2.1. Kant's Systematic Strategy

The Metaphysical Foundations can be understood properly only within the general Kantian conception of a philosophical system, a conception fundamental to Kant's strategy for achieving his philosophical aims. While we today might be inclined to view systematicity as a welcome but ultimately dispensable feature of objective knowledge, Kant regards systematicity as a distinguishing mark of objectivity: objective knowledge is objective precisely to the extent that it is systematizable.Footnote 12

Kant's commitment to systematicity flows from his answer to the basic question facing his theoretical philosophy: how are synthetic judgements a priori possible? His answer rests on his doctrine of the transcendental unity of apperception, according to which the unity of the judging subject is the fundamental condition of possibility for any experience that such a subject could judge about, and is therefore also the condition of possibility for objective knowledge in general.Footnote 13 This apperceptive unity of the subject is active in the sense that bringing about its unity is the thing the knowing subject most fundamentally does; the activity itself is unifying insofar as it is productive of the one experience had by that subject. The rules followed by this unified and unifying subject in its activity are the categories of the understanding.Footnote 14 There are, famously, twelve such categories, obliging Kant to explain how their variety is compatible with their being rules for just one unified activity of the subject and productive of just one experience. His explanation comes down to the claim that the many rules exhibit a basic unity in their variety—that is, they exhibit a systematic unity.Footnote 15 Thus for Kant the requirement that the a priori principles of our cognition be systematized stems from the transcendental unity of apperception, which provides the ultimate transcendental condition on synthetic a priori judgement, and thus on objective cognition generally.

Because of its deep transcendental source, this demand for systematic unity extends beyond the conditions of possibility for synthetic a priori judgements to those judgements themselves, encompassing the entire transcendental philosophy. The entire content of transcendental philosophy must have the form of a system, and a central task of that philosophy is to show how such unity is in fact achieved. Within transcendental philosophy itself, this task is not difficult, at least in principle; the answer can always be that systematic unity is guaranteed by the transcendental unity of apperception. But the demand to demonstrate systematic unity extends beyond the limits of the transcendental philosophy as well.Footnote 16 After all, the point of showing that synthetic a priori judgements are possible is to show how objective empirical cognition and experience are possible, since empirical cognition and experience are dependent upon the possibility of such judgements. But this dependence implies that empirical cognition in turn is rooted in the transcendental unity of apperception, and thus is subject to the demand for systematicity as well.

Now, if it is true that empirical cognition is subject to the demand for systematicity, then in order to demonstrate that his transcendental programme succeeds, Kant will need to demonstrate that our empirical cognition is necessarily systematizable. Within transcendental philosophy, this demand is satisfied, directly or indirectly, by referring the variety of transcendental principles, categories, and related elements back to the activity of apperception as their source. And it can seem that such a strategy will work for empirical cognition as well. If we grant Kant the claims of his transcendental philosophy, we grant that all our judgements about empirical objects share a set of transcendental conditions. This claim is equivalent to the claim that those judgements have at least the unity with each other such shared conditions imply. As a result, we know that any judgement about an object of experience has structure and even some content in common with, and therefore uniting it with, all other such judgements. Such commonalities might then reasonably be thought to provide an adequate basis for the systematization of our empirical cognition.

To see why these commonalities are unsatisfying from a Kantian perspective, we must focus on the fact that a system of objective empirical judgements coordinated by transcendental principles could still possibly include not only true judgements, but false judgements. This possibility arises because empirical judgements must include content delivered by sensibility, and thus must include a content not determined purely by the subject's own a priori cognitive forms. When it comes to judgements with empirical content, ‘objective’ for Kant thus does not imply ‘true’, and therefore objectivity conditions are not truth conditions.Footnote 17 It follows that a system of empirical judgements organized only by means of objectivity conditions would not necessarily exclude contingently false empirical claims meeting those conditions.

A systematizing principle that allows for false judgements, and at the limit allows for systems made up entirely of false judgements, falls short of Kant's systematic goal. As he makes clear in the first Critique, genuine systematicity ultimately provides not only a standard of objectivity, but also the criterion for distinguishing true from false empirical claims:

The unity reason demands in our empirical cognition is thus not just the unity exhibited by all judgements about possible objects of experience, but a unity that can function as a ‘sufficient mark of empirical truth’—that is, a mark of the unity of actual, rather than merely possible, experience. Kant's suggestion is that systematic unity of actual experience with the a priori necessary truths of transcendental philosophy can function as such a mark, provided we use the metaphysics of nature to develop the right kind of systematic principle for our cognition of the actual world. Clearly such a principle would have to be consistent with the transcendental philosophy. But, equally clearly, it must also be more determinate than the principles of transcendental philosophy, in order to rule out false objective judgements from the system of empirical cognitions. The Metaphysical Foundations is supposed to provide this principle.

