3.1. From the Metaphysical Foundations of Natural Science to the ‘Transition from the Metaphysical Foundations of Natural Science to Physics’: developing a new conception of phenomena

In what follows, I want to clarify the particular stance Kant took on Galileo against the empiricist tradition exemplified by Duhem's and van Fraassen's aforementioned remarks. Kant too, like Duhem and van Fraassen, saw in Galileo a turning-point in the history of science, but for very different reasons. By asking how pure natural science is possible, Kant was trying to justify why we can have and indeed do have a new science of nature from the time of Galileo onwards, against the empiricist tradition that takes nature as a bunch of phenomena to be saved by introducing hypotheses that do not claim to be true. It is from this particular perspective—I want to suggest—that we can read the Metaphysical Foundations of Natural Science (1786, henceforth abbreviated as MAN) and, more in general, Kant's philosophical enterprise from MAN until his last incomplete work ‘Transition from the Metaphysical Foundations of Natural Science to Physics’ published in the Opus postumum. I shall in particular take a look at the Xth/XIth fascicles of the Opus postumum (presumably written between August 1799 and April 1800, almost ten years after the third critique and four years before Kant's death).Footnote ¹² Indeed, it is in this last and incomplete work, which in Kant's intentions was meant to fill a gap that he felt was still open in his critical philosophy after the Critique of Judgment, that we find some interesting clues about Kant's new conception of phenomena and his view on Galileo's mathematization of nature.

In the Metaphysical Foundations of Natural Science, in the chapter called ‘Metaphysical Foundations of Dynamics’, Kant had defined the empirical concept of matter according to the category of quality as the movable that fills a space through a particular moving force. More precisely, he had introduced attractive and repulsive forces as two fundamental moving forces, through which matter can fill a space by either causing other bodies to approach it or to be removed from it. Kant derived these two fundamental moving forces a priori from two basic properties of matter, namely its ability to resist penetration (impenetrability) and, at the same time, its ability to strive to enlarge the space that it fills so as to counteract the opposite tendency expressed by the repulsive force.

In the ‘Transition’, almost fourteen years after the Metaphysical Foundations, Kant claimed that in order to complete the transition from the metaphysical foundations of natural science to physics, it was not enough to establish a priori attraction and repulsion as two fundamental moving forces in nature. It was not enough because there remains a gap between postulating these two fundamental moving forces in nature from a metaphysical point of view, on the one hand, and accounting for the more specific empirical properties of matter that the chemical revolution was discovering at the end of eighteenth century, on the other hand:Footnote ¹³

The increasing number of empirical properties of matter revealed by the chemical revolution at the end of eighteenth century was simply too rich to be encompassed by the two fundamental forces of attraction and repulsion, established a priori in MAN. Hence the necessity to bridge the gap between the all-encompassing metaphysical framework canvassed in the Metaphysical Foundations, on the one hand, and the multifarious range of more specific empirical properties of matter that natural scientists were discovering, on the other hand. This is the specific task that Kant aimed to accomplish with the ‘Transition to Physics’, where by physics Kant meant ‘the systematic investigation of nature as to empirically given forces of matter, insofar as they are combined among one another in one system’ (22: 298). The main concern of the ‘Transition’ was then to justify and ground a system of empirically given forces in nature. The problem is that in nature we may observe objects moving in space and time, changing physical state (from solid to liquid to gaseous) or displaying some properties (e.g. being elastic). But these are only appearances [Erscheinungen]. Only when we introduce moving forces as the underlying causes that make the objects move in space, or change their physical state, or displaying some physical or chemical properties, do we have a conceptually determined appearance or phenomenon as the proper object of scientific knowledge.

I think this is the crucial, distinctively new feature that Kant introduced in the conception of phenomena: a physical phenomenon—intended as a conceptually determined appearance—has built in it from the very outset the concept of a moving force as the cause of the observed appearance. It is the causal concept of a moving force that distinguishes phenomena from appearances, or better, that transforms appearances into phenomena, i.e. objects of possible experience into objects of experience.

