Kant's Construction of Nature

Michael Friedman's Kant's Construction of Nature is the first Anglophone book-length treatment of Kant's Metaphysical Foundations of Natural Science. Friedman has given us an extraordinary book—clearly the fruit of decades of thought and labor from a philosophical mind of the first order. It will be read and studied, I believe, for many years to come.The goal of the book is to give what Friedman calls a “reading” of Kant's Metaphysical Foundations that situates it in Kant's intellectual context. At around six times the length of the Metaphysical Foundations itself, Kant's Construction provides a wealth of detailed and sustained discussion of both the large themes and small points in the Metaphysical Foundations. Though not offering a traditional line-by-line commentary, Friedman ends up discussing virtually every paragraph of Kant's book.In this review, I'll focus on two of the largest themes of Friedman's book. First, according to Friedman, “Kant's overall aim in the Metaphysical Foundations...is to explain how the application of pure mathematics to the empirical concepts of mathematical physics becomes possible” (88). Kant's goal is to explain, concept by concept, how the fundamental concepts of Newtonian physics—for example, duration, mass, velocity, and force—come to be measurable magnitudes. And Kant needs to give this foundation for Newton's physics without relying either on the mechanism of Descartes and his followers or on Newton's absolute space and time. Second, Friedman argues that “the general dynamical theory of matter on which Kant builds a foundation for Newton's argument is by no means intended to turn clearly empirical properties of the force of universal gravitation into a priori demonstrative truths” (531). Kant argues in the Metaphysical Foundations that we can know a priori that every piece of matter exerts an immediate attractive force acting at a distance on every other piece of matter. Kant also argues that we can know a priori his three mechanical laws: the law of conservation of mass as well as Newton's first and third laws (the principles of inertia and of the equality of action and reaction). But in what sense are these truths a priori? Friedman's interpretation attempts a subtle balancing act: he wants on the one hand to respect the unique place that these physical laws have for Kant, which separates them from ordinary physical laws, while on the other hand to highlight Kant's detailed reconstruction of the experimental results that underlie Newton's physics.These two themes are on display clearly in Friedman's interpretation of one of the most well-known passages in Kant's book. At Ak 4:470, Kant claims that a proper natural science requires the application of mathematics.1I assert, however, that in any special doctrine of nature there can be only as much proper science as there is mathematics therein. For, according to the preceding, proper science, and above all proper natural science, requires a pure part lying at the basis of the empirical part, and resting on a priori cognition of natural things. Now to cognize something a priori means to cognize it from its mere possibility. But the possibility of determinate natural things cannot be cognized from their mere concepts; for from these the possibility of the thought (that it does not contradict itself) can certainly be cognized, but not the possibility of the object, as a natural thing that can be given outside thought (as existing). Hence, in order to cognize the possibility of determinate natural things, and thus to cognize them a priori, it is still required that the intuition corresponding to the concept be given a priori, that is, that the concept be constructed. Now rational cognition through construction of concepts is mathematical. Hence, although pure philosophy of nature in general, that is, that which investigates only what constitutes the concept of a nature in general, may indeed be possible even without mathematics, a pure doctrine of nature concerning determinate natural things (doctrine of body or doctrine of soul) is only possible by means of mathematics. And, since in any doctrine of nature there is only as much proper science as there is a priori knowledge therein, a doctrine of nature will contain only as much proper science as there is mathematics capable of application there.Kant's argument here depends on his conception of a proper science. A proper science is “that whose certainty is apodictic,” whose “grounds or principles...carry with them a consciousness of their necessity” (Ak 4:468). Such a science would thus “treat its object wholly according to a priori principles,” since only a priori principles can be apodictically certain.Given this notion of proper science, the outline of Kant's argument seems to be the following:A proper natural science is apodictically certain.So, its laws must be a priori and necessary.But to cognize something a priori = to cognize it from its mere possibility.For a determinate natural thing, to cognize it from its mere possibility requires that an intuition corresponding to the concept be given a priori.But to construct a concept = to give a priori an intuition corresponding to the concept.And mathematical cognition = knowledge from the construction of concepts.So, a natural science will be a proper science only inasmuch as mathematics is applied in it.On this reading, which Friedman admits is a “natural” reading (28), the application of mathematics that enables physics to be a proper science is just the “construction” (Konstruktion) of the concepts of physics.2 The propositions of the proper part of physics (such as Newton's first and third laws) are a priori, apodictically certain, and necessary because they can be proved by constructing the concepts of physics (along