As we will see in a moment, Kant's strategy is to achieve this required determinacy by adopting a principle that has a more determinate content than anything allowed in the strictly transcendental part of the system. But as we will also see, it is just this demand for a more determinate systematic principle for empirical cognition that gives rise to the apparent contradiction in Kant's conception of the metaphysics of nature. Such a principle, if it is to be more determinate than the principles discovered in transcendental philosophy, must be somehow basically empirical (on the assumption that the content of pure philosophical truths is either explicitly exhausted in transcendental philosophy, or implicitly exhausted therein under some form of deductive closureFootnote 18). Yet if such a principle were a garden-variety a posteriori one, then it would be just another bit of empirical cognition requiring systematization, and could not serve as the systematizing principle itself. Hence it seems Kant must find some other kind of principle.

In order to understand Kant's project in the Metaphysical Foundations and how it relates to the possibility or impossibility of finding such a more determinate, yet a priori principle, we will first need to understand the two distinctions mentioned above, namely, the distinction between general and special metaphysics, and the distinction between logical and real essence.

2.2. General and Special Metaphysics

Kant's distinction between ‘general metaphysics’ (the transcendental philosophy of the Critiques) and ‘special metaphysics’ (the metaphysics of nature of the Metaphysical Foundations) is designed to capture the difference in determinacy between their principles. While the general metaphysics of the first Critique deals with all possible objects of experience in general, special metaphysics deals with ‘determinate object[s]’ or ‘the particular nature of this or that kind of thing’ (4: 469–70).Footnote 19 Insofar as special metaphysics is orientated towards systematic unity, it seeks to establish a unity of determinate, actually existing objects under determinate laws, beyond the unity all possible objects exhibit merely in virtue of being objects.

Kant begins his discussion of the determinacy characterizing special metaphysics by noting that its objects are natural objects. The significance of their determination as natural depends, in turn, on our understanding of nature. ‘Nature’, Kant says, can be defined in two ways: its material definition tells us that nature is ‘the sum total of things insofar as they can be objects of our senses’; its formal definition tells us that nature is ‘the first inner principle of everything that belongs to the existence of a thing’ (4: 467).Footnote 20 The material definition of nature allows us to divide the field of natural science according to the two Kantian types of sense: inner and outer. Thus, ‘materially’ speaking, rational cognition of nature consists of rational psychology (inner sense) and rational physics (outer sense). The formal definition of nature, by contrast, picks out the ultimate goal of such cognition: knowledge of the first inner principle of everything that belongs to the existence of its objects. For various reasons, Kant rules out the possibility of rational psychology;Footnote 21 as a result, the special metaphysics of nature is restricted to rational physics, or to the discovery of the first inner principle of everything that belongs to the existence of an object of outer sense.

Although the concept ‘object of outer sense’ looks more determinate than the concept ‘object’, it still belongs to transcendental philosophy or general metaphysics; the distinctions used to arrive at this concept, including that of nature materialiter, are themselves all transcendental. It is Kant's next move—his introduction of the empirical concept of matter—that adds determinate content to the concept object of outer sense, and thus moves us into special metaphysics. Bringing in such empirical conceptual content, however, seems obviously to render any principles drawn from it empirical in their turn, and thus ineligible to serve as principles for systematization. Yet Kant insists that this is not so. He describes special metaphysics as dealing with the empirical concept of matter ‘in such a manner that, outside of what lies in this concept, no other empirical principle is used’, and goes on to describe this manner as one in which ‘transcendental principles are applied to the … species of objects of our senses’ (4: 470). The clear implication is that Kant has a method in mind for special metaphysics that should allow a priori knowledge of the first inner principle of all objects of outer sense by means of the application of transcendental principles to the content of the empirical concept of matter. The method Kant in fact deploys has two key aspects: first, its use of his distinction between logical and real essence; second, its use of geometrical representation.