Kant had already made this point very clearly in chapter 4 of MAN. In that chapter, the empirical concept of matter as the movable in space is defined according to the category of modality, and Kant's aim is to show how to transform appearance (Erscheinung) into experience (Erfahrung); more precisely, how to transform apparent motions into true motions. According to Friedman,Footnote ¹⁴ since Kant rejected Newton's view on absolute space and time, he needed to find a way of explaining true or absolute motions without resorting to absolute space as a privileged reference frame. Kant's strategy consisted in identifying the centre of mass of our solar system as a privileged reference frame. To this purpose, he needed Newton's law of universal gravitation, responsible for the planetary motions in the solar system, as a necessary and universal feature of matter as the movable in space. Only in this way could he show how to transform apparent motions into true or absolute motions, intended now as motions with respect to the privileged reference frame of our solar system. Kant starts then from observed relative motions of satellites with respect to their primary bodies: the orbits of the moons of Jupiter, the orbits of the planets around the sun as described by Kepler's laws are all examples of apparent or relative motions that can be subsumed under the category of possibility. The next step consists in assuming that relative motions approximate to true motions: the reference frame defined by apparent motions is meant to approximate to the inertial reference frame, which in Newton's theory would be identified with absolute space but which Kant identified with the centre of mass of the solar system, following Friedman's interpretation. At this point Kant's second law of mechanicsFootnote ¹⁵ (which is meant to encompass Newton's I and II law) can be applied. And it is on the basis of Kant's second law of mechanics—previously introduced and justified in ch. 3 of MAN—that Kant concludes that there must be an external cause for the relative accelerations of orbiting bodies. This external cause must be an impressed force, and—Friedman concludes—it follows mathematically from Kepler's laws (in particular from Kepler's first law) that this force must satisfy the inverse-square law. In this way, the true or absolute motions (inverse-square accelerations) are subsumed under the modal category of actuality. Without going any further into this discussion, the point I want to stress is that following Friedman's reading here, already in MAN Kant delineates a procedure to transform appearances into phenomena, or better to transform appearance (Erscheinung) into experience (Erfahrung). Most importantly, this procedure hinges on the concept of cause embodied in Kant's second law of mechanics and in its transcendental counterpart, namely the second analogy of experience.

If this analysis is correct, we can begin to catch a glimpse of the radically new conception of phenomena that Kant was introducing. Physical phenomena as conceptually determined appearances have already built in them the concept of, say, a dynamic cause responsible for the observed appearances and their kinematical (spatiotemporal) properties. But how do we know that we are not feigning gravitational attraction as a hypothesis to save appearances? How could Kant claim to know that the moving forces, as the dynamic causes of the observed appearances, are real?

In order to answer the above questions, the top-down approach typical of the Metaphysical Foundations of Natural Science—whereby the empirical concept of matter is schematized according to the four transcendental categories of quantity, quality, relation and modality, and ascribed a priori a series of fundamental properties (including attraction and repulsion)—cannot be of much help. And Kant's dissatisfaction with this top-down approach is testified by his search for an alternative, complementary approach from the time of the Critique of Judgment to the ‘Transition’ of the Opus postumum. We need a bottom-up approach that starts from appearances and empirically given forces, in order to show that those forces are not feigned to save appearances, i.e. they are not introduced as hypotheses to fit empirical regularities. In addition, we need to show that the increasing number of empirically given forces do not just form an aggregate, but a system instead. If physics is defined as ‘the systematic investigation of nature as to empirically given forces of matter, insofar as they are combined among one another in one system’, the key for the ‘Transition’ project was to show how such a system is possible.

Thus, I take that the crucial question Kant was trying to answer in the ‘Transition’ was the same question that concerns philosophers of science today: how do we know that we are not just and simply feigning hypotheses to save phenomena (in Duhem's and van Fraassen's sense)? Moreover, how do we know that our science does not reduce to a mere aggregate of empirical regularities, and that there is in fact some lawfulness in the empirical regularities we see in nature? In other words, how do we know that

1. 1) the alleged moving forces are the true causes of appearances;

2. 2) they form a system conferring lawfulness to what would otherwise be only an aggregate of empirical regularities?

