide Locke with a realist account of body–body causation, and more than enough to draw Hume's fire.
The natural world, then, is a complex of bodies that change by transmitting motion to one another. The ultimate origin of this motion is another matter; Locke clearly thinks God must have initially kicked things off (IV. x), though (p.172) there is no suggestion that he thinks God must continue to act to conserve or perpetually reproduce motion.6
To see how the intrinsic qualities of bodies constitute their powers, we must of course understand just what those qualities are. I shall argue that Locke's taxonomy of qualities mirrors that of Boyle, which lets us clear up a common difficulty in understanding Locke's view.
Like Boyle, Locke accepts that some of the qualities of bodies, though they would have them even in isolation from other bodies, are really relations (Q2s). And these relations turn out to be fundamental to their powers: ‘the Active and Passive Powers of Bodies, and their ways of operating, consist . . . in a Texture and Motion of Parts’ (IV. iii. 16: 547). For any given macroscopic body, its powers will be reducible to the situation or texture of the particles of which they are formed and the motion of these particles relative to each other plus, of course, the texture and motion of the particles of the other bodies to which they are related. Locke also implicitly distinguishes between Q2s and Q3s, that is, between relations between an object's components and relations between that object and others. ‘The simple Ideas whereof we make our complex ones of Substances, are all of them (bating only the Figure and Bulk of some sorts) Powers’ (II. xxxi. 8: 381). Locke is not merely reiterating his familiar point that many of the constituent ideas of substances are ideas of secondary qualities and thus of powers; even primary qualities, barring figure and bulk, are powers and thus relations.
If this is right, we can bring the distinction between primary and secondary qualities into sharper focus: just as for Boyle, primary qualities include Q1s and Q2s, while secondary and tertiary qualities are Q3s. Locke calls secondary qualities nothing but powers, implying that primary qualities are powers and something else (II. viii. 24: 141; but see II. viii. 8). Having noticed the lock and key passage in Boyle, Reginald Jackson proposed that the primary–secondary distinction is meant to hold between categorical properties and the relational and dispositional states that supervene on them.7 E. M. Curley has argued that this will not work, however, for Jackson's reading ‘requires situation not to be a primary quality.’8 Still, Jackson nearly had it right. If we apply the distinction we extracted from Boyle between Q1s and 2s (i.e., non‐relational and relational qualities internal to a given object) on one hand and Q3s on the other, we can say that situation or texture is still a primary quality of a body, because its relata are parts of that body itself. On my view, a primary quality is a quality, whether relational (Q2) or not (Q1), that an object has on its own, regardless of the (p.173) arrangement and population of other items in its world. A secondary quality like a color, however, relates the object to others, in particular, to perceivers. Secondary, like tertiary, qualities must take as their relata at least two distinct macro‐level objects; primary qualities are either non‐relational or relate only the constituents of a single object.9
What is more, our analysis of Q3s as powers and hence as multilaterally reducible clears up a persistent source of puzzlement for Locke's readers. For Locke seems to think that powers come and go with a thing's circumstances, whereas, if we take powers to be dispositions, a thing ought to have those dispositions regardless of the circumstances that would, as it were, activate them. By contrast, the multilateral reducibility of powers makes them dependent on the circumstances of the bodies that have them in a very strong way. This is why Locke can say that if one were to ‘Put a piece of Gold any where by it self, separate from the reach and influence of all other bodies, it will immediately lose all its Colour and Weight, and perhaps Malleableness too’ (IV. vi. 11: 585). If gold is disposed to cause in us the idea of yellow, won't it retain this disposition even if it is put somewhere ‘by itself’? But this is not Locke's position. Since secondary qualities are merely powers, they fail to obtain when the relevant qualities of their relata are not present.10 Nor is this peculiar to secondary qualities: even weight and malleableness would disappear in such an environment. As with Boyle, the logical structure of ascriptions of power is polyadic, not monadic.11 And polyadic properties obtain only when their constituents are present.