2.3. Logical Essence, Real Essence, and Synthetic Judgement

Most broadly, discovering the first inner principle of the existence of the objects of outer sense involves not only discovering, but also using, distinctively metaphysical principles, and Kant is clear that these principles are both a priori and synthetic.Footnote 22 Kant's famous transcendental-logical distinction between the analytic and the synthetic differentiates between the two ways the subject and predicate of a judgement can be related. When they are related analytically, the predicate is logically ‘contained in’ the subject; when they are related synthetically, there is no such containment.Footnote 23 Rather, if a synthetic judgement is true, the predicate has some variety of non-logical connection to the subject, and metaphysics (general or special) is in the business of discovering and articulating the non-logical connections underwriting such a priori judgements.

Kant's distinction between logical essence and real essence is a metaphysical distinction meant to differentiate properties of objects in a way that tracks the transcendental-logical distinction between analytic and synthetic predication. Understood this way, the logical essence of an object is the property or set of properties of that object picked out by the content of its concept, while the real essence of an object is the property or set of properties of that object picked out by those concepts truly predicated of it in synthetic a priori propositions.Footnote 24 Thus Kant's claim that special metaphysics takes the empirical concept of matter as its basis indicates two features of his special metaphysics: first, the logical essence of matter will be the starting-point for the discovery of the real essence of matter; second, synthetic a priori judgements expressing that real essence will have the concept of matter in the subject position and the concepts of its really essential properties in the predicate position.

Yet as we have already noted, it seems the synthetic judgements expressing the real essence of matter cannot be a priori judgements, given that their subject term, matter, is an empirical concept.Footnote 25 We can bring the difficulty here out clearly by recalling a few more features of the Kantian doctrine of concepts. An empirical concept, like any concept, has what Kant calls synthetic unity, by which he means that it unifies diverse concepts into a single content. But Kant distinguishes empirical concepts by means of the source of the synthetic content-unity they contain: while the unity found in pure concepts ‘arise[s] merely from the understanding’, the unity found in empirical concepts is ‘drawn [or] abstracted from experience’ (9: 92).Footnote 26 Kant claims that conceptual analysis reveals the synthetic unity of the empirical concept of matter to contain three concepts—extension, lifelessness, and impenetrability. It follows that the logical essence of matter consists of the unity of the properties designated by these concepts.Footnote 27 Of the three, says Kant, impenetrability ‘is the fundamental property (Grundeigenschaft) of matter, whereby it first manifests itself to our senses’ (4: 508), and it is clearly this element in the content of the concept of matter that renders it empirical.Footnote 28 We can therefore predict that synthetic a priori judgements with impenetrability as (or logically contained in) the subject term will play a prominent role in Kant's attempt to discover the real essence of matter.

Now consider these judgements and the metaphysical connections they assert. Kant's theory of synthetic judgement requires a non-logical connection between subject and predicate, but the only non-logical a priori ground for such a connection, outside the principles of the first Critique, is pure intuition. Since the principles of the first Critique cannot themselves generate the required determinacy, we know that the non-logical connection underwriting the relevant synthetic a priori judgements must be a pure intuitive one.Footnote 29 But, as we saw already, the unity obtaining between the components of an empirical concept is a unity necessarily borrowed from experience, and is therefore a connection grounded in empirical, not pure, intuition.Footnote 30 Hence it seems impossible that judgements in which the concept of matter (or, equivalently, the concept of impenetrability) occupies the subject position—that is, the very judgements required by special metaphysics—could be synthetic a priori judgements, as is also required.

Thus Kant's demand for systematicity has resulted in a demand for a systematic principle underlying natural science. This principle must have empirical content in order to have the required determinacy, but it also must be a priori in order to have the right systematizing scope and warrant. In order to generate an a priori principle from the empirical content of the concept of matter, Kant must find a pure a priori intuitive ground for synthesis. But it is just that ground that is missing from the concept of matter, in virtue of its empirical character. What Kant requires, then, is a way to preserve the apriority of special metaphysics by somehow getting around, but still admitting, the empirical character of the concept of matter.