In the next section 3.2, I take a look at Kant's answer to question 1). We shall see in section 3.3 his reply to question 2), and how it is related to his answer to 1). Once we clarify Kant's answer to point 1), we can get a better understanding of his radically new conception of phenomena, and why he believed that there are no ready-made phenomena in nature.

3.2. How do we know that the alleged moving forces are the true causes of appearances? The Galileo case

I want to suggest that Kant's reply to question 1) can be found in the passage of the Preface on Galileo that I quoted above, where Galileo is presented as someone that interrogated nature ‘through principles of reason, on the one hand, and through experiments thought out in accordance with these principles, on the other hand’ (Bxiv). Let us take a look at these two aspects of Galileo's case, starting with the role of observation and experiment.

Galileo's experiment with the inclined plane is instructive to illustrate Kant's view of phenomena as not ready-made in nature, and no wonder Kant mentioned it not only in the Preface to the second edition of the first Critique but also in the Opus postumum. Galileo started indeed with appearances, namely with observed relative motions of heavy bodies, whose kinematics he carefully studied. For the sake of experience, he inserted something a priori into these appearances: namely he took those relative motions as approximating to uniformly accelerated motions due to a moving force. Finally, with the experiment of the inclined plane, he extracted and demonstrated what he had previously inserted into appearances for the sake of possible experience, namely uniform acceleration due to a force. Of course, Galileo's focus was kinematics, not dynamics: he did not identify the moving force causally responsible for uniformly accelerated motions with gravitational attraction. This was Newton's achievement, building up on Galileo's kinematical studies. Galileo simply inferred a priori to a force causally responsible for the uniformly accelerated motion of free-falling bodies. It was only later with Newton that the force was identified and a full dynamical analysis given. But the very idea of a moving force as the true cause (‘vera causa’, in Galileo's language) of uniformly accelerated motion is already in Galileo's kinematics and in his opposition to Aristotelian physics. To Kant's eyes, Galileo paved the way to Newton by anticipating a concept of moving force that Newton filled in with gravitational attraction:

In this important passage, Kant claims that before Newton there was only empiricism in the doctrine of motion, and no concept of reason yet from which one could infer a priori—as from a cause to its effect—to a law for the determination of forces. To Kant's eyes, this was achieved by Newton, who championed a ‘metaphysical-dynamical’ approach, while scientists before Newton, such as Kepler for instance (but also Huygens and Descartes) defended a ‘mathematical-mechanical’ approach that tried to give an explanation of nature in terms of extended matter and geometrico-mathematical motions. It is only with Newton that fundamental moving forces were introduced and a dynamical analysis of nature became finally available, something that Kant regarded as crucial for the advancement of science.Footnote ¹⁶ Of course, from a historical point of view, Kant's take on Kepler here is questionable, because in his own ways Kepler too may be said to have provided a dynamical analysis of planetary motions in terms of his mystical doctrine of the anima motrix of the sun.Footnote ¹⁷ However, for the purpose of our analysis, what matters is the fact that Kant locates in Newton the crucial passage from the observation of relative motions with their kinematical properties to a proper dynamical analysis of nature:

The fundamental role that Kant assigned to moving forces, in particular to Newton's gravitational force in the ‘Transition’ as the efficient cause of appearances, e.g. of relative motions of planets kinematically described by Kepler as well as of relative motions of free-falling objects described by Galileo, sits squarely with the interpretive line I have been suggesting about Kant's view of phenomena as conceptually determined appearances. Let us then take a closer look at this passage from kinematics to dynamics in the Galileo–Newton case.