with further premises from general metaphysics, and analytic judgments)—and construction is the a priori presentation of an intuition corresponding to a concept. Moreover, other natural sciences fail to be proper because—as Kant says about chemistry—they contain “no concept to be discovered that can be constructed,” and so their principles “are not receptive to the application of mathematics” in the sense that matters to Kant (4:470).Friedman rejects this natural reading because he denies that the concepts of physics can be constructed in Kant's technical sense. He argues that if the fundamental concepts of physics (such as matter) were constructible, then we could know a priori that they are really possible. But, he argues—appealing to the General Remark to the Dynamics (4:525),3 and the claim from the first Critique that “existence cannot be constructed” (A179/B221)—that Kant denies that we could know a priori that the dynamical concept of matter is really possible (sec. 19).Having rejected this natural reading, Friedman needs an alternative reading of Ak 4:470—a reading that will interpret (i) what it means to apply mathematics in the right way, (ii) in what sense the laws of pure physics are a priori, and (iii) why a natural science has a priori laws just in case it applies mathematics in the right way. Friedman summarizes his alternative interpretation in the following way: “I argued that Kant does not mean that the empirical concept of matter is itself supposed to be mathematically constructed in pure intuition....Hence a special metaphysics of any more determinate species of objects in nature must explain the possibility of applying mathematics to the specific empirical concepts involved in a proper natural science restricted to this domain. It must explain how these particular concepts acquire their precise mathematical structure” (567, cf. 28–33). On this reading, the “application of mathematics” that characterizes the proper science of physics is weaker than construction. Though the fundamental concepts of physics, such as matter, cannot be constructed, it is still the case that for these concepts there is a “universally applicable measure” of the magnitude of these concepts—a “general method for estimating” their quantity (569, 331).4 Instead of deploying the constructions of these fundamental physical concepts in order to prove synthetic a priori truths, the special metaphysics of nature explains step-by-step how it is possible that these concepts come to have universally applicable methods of measurement.Why would an explanation of the possibility of universally applicable methods of measurement require a priori laws? In a passage a few pages after the last quoted passage, Friedman writes:[The three laws of mechanics] allow us to extend the static measure of weight to a universal measure of quantity of matter valid for all bodies in general on the basis of the new (Newtonian) mechanical quantity of mass. We presuppose the universal applicability of the mechanical laws of motion, the equality of inertial and gravitational mass, and the universally penetrating character of gravitational force in this procedure. And it is for precisely this reason that Kant builds all three into the characteristically dynamical concept of matter that he articulates in the Metaphysical Foundations.It is for this reason, too, that the mechanical laws of motion and the above properties of gravitational force (the fundamental force of attraction) count as a priori for Kant. (569)The claim here is that certain laws of physics have to be true in order for there to be a universal measurement technique for quantity of matter, or mass, and so these laws could not be empirical since any experimental confirmation of them would require measuring mass, and so would just presuppose them after all. A more evocative way of putting the point is to claim, as Friedman does at several places in his book, that the a priori laws of pure physics are in fact “implicit definitions”: “The upshot, from a modern point of view, is that Kant takes the mechanical laws of motion (implicitly) to define a privileged frame of reference in which they are satisfied: they do not state mere empirical facts, as it were, about a notion of (true or absolute) motion that is already well defined independently of these laws. The mechanical laws of motion are thereby revealed to be (synthetic) a priori principles governing the (true or actual) motion of matter” (21).5To return to the interpretive questions from two paragraphs back, Friedman seems to be arguing in the following way: (i) to apply mathematics in the right way is to have a universal measurement procedure for a concept; (ii) the laws of pure physics are a priori because they are presuppositions of (or “implicitly define”) a universal measurement procedure of a fundamental physical concept; and (iii) a natural science has a priori laws just in case it applies mathematics in the right way because application has presuppositions, and those presuppositions will necessarily be a priori. This reading would partially assimilate the project of the Metaphysical Foundations to the early logical empiricist program—first expressed explicitly in Reichenbach's (1965 [1920])The Theory of Relativity and A Priori Knowledge—of identifying the constitutive principles that make possible the coordination of pure mathematics to physical objects. Reichenbach there argued that there is within Kant's writings a notion of the a priori as “constitutive of the object of experience,”6 and a corresponding project of isolating these constitutive principles through a logical analysis of our current best physical theories. This conception of the philosophy of science and its constitutive principles was highly influential, both with later logical empiricists (who