3.1. Motion and Pure Intuition

Kant adopts a substitution strategy to deal with the difficulty posed by an apparent lack of a pure intuitive basis for synthetic a priori judgements about matter. Specifically, he looks for a pure intuition that can be substituted for the empirical intuition actually underlying the concept of matter, and he then uses that substitute intuition as the means to validate the relevant synthetic a priori judgements. His substitution strategy has two steps. The first is to point out that there is a close connection between matter and motion in empirical intuition, a connection so close that ‘the understanding traces all other predicates of matter belonging to its nature’ to motion (4: 476–7). In general, Kant seems to think, we are justified in regarding matter as the movable. While there are various questions about Kant's warrant for this claim about matter and movability we might raise, we can bracket these questions and focus instead on the fact that a connection between matter and movability alone is not enough to get Kant the substitute pure intuition he needs.Footnote 31 The reason such a connection will not suffice is that, as Kant himself insists, ‘the movability of an object in space cannot be cognized a priori’ (4: 482). In other words, movability is no more directly available a priori than is the empirical intuition underlying the unity of the concept of matter. And indeed, even an intuitive, not yet fully cognitive access to movability is impossible, since ‘in space considered in itself there is nothing movable’ (A41/B58).Footnote 32

This point about motion and a priori intuition is worth emphasizing, because it dictates the second step in Kant's substitution strategy. We might be tempted to think that Kant's descriptions of the method for determining space a priori in intuition—namely, geometrical construction—allows for some kind of abstract or pure intuition of motion. Construction, on Kant's view, is the exhibition or presentation (Darstellung) in pure intuition of a geometrical figure corresponding to a given concept.Footnote 33 In the context of his theory of construction, the static quality of geometrical figures is obscured by the fact that the process of construction was regarded, both by Kant and by the larger tradition, as the mental activity of producing geometrical figures through a kind of imaginative drawing.Footnote 34 Thought of in this way, geometrical figures are produced by what is naturally conceived of as a constructive drawing motion of some sort. In the larger transcendental context of Kant's philosophy, the static quality of the object of pure intuition is further obscured by Kant's explanation of how the forms of intuition themselves are produced by the transcendental imagination. This explanation involves appeal to what we might call a transcendental motion, originally productive of the form of space itself.Footnote 35 Clearly, Kant's appeals to these other, non-empirical kinds of motion may persuade us to adopt the idea that some a priori direct presentation of motion is possible. To be so persuaded, however, would be a mistake. Even granting transcendental and constructive motion as necessary to the process of generating a geometrical figure, it in no way follows that the figure so generated contains or involves any motion per se, or that the generative motions in questions are themselves objects of intuition. And given Kant's insistence on the impossibility of an a priori exhibition or presentation of motion, we have positive reasons to resist drawing any such conclusion.Footnote 36

Knowing that matter is the movable, therefore, does not by itself get Kant the pure intuition he needs. He is therefore forced to use indirect means for obtaining his substitute intuition. This indirect option requires that Kant devise a method for interpreting what is available in pure a priori intuition—namely, static geometrical figures—not as directly presenting, but as representing, actual and possible motions.Footnote 37 Arriving at such an interpretative method is the second step of Kant's substitution strategy. If such a method can be found, then we can use the static figures as pure intuitive substitutes for the empirical intuitions actually underlying the concept of matter, by means of the connection between matter and motion. Possessed of such substitutes, we will be in a position to make the synthetic a priori judgements connecting the logical essence of matter with its real essence.

3.2. Static Geometrical Figures and the Representation of Motion

Explaining how a static geometrical figure can be interpreted as representing motion, and understanding which such figures can be so interpreted, is the task of the first chapter of the Metaphysical Foundations: the Phoronomy. The challenge, according to Kant, arises from the fact that geometrical figures are merely spatial, while motion involves time as well. Thus we must somehow grasp static geometrical figures as capturing ‘not solely, as in geometry, the space described, but also the time in which, and thus the speed with which, a point describes the space’ (4: 489).Footnote 38 But if it is true that pure intuited figures themselves cannot directly present any motion, then the key task is to show how the temporal aspects of a motion can be seen in a static figure.Footnote 39 Only then will a purely a priori ground for the synthetic judgements linking logical and real essence be possible, and thus only by generating such an interpretative method can we achieve the systematic unity demanded by reason.

The interpretative method Kant derives is a relatively simple one. He begins by adopting the straightforward rule that we should regard every line segment, no matter what its length, as representing a motion occurring in one unit of time.Footnote 40 Thus the temporal component of motion is not presented directly in the figure by means of an independent geometrical element, but is represented in the figure by the fact of the delimitation of each segment occurring in it. While such an approach is unproblematic for simple lines representing simple motions, it is not immediately clear how we might use this method to represent composite motions (or, equivalently, how we might interpret figures containing multiple line segments as representing motions). To see the difficulty here, we can use one of Kant's own examples.