The experiment Kant refers to is the famous experiment of the inclined plane that Galileo discussed in the Third Day of his Discourses and Mathematical Demonstrations concerning Two New Sciences (henceforth abbreviated as Two New Sciences, 1638). Galileo's aim was to prove that Aristotelians were wrong in claiming that free-falling bodies were moving towards a natural place. Galileo starts by describing an alternative possible type of motion, called uniformly accelerated that ‘starting from rest, it acquires, during equal time-intervals, equal increments of speed [temporibus aequalibus aequalia celeritatis momenta sibi superaddit]’.Footnote ¹⁸ In other words, a uniformly accelerated motion is such that the ratio between Δv (i.e. the equal increments of speed or celeritatis momenta) and Δt (i.e. equal time-intervals) is constant. But this is only a definition, and—as Sagredo, one of the characters of Galileo's Two New Sciences, points out—as with any definition, one may doubt whether this definition is verified in the kind of accelerated motion that heavy bodies in fact employ in free fall. Salviati, who in the Two New Sciences speaks for Galileo himself, replies

The refusal to investigate the causes of uniformly accelerated motion in the quotation above should be understood—I want to suggest—as a stance against the tradition that takes phenomena as ready-made and reduces science to introducing a series of hypotheses that can save them (i.e. the same tradition that Duhem saw exemplified in what he called the method of the astronomer). Galileo seems to be taking the distance from this tradition in declaring himself not interested in speculating about the causal hypotheses that can save the phenomenon of uniformly accelerated motion. Instead, he is interested in demonstrating some of the properties of accelerated motions. But how could Galileo prove that free-falling bodies do indeed have uniformly accelerated motions?

It is at this point that Salviati introduced a key assumption or as he calls it supposition: ‘This definition established, the Author makes a single assumption, namely: the speeds acquired by one and the same body moving down planes of different inclinations are equal when the heights of these planes are equal’.Footnote ²⁰ This is the key assumption that is supposed to be true, and from which Galileo's demonstration of the law of free fall follows. Despite Galileo knew of the law of free fall as early as 1604 as originally announced in a letter to Paolo Sarpi on 16 October following a long period of experimenting with inclined planes in Padua, at the time he did not have what he called a natural principle from which to deduce the law. And the fact that thirty-four years later in Two New Sciences, when almost blind and under house-arrest in Arcetri, he felt the need to spell out the key assumption or supposition behind the mathematical demonstration of the law of free fall testifies to the central role that this supposition plays in Galileo's mathematization of nature.Footnote ²¹

The supposition says that the speeds acquired by the same body descending along say the inclined planes CA and CD, respectively, are equal since the heights of theses planes are equal, namely CB [see Figure 1].

Figure 1.

More in general, this is the same speed that would also be acquired by the body falling vertically from C to B. In order ‘to increase the probability [of this assumption] to an extent which shall be little short of a rigid demonstration’, Salviati presents the following thought experiment (‘esperienza’).Footnote ²² Imagine a vertical wall with a nail driven into it, and from the nail let us suspend a fine vertical thread with a lead bullet from A to B [see Fig. 2].

Figure 2.

Then consider the horizontal line DC, at right angles to the vertical thread AB. If we now bring the thread with the bullet into the position AC and we set it free, we can observe it to descend along the arc CBD, until it almost reaches the horizontal DC. From this we infer that the bullet in its descent through the arc CB acquired a momentum [‘impeto’] on reaching B which was sufficient to carry it through a similar arc BD to the same height. The same applies to all other arcs BG and BI (starting from points E and F, respectively). Salviati then concludes:

This is further generalised and taken to be valid not just for arcs but also for the chords subtended to these arcs, and hence for inclined planes as required by the supposition. There is however an obvious inferential leap in this procedure and Salviati concedes that ‘we are not able, by similar means, to show that the event would be identical in the case of a perfectly round ball descending along planes whose inclinations are respectively the same as the chords of these arcs.’ This difficulty notwithstanding, Salviati concludes ‘but this obstacle, which interferes with the experiment, once removed, it is clear that the momentum [impeto] (which gains in strength with descent) will be able to carry the body to the same height. Let us then, for the present, take this as a postulate, the absolute truth of which will be established when we find that the inferences from it correspond to and agree perfectly with experiment’.Footnote ²⁴ In other words, Galileo's quasi-demonstration for the supposition depends on accepting the postulate; but the postulate is not self-evident and in fact it goes against intuitive experience. This supposition, and the postulate on which it relies, incorporates what I take to be the a priori element in Galileo's procedure, namely that the moving force causally responsible for the observed appearances must be such that the rate of acceleration must be constant (i.e. equal increments of speed in equal time-intervals, as is indeed the case with gravitational acceleration).