With this as background, we are now in a position to see precisely how Locke thinks cause and effect are connected. Let us begin by looking at the kind of completed science of the natural world Locke thinks is in principle possible. Like the Aristotelians, he holds that such a science would be demonstrative. That is, it would start with a priori necessary truths and, by entering the facts of the particular case (e.g., which bodies are situated where, and with what microstructures), logically imply the state of affairs that would result. For example, Locke writes that, (p.174)
If we could discover the Figure, Size, Texture, and Motion of the minute Constituent parts of any two Bodies, we should know without Trial several of their Operations one upon another, as we do now the Properties of a Square, or Triangle . . . The dissolving of Silver in aqua fortis, and Gold in aqua Regia, would be, then, perhaps, no more difficult to know, than it is to a Smith to understand, why the turning of one Key will open a Lock, and not the turning of another. (IV. iii. 25: 556)
In principle, then, someone who knew the real essences of bodies x and y (and whatever other bodies were concerned, including those ‘invisible Fluids’) could infallibly infer how x and y would behave. To do this, one needs to know not just those real essences, but the truths that govern their actions.12
What are these necessary truths? Unsurprisingly, they are the truths of geometry. These, plus the shapes of the lock and the key, are all that are required for knowing how one might be used to act upon the other; similarly, the size, figure, bulk, etc., of the insensible parts of bodies are the ultimate cause and explanation of their antics.
Here is the payoff for having struggled through Locke's foundational conceptualism. There, we saw that, like the ideas of mathematics, ideas of relations can be justifiably applied, even though they are not copied directly from experience. So even though we construct the ideas of power and causation, that the world sometimes answers to them can in principle be ascertained. Indeed, at a very basic level, simply witnessing changes in the world tells us that there are at least passive powers. Under ideal epistemic conditions, we would know what explains these macro‐level events. What is more, in neither case would our knowledge depend on what objects the world actually contains. To know the properties of gold, ‘it would be no more necessary, that Gold should exist, and that we should make Experiments upon it, than it is necessary for the knowing the Properties of a Triangle, that a Triangle should exist in any Matter’ (IV. vi. 11: 585). In this sense, a completed Lockean science would be a priori. Locke's comparison between the properties of gold and those of a triangle is no accident: both reflect his commitment to conceptual foundationalism.
Moreover, in speaking of the properties of gold and a triangle in the same breath, Locke is drawing our attention to a further connection. He is using ‘properties’ in the traditional sense, that is, to refer to features of an object that, while not constitutive of its essence, necessarily flow from that essence.13 So although it is not part of the definition of a right‐angled triangle that it (p.175) obey the Pythagorean theorem, one can nevertheless deduce this from the idea of that triangle. Similarly, the physical object answering to the name ‘gold’ has a real essence, a certain arrangement of microphysical parts, that would in principle allow us to deduce its behavior (assuming we knew enough about those other objects in the world with which it interacts). In other words, the logically necessary connections that would be captured by an ideal science are, in contemporary terms, synthetic.
To see this, consider a well‐known passage from the Essay:
We can know then the Truth of two sorts of Propositions, with perfect certainty; the one is, of those Trifling propositions . . . And secondly, we can know the Truth, and so may be certain in Propositions, which affirm something of another, which is a necessary consequence of its precise complex Idea, but not contained in it. As that the external Angle of all Triangles, is bigger than either of the opposite internal Angles; which relation of the outward Angle, to either of the opposite internal Angles, making no part of the complex Idea, signified by the name Triangle, this is a real Truth, and conveys with it instructive real Knowledge. (IV. viii. 8: 614)
This goes to the heart of the geometrical model. Unlike the cognitive model, it does not presuppose that the tie between cause and effect is analytic. It is not as if a Lockean real essence just includes in its very nature the information that it will behave in such and such a way. There is no way it could, since powers are relations, which are multilaterally and not unilaterally reducible. This last point is one of the most important, and least often grasped, differences between Locke's real essences and those of the scholastics.
Recall that a scholastic power ‘points to’ its possible effects. Given their position on relations, the scholastics are forced to collapse powers into monadic properties. This is one common source, from the modern period to our own, of puzzlement: it is very hard to see how a single feature of an object could ‘point’ beyond itself, not just to other features of the actual world, but to non‐actualized possibilia. By telescoping powers into genuinely two‐place relations, Locke avoids this Meinongian predicament. Echoing Boyle's lock and key discussion, Locke suggests (IV. iii. 25: 556) that the geometrical model can ground genuine necessities in bodies without invoking the intentionality of powers or of God. But just how are they to be grounded?