Kant defines composition of motion as ‘the representation of a single motion as one that contains two or more motions at the same time … insofar as they constitute one motion combined’ (4: 489). Now, consider an object (regarded in phoronomy as a point) whose motion is to be represented as the composition of two motions in the same direction.Footnote 41 Let us designate one of these two motions AB and the other ab, and suppose that AB is represented geometrically by a line segment AB and ab by ab. We might be inclined to represent the composite motion of the point in question by means of a figure ABC, formed by placing line segment BC, of the same length as ab, end-to-end with AB. Yet given Kant's rule according to which each line segment must be understood as representing the distance traversed by a motion in one unit of time, if ABC represents the motion of the point, then we must regard ABC as representing a distance traversed in two units of time, since it is a figure containing two line segments. Interpreted in this way, ABC represents a motion in which AB is simply continued, spatially and temporally, after its end (represented by point B) by ab (represented here by BC). Under such an interpretation, the motion represented by ABC is a ‘composite’ motion only in the weak sense that it is a spatial and temporal continuation of AB by ab. But this weak sense of composition does not fit Kant's requirement for true composition, since when interpreted this way, ABC does not represent ab as occurring at the same time as AB, but rather after it. We get, in some sense, an addition of motion, when what we wanted was a composition. In the simple case where AB and ab are equal, and thus AB and BC are equal, ABC represents a motion in which a distance twice that traversed in AB is traversed in twice the time taken by AB. But a proper composition, again in the simple case, would be a motion traversing twice the distance traversed in AB, but in the same time—that is, one in which AB was combined with ab into a motion with twice the speed.

The challenge for Kant here is to represent strong or proper composition with the same static geometrical tools already used to represent mere addition of motion. More specifically, the challenge is to interpret ABC itself as representing such a composition, but in a way that obeys the rule requiring each segment to represent a distance traversed in one unit of time.Footnote 42 Kant's claim is that we can understand ABC as representing a proper composition of AB and ab by reinterpreting the meaning of BC. This reinterpretation relies on Kant's version of the relativity of motion, according to which motion ‘can be viewed arbitrarily as motion of the body in a space at rest, or else as rest of the body, and … motion of the space in the opposite direction with the same speed’ (4: 487). Availing himself of this principle, Kant proposes that if we take AB to represent the motion AB of the point in absolute space, we can ascribe the motion ab to a relative space within which AB is included. We can then interpret BC as representing the motion, in the direction from C to B, of that relative space. In this way, we can interpret ABC as representing—precisely by means of the figure's containing two distinct segments—the two motions as motions of the one point in one time (one a motion of the point proper, the other a motion of it along with its space). The result is an interpretation of ABC such that it represents composite motion properly so called.

Kant's rule of interpretation, according to which composition of motion must be represented by attributing one of the motions composed to a point in absolute space and the other to the corresponding relative space in the opposite direction, is given as the sole Proposition (Lehrsatz) of Phoronomy (4: 490). With this interpretative rule in place, Kant has taken the second step in his substitution strategy, and a major step towards his ultimate metaphysical goal. For if we accept that matter is the movable, and if we can understand each of the properties in the logical essence of matter in terms of this movability, then by the construction of figures suited to phoronomical interpretation we can relate each of these properties to a pure intuition that can be used to ground synthetic a priori judgements about matter. These judgements, presumably, will ultimately lead us to the real essence of matter, and thus to our systematizing principle.