From the supposition Galileo then derives two theorems, in particular ‘[Theorem II] If a moveable descend from rest in uniformly accelerated motion, the spaces run through in any times whatever are to each other as the duplicate ratio of their times; that is, are as the squares of those times’. The demonstration of this theorem is very ingenious indeed: Galileo could not in fact avail himself of calculus to calculate instantaneous velocities. Nevertheless, he was able to prove that the ratio between space intervals was equal to the ratio between the squares of the time intervals required to traverse those spaces.Footnote ²⁵ But Simplicius, who represents the naïve Aristotelian in Two New Sciences, at this point intervenes in the discussion to cast doubt on this entire procedure and to ask for some experimental evidence to prove that these mathematical conclusions are indeed true. To which Salviati replies by describing the famous experiments with the inclined planes that Kant refers to.

Consider a bronze ball descending along a groove in a wooden beam tilted by elevating one end of it above the horizontal plane at will, and measure with precision the time it takes for the ball to descend along the entire groove. By repeating the experiment with the same ball descending this time only one-quarter the length of the groove, Galileo found out that the time it takes to descend one-quarter of the groove is precisely one-half of the time it takes to descend the entire groove. By repeating the experiment for other lengths (two-thirds, or one-half) many times, it was always found that spaces were to one another as the squares of the times (and this held for all possible inclinations of the plane). Thus, despite the fact that Galileo could not measure instantaneous velocity, but only space intervals and time intervals, he was able to derive relations between space, time, velocity, and hence acceleration that allowed him to demonstrate the uniformly accelerated motion of bodies descending through an inclined plane. Galileo did not give any numerical value for the acceleration of the rolling ball; nevertheless the result he found about s = at ² (when the initial velocity is 0) smoothed the path to Newton, who identified the moving force causally responsible for those accelerated motions with gravitational acceleration (a was replaced by the gravitational constant g) which is indeed at work both in the case of balls rolling down an inclined place and in the case of free-falling bodies.

For the purpose of my Kantian analysis, I want to draw attention to Galileo's deductive procedure of starting with a supposition and a postulate and deriving a series of theorems from them. This procedure has nothing to do with and should not be confused with hypothetico-deductivism, as also the Galilean scholar W. L. Wisan has rightly noted.Footnote ²⁶ From a Kantian perspective, the goal of the inclined plane experiment was to extract from the appearance (motion of a bronze ball along an inclined plane) the property of uniform acceleration that Galileo had himself a priori inserted in the appearance for the sake of possible experience. Hence, from a Kantian point of view, we should not think that what we observe, say, a free-falling object, is the rough-and-ready observable phenomenon (in van Fraassen's terms) to be saved by introducing hypotheses that do not give us a literally true description of the way things are (since there may well be alternative hypotheses that save the same phenomenon equally well). If we stick to the level of observable phenomena (again in van Fraassen's terms), then Galileo may seem no more right than Aristotle. What appears to us as a free-falling object can well be accounted for either by the hypothesis of motion towards a natural place, with Aristotle, or by the hypothesis of uniformly accelerated motion, with Galileo. And the role of Galileo's experiment would simply reduce to testing these alternative hypotheses, according to some sort of hypothetico-deductive procedure.