came to prefer the term “implicit definition”) and with Friedman himself in Friedman 2001.I'll be arguing momentarily that despite initial appearances, this Reichenbachian interpretation cannot be Friedman's final, considered reading of Kant's text. But first let me illustrate this conception of the metaphysics of corporeal nature by looking at Friedman's extraordinarily rich, subtle, and illuminating description of how the concept quantity of matter acquires a mathematical structure. The two dynamical concepts of quantity of matter (the quantity of repulsive force exerted and the quantity of attractive force exerted) are combined with the mechanical concept (inertial mass, which is manifested in the quantity of motion communicated by impact) step-by-step into a univocal concept of mass that can be measured using methods applicable to all matter, no matter what their specific variety is, whether they are moving or at rest, or whether they are celestial or terrestrial. The table gives a partial representation of these conceptual connections. For instance, using observations of celestial motions as a test for the gravitational mass of these heavenly bodies presupposes the truth of Newton's law of universal gravitation and his third law. Only on the basis of Newton's moon test and Kepler's observations of planetary orbits can we conclude that these observations of celestial motions are measuring the same thing—gravitational mass—as our observations of terrestrial bodies using a balance. That inertial mass is equivalent to this notion of gravitational mass is secured only through Galileo's law of free fall. And so on.Kant's explanation of the possibility of the universally measurable concept mass then proceeds in stages, explaining how each individual concept can be measured and how each concept is connected to the others. The explanation at any given stage makes use of the results of prior stages, along with the results of general metaphysics (provided in the first Critique), and—importantly—the empirical facts (underlined in my table) that a Newtonian scientist could fully justify using only the conceptual resources available at that stage. This step-by-step mathematization is the “construction” (in German, we'd say “aufbauen”) in Friedman's title.Friedman's account of the “mathematization” of the concept quantity of matter is simply incompatible with the Reichenbachian reading of the a priori that was sketched a few paragraphs back. Friedman identifies specific physical facts and natural laws—such as Galileo's law of free fall and Newton's moon test—that he claims Kant took both to be empirical and to play a role in “implicitly defining” the concept quantity of matter.7 For this reason, Kant as Friedman interprets him is not like later philosophers such as Poincaré (2001, sec. 5), who is perfectly willing to say that the inverse law of is not in fact empirical but an This is an of the large of Friedman's reading of the Metaphysical Foundations that I that Kant no means intended to turn clearly empirical properties of the force of universal gravitation into a priori demonstrative truths” (531). On the one Friedman wants to respect Kant's that a law such as the law of the conservation of mass is a synthetic a priori on the also that for Kant this law is only if there is a universal measurement procedure for mass, which itself depends on a of empirical facts and does Friedman's reading both these does he a priori from empirical physical laws while also that in sense these a priori laws have an empirical Friedman's most is to the a priori laws of physics as of the a priori principles of general intended to the way in which the Newtonian mathematization of the concepts of mass, and can be considered as a specific or of the of and in Kant's And it is for precisely this reason, for Kant, that his general dynamical theory then as as to (531). This of the a priori is not only clearly from the Reichenbachian of the a priori. It is I believe, Friedman's while the Reichenbachian the role of a or intended only to to Kant's project of identifying the of the universal measurement for Newton's fundamental is to what it means for the fundamental concepts of physics to be specific of the The Critique of gives us in the the law of general metaphysics that is in all The Metaphysical Foundations gives us the law of special metaphysics that the quantity of matter is in all in our only the concept matter the a priori concept even the concept matter is this way of the specific of a priori concepts does not the in what sense are the a priori laws of physics (or as Friedman of laws of general metaphysics other laws of special metaphysics are It is certainly not that a physical law contain a concept such as matter that a general the inverse law of does despite are synthetic a priori propositions of special metaphysics (such as the claim that every piece of matter exerts an attractive force acting at a distance on every other piece of matter) that are not in any or sense of the laws of general metaphysics that Kant identifies in the first the in a more way. The Metaphysical Foundations is in the each paragraph is as an or and each is given an that to paragraphs and other facts that Kant takes to be In the natural reading of Ak sketched the laws for pure physics are a priori precisely because the of available premises only laws of general metaphysics and propositions of pure mathematics. of the laws of general metaphysics, Friedman clearly the a priori laws of physics to for their at on facts of general metaphysics and mathematics. But can the of these specific also to empirical are places Friedman For instance, in the that Ak Friedman is for this reason, too, that the mechanical laws of motion and the above properties of gravitational force (the fundamental force of