3.3. From Impenetrability to Essential Forces

In the Dynamics, Kant considers matter's logically essential property of impenetrability, and shows how impenetrability can be understood in terms of motion. Kant's considerations here can be reconstructed fairly plainly. We know from its logical analysis that matter is impenetrable. The relation of impenetrability to movability is apparent when we consider that penetration into a space is a kind of motion. Impenetrability, then, is just resistance to that penetrating motion. Accordingly, the Dynamics begins with the claim that matter is ‘the movable insofar as it fills a space’, where ‘[t]o fill a space is to resist every movable that strives through its motion to penetrate a certain space’. But to resist a motion is to cause it to be diminished, and so when we say matter is impenetrable, we predicate of it ‘a property relating as cause to effect’ (4: 496). As we know from the Proposition of Phoronomy, ‘nothing can be combined with a motion, which diminishes or destroys it, except another motion of precisely the same movable in the opposite direction’ (4: 490). Thus the cause of the resistance through which matter diminishes penetrative motion into its space is a cause of motion.Footnote 43 Kant's term for a cause of motion is force, and specifically moving force, and thus matter as impenetrable contains a moving force. On this basis, Kant formulates Proposition 1 of the Dynamics, according to which ‘matter fills a space … through a particular moving force’ (4: 497), a force explicitly identified in Proposition 2 as a repulsive force.Footnote 44 The property of filling space through repulsive moving force, however, is not among the properties making up the logical essence of matter; we know this from Kant's appeal to pure intuition via his invocation of the Proposition of Phoronomy in the course of his argument. Yet in Proposition 6, Kant claims that this property is essential to matter.Footnote 45 If this force is essential, and not part of the logical essence of matter, then it must be part of the real essence of matter.

We can see Kant's metaphysical method, and the role played by the phoronomical interpretation of geometrical figures in that method, if we examine this argument a little more closely. The judgement attributing an essential repulsive force to matter can only count as a metaphysical one expressing (a component of) the real essence of matter if it is a priori. Its apriority, in turn, clearly depends on the validity of the phoronomical procedure (as well as on various synthetic a priori principles from the first Critique). According to that procedure, we can interpret a geometrical figure as representing a change in the motion of some body L as it approaches some other body K by regarding that figure as representing a composition of motions. More precisely, the figure would represent, by appropriate line segments, both the original motion of L towards K, and a second motion of the corresponding relative space in the direction from K towards L. By the principles of the first Critique (specifically here, the Second Analogy), this second motion must have some cause; in calling K impenetrable, we claim that K is the cause of this second motion. But in saying that K is the cause of a motion, we say it is possessed of a repulsive moving force.

The key point here is that in regarding the impenetrability of matter as bringing about a change in motion, we are required to represent impenetrability through a composition of motion. If we want to represent such a composition through an a priori pure intuition, we can do so, but we must arrive at the relevant geometrical figure by considering the phoronomical rules for its interpretation. Were those rules different, we might be committed to ascribing some other property to matter's real essence. But the Phoronomy has demonstrated the necessity of these rules. We thus know, through appeal to an a priori intuitive representation, that matter as the impenetrable movable has such a repulsive force in its essence, even though that force does not appear in its logical essence. In other words, assuming that our entitlement to our interpretative procedure is itself a priori, we know the synthetic a priori truth that there is a repulsive force belonging to the real essence of matter.

Kant attributes a further force to the real essence of matter as well: a fundamental force of attraction. He reasons that if matter had only an essential force of repulsion, it would dissipate itself infinitely in space, to the point where the repulsive force it exerted in any given region would be, even if nonzero, nevertheless of ‘no specified quantity’. But an infinitely small repulsive moving force in any region of space would lack any capacity to diminish motion, and consequently there would be no impenetrability anywhere. Yet we know from an analysis of its concept that matter is impenetrable. Thus Kant concludes that ‘matter requires for its existence forces that are opposed to the expansive forces’ (4: 508). Opposed to the essential repulsive force, then, is an ‘attractive force’ that ‘belongs to the possibility of a matter as matter in general’, a force that is ‘a fundamental force belonging to its essence’ (4: 509).

Here again the phoronomical constraints on interpreting geometrical figures are central to Kant's argument. He argues that we cannot conceive of the material universe as a totality of merely mutually repelling bodies possessed only of repulsive force, since then the repulsive force essential to each would be infinitely dissipated. Thus we know that, in order to check the dissipation of repulsive force, matter must have a second force acting in it. The phoronomical rules for the composition of motions, however, require that this second force act in a direction precisely opposite to that of the repulsive force. Hence the second force acting in matter must be directed towards the centre of each part of matter. Again, if composed motion could be represented in pure intuition in some other fashion, matter might have some other real essence. But the phoronomical method is the only possible one.Footnote 46 In this way, Kant argues that special metaphysics allows us to discover repulsive and attractive forces as principles of the impenetrability belonging to the existence of any object of outer sense.

3.4. The Real Essence of Matter and Systematic Unity

Kant goes on in the Dynamics to discuss further properties of matter, but these discussions assume the essentiality of the fundamental forces. The first obvious bit of systematization of natural science in the Metaphysical Foundations, namely the derivation of Newton's first and third laws of motion in the Mechanics (the third chapter), also clearly depends on the previous demonstration of such essential forces. And once the Phenomenology (fourth chapter) takes up the way to distinguish true from apparent motion, the plan for the full systematization of our empirical cognitions is clear: insofar as these cognitions can be fully translated into descriptions of the true motions of material objects, they can be systematized under the laws for such motions.Footnote 47

Kant's procedure in the later chapters, and their relation both to the earlier chapters and to the transcendental philosophy, are of considerable interest in their own right. But our question about the coherence of Kant's special metaphysics and its role in achieving Kant's systematic philosophical aims can be pursued by focusing on what we have seen already in the Dynamics, and by noting that whatever else he accomplishes in the Metaphysical Foundations, he never achieves his own explicitly stated and systematically justified goal of reducing the two essential forces of attraction and repulsion to one essential force, or to one common metaphysical ground. That is, despite all the efforts he makes, Kant does not in fact find ‘the first inner principle of all that belongs to the existence’ of matter (4: 467).

My argument is that this failure is a real one. To see why it is and what it means, we should recall exactly why Kant is looking for such a first inner principle at all. Reason ‘prescribes and seeks to bring about … the systematic in cognition, i.e., its interconnection based on one principle’ (A645/B673), and the establishment of such systematicity counts as ‘reason's own empirical use’ (A643/B671). In this empirical use, reason ‘presupposes an idea, namely that of the form of a whole of cognition’ and through this idea ‘postulates the complete unity of the understanding's cognition, through which this cognition comes to be … a system interconnected in accordance with necessary laws’ (A645/B673). The function of the essential forces of matter in such a system is to coordinate a series of empirical relations and laws under higher principles; the concept of essential force is used to ‘reduce the apparent variety’ of empirically detected forces in nature to as few forces as possible, until even the ‘comparatively fundamental forces’ of attraction and repulsion are thought under a higher idea, ‘so as to discover their unanimity and thereby bring them to a single radical, i.e., absolutely fundamental, force’ (A649/B679).

The discovery of a first inner principle of matter, a single and unique real essence, is thus not quite an ultimate aim of reason as such, but one of its intermediate aims, insofar as such a discovery would make realizable reason's deeper goal of systematicity. This intermediate aim is one set by the basic condition of cognition in general: the unity of apperception. The systematic unity demanded by reason is therefore not to be regarded as an imposition on the understanding from without, as though the understanding might just as well function correctly and coherently in the absence of such unity; it is rather the condition of possibility of the understanding itself, and is thus one of those aspects of our cognition ‘grounded in the nature of our powers’ and their ‘correct use’ (A642/B670).

Yet in the Metaphysical Foundations Kant never gets more fundamental than the repulsive and attractive forces—he arrives at no absolutely fundamental force. The natural conclusion, then, would be that special metaphysics has failed to achieve its systematic goal. Yet the directness and clarity with which Kant recognizes the incompleteness of his matter theory suggests something other than total disappointment and failure on his part. ‘The concept of matter is reduced to nothing but moving forces’, Kant writes, ‘But who pretends to comprehend the possibility of the fundamental forces’ (4: 524)? Knowledge of ‘the first grounds of things’, including knowledge of an unconditioned absolutely fundamental force, is an ‘inconceivable’ goal of reason (4: 564), and when reason grasps the impossibility of finding an object for such an idea, says Kant, it turns away from the consideration of it and back towards a study of ‘the ultimate limits of its own unaided powers’ (4: 565).

We should of course be inclined to take this general and abstract admission of the unrealizability of his explanatory and systematic goal for what it is: an exemplary case of Kantian modesty. Indeed, what we have here is just the claim that the attempt to ground the real essence of matter in an absolutely fundamental force should be taken as an instance of Kant's famous doctrine of the regulative use of the transcendental ideas. Since Kant himself restricts these ideas to such a regulative use, he can hardly be said to be unaware of the results of doing so.