No wonder then many philosophers of science—including Feyerabend's famous analysis of Galileo's tower argumentFootnote ²⁷—have concluded that there was an element of propaganda in Galileo. In the end, Galileo was inventing new auxiliary dynamic hypotheses (be it circular inertia for the tower argument, or the aforementioned one about uniformly accelerated motion), and there was no intrinsic reason for the scientific community to shift to Galileo's new science, apart from the propaganda that finally gathered scientists' consensus around Galileo. I think that Feyerabend captured very nicely the theory-ladeness of observation in Galileo's strategy, but went astray in concluding that Galileo ‘invented’ a new conceptual system and used propaganda to defend it. This conclusion follows—I believe—from a widespread scepticism among philosophers of science about the possibility of choosing between alternative hypotheses that can both accommodate the available evidence. And this scepticism is of course nothing but a consequence of the empiricist tradition about ‘saving the phenomena’.

By contrast with this tradition, I want to suggest that the particular use Galileo made of the postulate in backing up the supposition, from which the law of free fall follows, incorporates what I take to be the a prioriFootnote ²⁸ element that Kant might have rightly seen in Galileo's procedure. Namely, for the sake of experiencing uniformly accelerated motion, we must constitute the kinematical properties of free-falling bodies according to the aforementioned supposition (no matter how counterintuitive the postulate necessary to back it up). But Galileo not only constituted the kinematical properties of free-falling bodies according to this supposition, he tried also to subsume these kinematical properties under the causal concept of a moving force that he called momentum gravitatis or ‘impeto’.Footnote ²⁹ And no matter the fact that Galileo's notion of impeto (as weight times speed) was still reminiscent of the Archimedean science of weight and was not the exact causal story about free-falling bodies. What matters is that for the very first time, physics was not regarded as introducing hypotheses to save the phenomena, but instead as a science whose secure foundations depended on the specific mathematical–physical way in which phenomena were constituted. This is the central contribution Galileo's mathematization of nature made to the scientific revolution. This is the central role Galileo occupies in the transition from Aristotelian to Newtonian physics, as Kant saw it.

To sum up, Kant suggested a radically new conception of phenomena, according to which a phenomenon, say the phenomenon of a uniformly accelerated free-falling object, is something that from the very outset we have mathematically–geometrically constituted as an object having certain spatiotemporal properties (for instance, the property of acquiring the same speeds over different inclined planes with the same height), and, most importantly, subsumed under a causal concept by tracing those spatiotemporal properties back to some moving force, such as Galileo's momentum gravitatis or ‘impeto’. Only in this way, can we transform kinematical appearances into physical phenomena that become the actual objects of scientific inquiry.Footnote ³⁰

In this specific sense, Galileo exemplified Kant's Copernican turn by showing how the phenomena that scientists investigate are not ready-made for us to either save them or give a literally true story of them, but instead they have built in them some a priori elements that we have then to extract and prove through experiment. We can now understand why, according to Kant, Galileo marks the beginning of modern physics by displaying a unique and distinctive scientific methodology: we can gain scientific knowledge of nature only through principles of reason, on the one hand, and through experiments thought out in accordance with these principles, on the other hand. In other words, we can gain scientific knowledge of nature only by making appearances conform to our way of representing, rather than trying hard to make our hypotheses conform to nature. And this is why, as I hope to have clarified, Galileo's method inspired Kant's Copernican turn, and as such it is all the more relevant to address the problem of knowledge that still troubles us today. In this way and in this way only, could Kant answer positively the aforementioned question about how we know that 1) the alleged moving forces are the true causes of appearances (as opposed to hypotheses feigned to save them).