attraction) count as a priori for Kant. This does not however, that he attempts to by pure reason, independently of what has discovered by and explicitly in that this analysis is, in an in so as there is an alternative mechanical concept in with the of absolute (as to And his of this concept the alternative concept in the on more than the empirical of Newton's theory in with the mechanical like this that the propositions of the metaphysics of as Kant's three mechanical and are only on the basis of premises from and despite a priori. For my this is a of the a after Kant clearly that and from are two of a priori truths there is a interpretation of the a priori that Friedman could be at in passages like this interpretation that not clearly and fully in Friedman's book, the of the interpretive he wants without to an of the a priori. Friedman claims that empirical facts Kant's of one concept of matter On Kant's concept of matter, matter has two a repulsive force that on and an attractive force that at a On the concept, properties are it space through its mere and it at a Kant's for the dynamical concept of matter is in the of the Metaphysical Foundations. For instance, in of the Kant that “the quantity of matter is the of the in a determinate (Ak On Friedman's view, that this concept is well defined as on a of empirical For this reason, Friedman claims that Kepler's laws of planetary orbits are in Kant's empirical of matter the empirical fact that gravitational and inertial mass are equivalent is the dynamical concept of matter me a about how such an interpretation would On this it is Kant's that are and in a of empirical This claim be since as the within metaphysics and empirical science to are analytic truths and would to be necessary and a priori. Kant argues that of empirical concepts such as matter from mathematical in two First, while a mathematical is a and so itself the of the an of an empirical concept is and so it to to the of the Second, while a of a mathematical concept (as a is certain and not be the of mathematics, an of an empirical concept (as a is and will to be as empirical science Kant argues that this is by and will be the empirical science is itself of empirical well with what Friedman says about the fundamental concepts of of matter is in our and thus has only if the for specific of matter in turn to be and this depends on all of empirical facts only through for Friedman's Kant, we come to prefer one of of dynamical only after a of physical Newton's to physics is by its empirical way of Friedman's specific of the a priori provides a new way of Ak that is both from the natural reading that Friedman rejects and the Reichenbachian reading that is by of Friedman's interpretation of Ak 4:470, I must three (i) what it means to apply mathematics in the right way, (ii) in what sense the laws of pure physics are a priori, and (iii) why a natural science has a priori laws just in case it applies mathematics in the right way. On this new as in the Reichenbachian reading, to apply mathematics in the right way is to have a universal measurement procedure for a concept. But a law of pure physics is a priori because it is a specific of general laws, this means that the physical law is from mathematical facts, laws of general metaphysics, and that are and in empirical This reading the balancing Friedman physical laws such as Kant's three mechanical laws are privileged because they from general laws, and mathematical facts, while empirical laws such as the inverse law of universal gravitation require as premises empirical And Kant still the detailed empirical basis for these pure laws by the and empirical basis of empirical is more philosophical required to make and determinate sense of this conception of empirical and there is more detailed interpretive to that the and of Kant's for physics can be within the But I do this is has a basis in Kant's and is at in many passages in Kant's Construction of I that Friedman is still with no to (iii) and so no reading of the argument from Ak that a natural science has a priori laws just in case it applies mathematics in the right way. Friedman Ak as arguing that there needs to be an explanation for how the empirical concepts of physics come to have universal measurement and that this explanation will necessarily require special a priori if we prefer the specific of the a priori (as to the Reichenbachian then there is no reason why this explanation would require a priori principles as to just empirical I that here Friedman's use of the of “implicit is more than it to Friedman interprets “application of mathematics” in a way, so that to apply mathematics in the right way is to have a universal measurement procedure whose are specific of general This interpretation would certainly the reason, since a science that has an empirical concept the measurement of which requires a explanation will necessarily have a priori principles and so will be a proper science. But a new up in the would a natural science with special a priori principles necessarily have an empirical concept the measurement of which requires a a proper science just have concepts whose measurement presupposes only empirical facts, or not even have any measurable concepts at For these my is to read Ak in the natural way, the “application of mathematics” in the proper science of physics as of as the “existence of a universal measurement procedure whose are specific of general But the has and the philosophical Friedman its for us a book of such and philosophical special to who not only let me his but also the of this with me and me to the passage from I also to Michael Friedman for discussing these with for his reading, and for for this I to the and of the of the Kant at in these were first

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