Yet we should not imagine that invoking the regulative use of the concepts of reason converts the failure here into a victory; all the regulative restriction amounts to is an admission of the necessity of this failure. What we should be more interested in is the cause of the failure, or in this case, the moment in Kant's method when the impossibility of arriving at the single real essence of matter is set in systematic stone. Kant himself does not specify a single such moment, but we have seen a few candidates in the course of the reconstruction above. There is the beginning empirical conditionedness of our possession of the concept of matter, and there is the apparent empirical conditionedness of the claim that all properties of matter are to be referred to motion. Finally, there is the fact that the ground of our purported synthetic a priori claims is itself a substitute ground generated by an interpretative procedure. Any one of these, or perhaps all together, show us ‘the ultimate limits of [reason's] own unaided powers’ in the incompleteness of the Metaphysical Foundations, and thus how this text fits in as part of Kant's Critical project overall.

Again, we should resist the inclination to regard the regulative use of reason here as one in which the idea of a fundamental force appears as a mere hypothesis or a heuristic for the efficient practice of empirical natural science—as though Kant were giving a bit of helpful laboratory advice to a junior colleague. On such a reading, Kant's strenuous efforts in his substitution strategy would make no sense, since a mere heuristic cannot demand that such a stringent interpretative principle be developed. Were a fundamental force a mere hypothesis, any particular use of geometrical figures to model it would have only experimental or a posteriori warrant through its pragmatic success, rather than being subject to strict a priori constraints on its proper use. And in any case, Kant himself explicitly rejects this understanding of the regulative use of reason, claiming instead that the idea of an absolutely fundamental force ‘pretends to objective reality’, with the result that ‘an apodictic principle of reason is erected’ (A650/B678); in fact it is this principle that Kant regards as securing the ‘coherent use of the understanding’ required for ‘the sufficient mark of empirical truth’ (A651/B679). The pretence here is, as it were, in deadly earnest—reason really pretends, and really erects the principle. Of course, it is entirely correct to point out that the demand here is only that: a demand for, and not a proof of, the objective reality of such a force. Yet to do so is not to get Kant out of the problem, but to describe it. If P is demanded for Q, then, lacking P, we lack Q; if an objectively real ultimate fundamental force is demanded for the coherent use of the understanding, then, lacking such a force, we lack such a use. To classify the idea of such a force as regulative is simply to assert that we lack it necessarily; otherwise put, if the understanding is always in search of the condition of its coherence, then it always lacks coherence.

Thus it is my claim that the insistence of reason on the objective reality of a fundamental force captures the tension operating within the Metaphysical Foundations and shows the mistake we would commit by trying to resolve this tension, either by saying that reason knows all along that it cannot have access to the real essence of matter, or by saying that reason in fact can have such access. Reason insists on the apodictic principle that there is such a single fundamental force, and on its objective reality (that is, its discoverability, not merely its abstract desirability)—whence the demand for an a priori special metaphysics of nature and all the methodological twists and turns used to get one. Without a rigorous attempt at such a metaphysics, reason cannot regard the understanding as pursuing its (both reason's and the understanding's own) goals. But reason also insists on the conditionedness of our experience, and so on the distinction between the a priori and the a posteriori. The conditionedness of our experience of determinate objects means that no matter what technical devices we might be able to generate for the geometrical representation of motion, the empirical character of the concept of matter will render the synthetic judgements based on that concept non-a priori, and thus will render such a metaphysics incomplete.

What is perhaps surprising here is that the failure of the Metaphysical Foundations to generate an a priori real essence of matter must be, on Kant's view, a good and indeed necessary result, despite the fact that the pursuit of such an essence is also necessary. A successful demonstration that the content of the Metaphysical Foundations is a priori would violate the Critical limits of the understanding, while a successful demonstration that such content could only ever be a posteriori would deny reason's apodictic principle of the objective reality of a single absolutely fundamental force. Any reading of Kant's system, then, that proceeds on the assumption that Kantian reason cannot issue genuinely contradictory demands is a reading that runs counter to Kant's own method for carrying out a critique of metaphysics and producing a subsequent reformed metaphysics.

In terms of the actually generated content of the special metaphysics of nature, we can see how this dialectical result shows up ‘on the ground’. The determinacy of the essential forces of attraction and repulsion is the very thing that lends them their superior systematizing power with regard to empirical laws when compared to the categories and principles of the first Critique. This determinacy is, and can only be, grounded in their non-transcendental, i.e. their empirical, status. But precisely insofar as this empirical character distinguishes the principles of special metaphysics from those of general metaphysics, it is both the key to the possibility of special metaphysics, and the insurmountable obstacle to its successful completion.