3.3. How do we know that moving forces form a system conferring lawfulness to empirical regularities? The Newton case

An obvious question arises at this point. What has the concept of cause—which, if the above analysis is correct, Kant saw as inserted in the Galilean phenomenon of free-falling bodies from the ground up—got to do with principles of reason? Is not causation a principle of the faculty of understanding, namely the second analogy of experience, rather than a principle of the faculty of reason? A propos of this specific point, Michael Friedman has pointed out how ‘the dynamical principles of the understanding—in particular, the analogies of experience—are regulative rather than constitutive’Footnote ³¹ because they provide us with a regulative ideal. For instance, causation (the second analogy of experience) is instantiated in Kant's II law of mechanics (which, recall, is a combination of Newton's I and II law); in particular, it is instantiated in Newton's F = ma and hence in Kant's II law that requires an impressed force F as the cause of any change of uniform motion into accelerated motion. But Kant's II law of mechanics, with its a priori nature and transcendental backing in the second analogy of experience, per se cannot guarantee that there are phenomena in nature that instantiate such an impressed force as the causal factor responsible for their change of motion. We can only infer their actual existence a posteriori, namely via observation and experiments. Yet the second analogy of experience provides us with a rule for seeking after such phenomena: without it, we would not even be able to identify some empirical regularities as instantiating accelerated motion (as opposed to uniform motion), and hence as instantiating an impressed force causally responsible for it. It is in virtue of this regulative function—which in the first Critique Kant deemed to be distinctive of the faculty of reason—that I think we can legitimately regard causation as one of the ‘principles of reason’ Kant refers to a propos of Galileo in the Preface. Galileo transformed the appearance of free-falling bodies into a physical phenomenon to study by inserting from the ground up the concept of cause via a moving force, whose nature nonetheless he did not investigate. It was Newton who completed the work that Galileo begun, by investigating the properties of this moving force that Galileo had simply hinted at, as a regulative ideal of scientific inquiry.

While the analogies of experience, in particular causation, can be regarded as having a regulative function (despite being principles of the faculty of understanding), on the other hand, there is one principle of the faculty of reason that Kant repeatedly presented as the regulative principle par excellence: this is the principle of systematic unity or systematicity. In the Appendix to the Transcendental Dialectic, Kant spoke of systematicity as a regulative ideal of scientific inquiry ‘bringing unity into particular cognitions’ and hence transforming a ‘contingent aggregate’ into a ‘system interconnected in accordance with necessary laws’.Footnote ³² Despite this regulative function, Kant however did not regard systematicity only as a desirable feature of the faculty of reason in its striving towards the never fully attainable goal of a complete science of nature, but instead as a necessary requirement for a coherent use of the very same faculty of understanding, and even as a ‘mark of empirical truth’ (see A651/B679).

I think we can foresee here an important link between systematicity and causation as having itself a regulative function. For the faculty of understanding to work properly, and hence for the second analogy of experience to apply, we need an overarching regulative principle of reason, namely systematicity, which can guide us to bring unity into particular cognitions and to transform a contingent aggregate into a system interconnected in accordance with necessary laws. In other words, we need to go beyond the specific causal judgments concerning, for instance, the causal factor responsible for uniformly accelerated motion, and seek after a broader system of moving forces causally responsible for the great variety of phenomena in nature (from cohesion, to liquefaction, to elasticity, etc.).

Kant assigned an increasingly important role to systematicity in the First (unpublished) Introduction to the Critique of Judgment, where systematicity is no longer assigned to the faculty of reason, but to the faculty of reflective judgment. The task of reflective judgment consists in arranging lower-level empirical regularities into a system of higher-level laws, which are nonetheless still empirical. In this respect, the faculty of reflective judgment too has a distinctively regulative function, with its own transcendental principle that postulates the systematic unity of empirical concepts and laws as a regulative ideal so that a system of empirical science becomes possible.Footnote ³³ And systematicity as a regulative principle of reflective judgment becomes a key feature in the ‘Transition’ project.Footnote ³⁴ No wonder there are plenty of references to physics as a system or as a ‘systematic investigation of nature’ throughout the Opus postumum. There is a clear continuity between systematicity as advocated in the Critique of Judgment and in the ‘Transition’, whereby physics is defined as ‘the systematic investigation of nature as to empirically given forces of matter, insofar as they are combined among one another in one system’. Kant's task in the ‘Transition’ was to endorse the bottom-up approach typical of the faculty of reflective judgment (with the regulative principle of systematicity) in order to show whether, and eventually how the wide range of empirically given forces in nature could form a system.