The lack of adequate ideas of real essences prevents us from having the kind of demonstrative science Locke envisions. This is because our ideas of bodies, while they justify us in forming many ideas of relations among them, do not show us all of the necessary relations and connections (IV. iii. 16: 548). This is the recurrent theme of book IV: having no ideas of the ‘particular primary Qualities of the minute parts of [sage or hemlock], nor of other Bodies which we would apply them to, we cannot tell what effects they will produce’ (IV. iii. 26: 557). To be sure, we do detect some necessary connections among the primary qualities of bodies, e.g., that figure presupposes extension. But these are either trifling (p.176) propositions or perilously close to them. Informative necessary connections between substances and powers must elude us as long as we lack ideas of real essences, for the simple reason that these connections are relations among the insensible parts of bodies.
Thus, while Lockean real essences perform almost none of the functions of Aristotelian forms—they do not serve as migration barriers;14 they do not as a matter of analytic truth contain the powers of the bodies that have them—they are similar to Régis's replacement‐forms in that they are second‐order properties of bodies. These properties of the modes of bodies can in principle serve as premises in an Aristotelian demonstration. Locke is at once the first thoroughly modern empiricist and the last Aristotelian.
(1) It is worth just noting Locke's explicit argument against another model of causation, the so‐called ‘influx’ model, which I have not so far discussed, partly because it is, even among Aristotelians, a minority view. Still, it has its defenders in the period. John Sergeant, for instance, claims that ‘What I conceive of Causality is, that ’tis the Power of Participating or Communicating some Thing, or some mode of Thing, to the Patient, which was before some way or other, in the Thing that caus'd it . . . that which is thus communicated is the Real Ground on which the Real Relation of the Effect to its Cause is founded’ (Sergeant 1984: 255). In the margin, Locke writes, ‘So fire that softens wax and hardens clay has some way or other softness and hardness in it?’ (ibid.). The influx model entails that a given agent can have contrary properties at the same time and so cannot be correct. Now, the Aristotelian might well reply that effects depend not only on the active powers of the agent but on the passive powers of the patient (a distinction Locke himself draws in the Essay), so that one and the same agent can give rise to different effects. This move, however, seems unavailable on the influx model, since it depends on the numerical identity of the property supplied by the agent and then received by the patient; if the property somehow changes in the transaction, there's no sense to be made of the claim that it pre‐existed in the agent.
(3) Given that my goal is chiefly to examine the debate over the physical world, we can happily ignore the complications of active powers altogether.
(6) The issue is complicated by IV. iii. 29: 560, where Locke says that such things as ‘the Resurrection of the dead, the future state of this Globe of Earth . . . are by every one acknowledged to depend wholly on the Determination of a free agent,’ namely, God. I read this, not as the claim that God must continue to produce motion at every moment in the physical world, but as the claim that the future of the world is, in the broadest and least controversial sense, in God's hands.
(9) Throughout, I mean by ‘object’ a macroscopic object, not a corpuscle.
(10) Contrast this position with George Molnar's. Molnar holds that the physical intentionality that ties a power to its effects cannot be a ‘real’ or ‘genuine’ relation. As Molnar puts it, ‘the nexus between the intentional state and the object to which it refers is not that of a genuine relation. In the case of a genuine relation, for example a causal relation, all relata must exist. Not so with intentionality’ (2003: 62). It is easy to imagine Locke and Boyle insisting that, if the tie between power and effect is anything, it is a genuine relation in Molnar's sense, i.e., all relata must exist for that relation to obtain. And on their behalf, it is hard to know what to make of a non‐genuine or quasi‐relation, which Molnar's view requires.
(11) Pace Alexander (1985: 165 ff.). Alexander distinguishes between powers in the epistemic and ontological senses. The former, he grants, are relational; but he thinks that Locke takes powers as they exist in bodies to be ‘intrinsic and non‐relational’ (166). This is problematic, however. We have already seen many passages (such as IV. vi. 11: 585) in which Locke is speaking of powers not merely as we conceive them, but as they are in themselves. In the isolation test of IV. iv. 11, for example, it is clear that powers considered in things are nevertheless relational.
(12) Note that Locke says only that we should know several of the bodies’ operations on one another. Why does he hesitate here? The answer, I think, is to be found in the way Locke sets up the counterfactual situation: if we knew the intrinsic qualities of any two bodies, we'd be able to predict some, but not all, of their operations. Some, but not all, because, as I point out above, knowing all would require knowing the intrinsic qualities of not just two bodies but all the other relevant bodies.
(14) Possession of a fully realized Aristotelian essence prevents a being from acquiring a new such essence without being destroyed. Lockean real essences do not impose any such constraint; indeed, it is an article of faith in mechanism that in principle any body can switch kinds by having its microstructure altered.