Thus, we can now go back and answer question 2) above, namely how we know that such forces form indeed a system conferring lawfulness to what would otherwise be only an aggregate of empirical regularities. It is only in virtue of a regulative principle such as systematicity that we can seek after a system of moving forces, through which and within which only one can claim that the alleged moving force necessarily causes the observed appearance (e.g. gravitational attraction necessarily causes free-falling bodies to move with uniformly accelerated motion). Systematicity is what confers nomic necessity upon an otherwise contingent aggregate of Humean empirical regularities. I want to suggest then that it is this regulative principle of reason that complements observation and experiment in Kant's analysis of Galileo's mathematization of nature.

Although with his experiment of the inclined plane, Galileo arrived at the law of free-falling bodies, he fell nonetheless short of investigating the properties of the force causally responsible for uniformly accelerated motion. In order to move from the identification of a moving force as the true cause (the Galilean vera causa) of those motions to a properly physical/dynamical analysis of those motions, is not enough to apply the concept of cause. It is not enough because Kant had already shown in MAN back in 1786 how the concept of cause (the second analogy of experience) underpinned phenomena via the metaphysical principles of pure natural science (namely, via Kant's II law of mechanics). In order to complete the transition from the metaphysical foundations of natural science to physics—the very same ‘Transition’ Kant was working on in the last decade of his life and that he felt was urgently needed to fill a gap in his transcendental philosophy—we need more than just the concept of cause: i.e., we must identify the moving force as a force due to gravity and we must study its nature and properties as Newton did. In order to ground Galileo's kinematics into a proper ‘system’ of nature, we must shift from what Kant calls the ‘philosophical foundations’ (with the concept of cause) to what he calls the ‘mathematical principles of the philosophical doctrine of nature’, namely Newton's Philosophiae Naturalis Principia Mathematica:Footnote ³⁵

To Kant's eyes, the passage from Galileo to Newton represents the historical instantiation of what the regulative principle of systematicity commends. Via Galileo and Newton, Kant saw historically realised the system that confers lawfulness to an otherwise contingent aggregate of Humean empirical regularities. In the case of the force of gravitation, we can properly speak of a system that unifies a great variety of phenomena under a single moving force/cause. And it is thanks to being part of this system that every phenomenon (from the planetary motions studied by Kepler to free-falling bodies studied by Galileo) is entrusted with nomic necessity. Nature's lawfulness is then a consequence of phenomena being systematized under a single common cause, under a single dynamical force such as gravitational attraction. To Kant's eyes, Galileo's experiments and Newton's systematization of phenomena under the single force of gravitation represented the two complementary poles of a sought-after ‘Transition to physics’.

Despite what Kant portrays as a serendipitous transition from Galileo to Newton, this story does not have a happy ending. The more general question that Kant was trying to answer in the ‘Transition’ and that was bound to remain open was whether any similar system could be found for many other types of phenomena revealed by pneumatic chemistry and aether theories at the end of eighteenth century. Is there any similar system able to unify all moving forces in nature responsible for solidification, liquefaction, chemical combination of gases, transmission of light and sound, and even biological phenomena? Kant wondered whether it was possible to embed the Newtonian system into a much broader system providing a unified framework for the increasing variety of phenomena revealed by the physical sciences of his time. This was Kant's specific task in the ‘Transition’, a task that he could not fulfil. But we can catch a glimpse of Kant's heroic efforts from many passages of the Opus postumum. In vain did he attempt to identify Lavoisier's caloric (suitably reinterpreted as heat-matter [Wärmestoff] and even identified with aether) with an all-pervasive substance responsible both for the transmission of light and for states of aggregation of matter, and, hence, with a possible candidate for the sought-after unification of an increasing variety of phenomena.Footnote ³⁶ While the answer to this specific question could not be found and Kant's fragments leave us enough leeway to speculate about his views on aether, caloric and the more general project of the Opus postumum, the ‘Transition’ casts light on Kant's life-long stand on phenomena, which I have tried to spell out in this paper. We do not have ready-made phenomena, but somehow we make them. And we make them via observation and experiment on the one hand, and principles of reason, on the other hand: