Kant on Reality, Cause, and Force: From the Early Modern Tradition to the Critical Philosophy 9781108430777, 9781108355049, 9781108420693

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KANT ON REALITY, CAUSE, AND FORCE FROM T HE EARLY MODERN TRADITION TO THE CRITICAL PHILOSOPHY TAL GU~ ZER

KANT ON REALITY, CAUSE, AND FORCE From the Early Modern Tradition to the Critical Philosophy

TAL GLEZER Max PlAnck Imtituu for the History ofScience. Berlin

DCAMBRIDGE

V

UNIVERSITY PRESS

KANT ON REALITY, CAUSE, AND FORCE

Kant's category of reality is an often-overlooked element of his Critique ofPure Reason. Tal Glezer shows that it nevertheless belongs at the core of Kant's mature Critical philosophy: it captures an issue that motivated his Critical turn, shaped his theory of causation, and defined the role of his philosophy of science. Glezer's study traces the roots of Kant's category of reality to Early Modern debates over the intelligibility of substantial forms, fueled by the tension between the idea of nonextended substances and that of extended objects. This tension influenced Kant's pre-Critical work, and eventually inspired his radical break toward transcendental idealism. Glezer explores the importance of reality for Kant's conceptions of cause and force, and sheds new light on his philosophy of physical science, including gravity. His book will interest scholars of Kant and of Early Modern philosophy, as well as historians of scientific ideas. is a researcher at the Max Planck Institute for the History of Science in Berlin.

TAL GLEZER

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Library of Congress Cataloging in Publication data Names: Glezer. Tal. author. Title: Kant on realilY. cause. and force: ftom the early modern tradition 10 the critical philosophy 1Tal Glezer. Description: New York: Cambridge UniverSity Press. l018.1 Includes bibliographical references and index. Identifiers: tCCN lOl704497 6 1 ISBN 9781108420693 (hardback) 1 ISBN 978 I 108430777 (paperback) Subjects: LCSH: Kant. Immanuel. 1724-18°4. 1Reality. 1 Causation. 1 Kant. Immanuel, 1724-18°4. Kritik der reinen Vernunft. Classification: LCC B2798.G58 20171 DOC 193-dc23 LC record available at https:/Ilccn.loc.govlzoI7044976 ISBN 978-1-108-42069-3 Hardback [SBN 978-1-108-43°77-7 Paperback Cambridge University Press has no responsibility for che persistence or accuracy of URLs for external or third-party internet websites referred to in this publication. and does not guarantee chat any content on such websites is. or will remain. accurate or appropriare.

To my parents

Contents

Acknowledgments List ofAbbreviations

page xi xiii

Introduction: "What Corresponds PART I

to

Sensation"

SUBSTANTIAL FORMS AND REALITY

Reality and Substantial Forms in Descanes and Suarez 1.1

1.2 1.3

2

Vis Viva and the Essence of Matter 2.1 2.2

2.3 2.4

2.5 2.6

3

Vis Viva and Quantity of Marion Vis Viva and "Quantity of Progress" Vis Viva and Potential Energy

Parential Energy and Substantial Forms Living and Dead Forces, Primitive and Derivative Forces in Leibniz's Specimen Dynamicum The Principle of Sufficient Reason and the Intelligibility of Substantial Forms

Leibniz on the Law of Continuity J.I 3.2

3.J

PART II

4

Reality Containment and Substantial Forms in Descartes and Suarez Causation and Substantial Forms in Descartes and Suarez Descartes on the Intelligibility of Substantial Forms

Leibniz on the Law of Continuity in Mathematics Leibniz on the Law of Continuity in Physics Leibni:z.'s Law of Continuity and Genus-Species Subordination

THE MAGNITUDE OF REALITY

Reality and Magnitude in Kant's Negative Magnitudes 4.1

4.2

The Validity of Mathemarical Concepts in Philosophy Negarive Magnitudes and Real Opposition

vii

17 19 22 26

32 33 35 38 40 42

viii

Contents 4.3 4.4

Kant's Main Argument in Negative Magnitudes Ground and Consequence, and the Law of Continuity in Negative Magnitudes

5 The Category of Reality and the Law of Continuity p 5.1 5.3 5.4

6

Objectivity and the Quantification of Reality 6.1 6.1 6.3

7

7.1 7-3 7.4

PART III

77 78 80

84 88 93 94 97 100 10 7 108 III

lIS II9

'1 ill' Continuiry of Alteration in the MFNS

127 128 133

"An Unbounded Diversity of Empirical Laws" 'I he Applicability of Transcendental Principles in Experience

138 139 142 148

Reality and the System of All Possible Empirical Concepts

IS4

on the proposition that nothing happens in the world through a leap , and it has not yet been in the proper light even for Maupertuis. There is a logical, mathematical, physical law. a. Logiea/law. Whatever applies in general to a cenain magnitude that can become smaller, this also applies to it if it is vanishingly small. - All free actions are imputable - consequently the smallest degree of this, the natural actions, are also imputable. b. Mathematical law, if a body is brought from rest into motion, then it goes through all of the smallest degrees of speed up to the highest degree of speed with which it has power, and if it is again brought to rest: then this happens through smaller degrees of speed. A light ray that reRects back from a mirror, reflects not all at once, but rather through the smallest degrees of deviation. c. Physieallaw: the imperfect raises itself to the more perfect through the smallest degrees of perfection. E.g., the lifeless - plants, living plants, polyps, oysters, animals, until human beings. Maupertuis opines that a general Rood tore many steps from this ladder, which the bones of unknown animals in excavations indicate, and thereby disturbed the connection for liS. (28:41-2)'

This classification remains more or less intact in Kant's writings over the decades, and it is also found in some relatively late series of his lectures on metaphysics. 2 Typically, as in the preceding passage, Kant distinguishes among (a) a "logical" law of continuity, expressing the idea that the same , Kant. Lectum 011 Mttaphysics. p. 5. For instance, the lectures recorded by H. L. A. Dohna in 1792-3, in particular Metaphysik Dohna §40:

!

(The dynamic law of continuous motion ics, p. 363) Cf. Section 3.1. Cf. Sections 3.2 and 3.3.

80

The Magnitude of Reality

5.2. Laws of Continuity in Kant's Inaugural Dissertation In the preface to Negative Magnitudes, as we have seen, Kant briefly argues for admitting the concepts of infinite divisibility and the infinitesimal into metaphysics: roughly, Kant assumes that since these concepts can be validly applied to describe the structure of time itself, they can also be applied to describe the structure of a reality - a force - acting within time. A similar presupposition is made by the more detailed argument for the metaphysical validity of negative magnitudes in section III of Negative Magnitudes, where the continuity of time is taken to imply that a change in objects cannot occur, as it were, in a gap between moments in time; rather, there must be a moment of change, and so we must adopt the concepts necessary to represent it.S I have already observed that these arguments tacitly assume something like Leibniz's law of continuity; here, I wish to add the observation that it is easy to recognize in these arguments an inkling of what, in the Inaugural Dissertation, becomes the proto-Critical doctrine that time is a form of sensibility that necessarily informs all objects of experience. These twO observations are closely connected, since Kant comes to enlist the very same proto-Critical doctrine he uses to defend the objective validity of temporal concepts also in defending the validity of the law of continuity. Kant himself draws this connection in the Inaugural Dissertation, where he says that "time is a continuous quantity and is the principle of the laws of continuity in the alterations of the universe" (2:399).6 To see how exactly the connection is made, we now turn to consider two places where Kant takes upon himself to justify or prove Leibniz's law of continuity within the philosophical framework of the Inaugural Dissertation. The first place is in §14 thereof, and the second is in a lecture from Metaphysik LI delivered in the same period. In §I4, "On Time," Kant argues that time is a form of the faculty of sensibility, and that, as such, it is an a priori principle or condition for any object that can be sensed. Therefore, certain features of time must also ! 6

C( Section 4· 3. This is Beck's translation (lVznts Latin Writing!, p. 134). Beck's nanslation here is more plausible than G. B. Kerferd's translation included in the Cambridge Edition of the WlrkJ ofImmantt!llVznt, which is "time is a continuous magnitude, and it is the principle of the laws of what is continuous in the changes of the universe" (7heoretical Phi/oJophy I755-I770, p. 391). Perhaps the discrepancy berween the translations rests on an ambiguity in the Latin - "tempus est quantum continuum et legum continui in mutationibus universi principium" - wbere continui, I assume, is to be taken as the genitive of continuum (i.e. "of tbe continuum") raTher than as Tbe genitive of continu,,! (i.e. "of [somerhing] continuous").

The Category of Reality and the Law of Continuity

81

be features of sensible objects: such objects "necessarily accord with the axioms which can be known about time ... For it is only under these conditions that they can be objects of the senses and can be co-ordinated with each other" (2:402). On this basis, Kant argues that all change is incremental, a principle he calls "the metaphysical law of continuity": Now, the metaphysical law of continuity is as follows: All changes are continuous or flow: that is to say, opposed states only succeed one another through an intermediate series of different states. For two opposed states are in different moments of time. Bur hetween rwo moments there will always be an intervening time, and, in the infinite series of the moments of that time, the substance is not in one of the given states, nor in the other, and yet it is not in no state either. It will be in different states, and so on to infinity. (2:399-4 00)

It may not be immediately clear how exactly this argument is supposed to work: Kant begins with the claim that, once time is recognized as a form of sensibility, the continuity of time implies that between any two opposed states of an object there is a third state of that object that is later than the one and earlier than the other, but then he seems to slide from the claim that there is a state that is temporally intermediate to the claim that this state is also qualitatively distinct, and concludes that between any two opposed states of an object there is a third, qualitatively intermediate state. This move may seem unwarranted, bur support for it can be found if we take Kant to assume that the continuity of time also implies that between any two qualitatively opposed states there must be a moment at which the change from one state to the other occurs. Then, at the very moment of change, the state of the object must differ from both opposed states on pain of contradiction. This reading is borne out by Kant's subsequent defense of the "metaphysical law of continuity" against a challenge posed by the mathematician Abraham G. Kastner: 7 Kastner notes that Leibniz's law of continuity would preclude the motion of a point along the sides of a triangle abc at a uniform speed, since such motion would involve an instantaneous change in the point's velocity as it turns a corner. Kastner then challenges the supporters of the law of continuity to produce an argument to show that such a motion is indeed impossible, and does not constitute a counterexample to the law of continuity. Accepting the challenge, Kant maintains in the Inaugural Dissertation that the point's motion cannot be of uniform speed , A. G. Kastner, Allfollgsgriintk do hohanl Mechanik: Nach do antiken, rein geometrischm Method,' (17\8), pan III, §IHH.

The Magnitude of Reality throughout but must arrive at a state of rest when it reaches point b, since then it can neither be at the state of moving from a to b nor be at the state of moving from b to c: If something moveable passes in continuous motion [viz. uniform speed] along the lines ab, be, and ea, that is to say, along the whole perimeter of the figure, it necessarily follows that it moves through poine b in the direction ab and also through the same point b in the direction be. But since these movements are diverse they cannot exist simultaneously. Therefore, the moment of the presence of the moveable point at the vertex b, in so far as it is moving in the direction ab, is different from the moment of the presence of the moveable point at the same vertex b, in so far as it is moving in the direction be. But between the two moments there is a time. Therefore, the moveable point is present at the same point through some time, that is to say, it is at rest, and therefore it does not proceed in a continuous motion. (2:400 )8

The appeal to the problem of the moment of change highlights the similarity between the argument from section III of Negative Magnitudes mentioned earlier 9 and this argument from the Inaugural Dissertation. Although these arguments aim at different conclusions (as the former is supposed to show that every change results from real opposition, whereas the latter is supposed to show that every change is gradual), they both contain an analysis of the notion of change in general, imposing the requirement that opposed properties (determinations, or states) be represented in a manner that allows an intermediate property to mitigate the problem of the moment of change. Another example from the same period is the passage entitled "On the Leap and the Law of Continuity" in Metaphysik LI (28:200). This passage likewise relies on the status of time as an a priori form of sensibility in order to project its continuous structure onto sensible objects, claiming that since the mind can survey an object only one part at a time (a process Kant calls "expounding," exponieren), the object must be divisible into as many parts as the time it takes to be surveyed: , Compare the following passage from the comemporary Metaphysik L,: Kam argues that because time is continuous, and every two moments are separated by a third. "rhere is no srare immediately following another. For if a body transfers from one state into another, then there must be a moment in which it goes out of the preceding state, and a momem in which it comes inro the follOWing state. Between these twO moments is a time in which it is neither in the one nor in the other state, thus in an intermediate state, which is a ground why it transfers into the following state. [Therefore.] no body alters its direction immediately without an intermediate rest, e.g., in a triangle. A poim does not move immediately from one direction imo another without an intermediate rest" (28:203, Lectures on MetaphysiCS. p. 26). , In Section 4+

7he Category ofReality and the Law of Continuity This law of continuity is a proposition that Leibniz first set forth, but that until now only few have grasped. Thus in order to make it graspable, we want to consider it from another side, and then apply these cases to it. Every appearance is, as representation in the mind, under the form of inner sense, which is time. Every representation is so constituted that the mind goes through it in time; that is, the mind expounds the appearance; thus every appearance is expoundable ... All objects of the senses are expoundable in our power of representation; that is: we can determine our mind gradually in time; one also calls that the going through of appearance, where one goes successively from one part to the other. From this it follows that there is no appearance and no part of a given appearance that could not be divided to infinity. (28:202)10

Again, this passage seems to have a forerunner in Negative Magnitudes, as it is close to the argument for the infinite divisibility of phenomena and the validity of infinitesimals found in section I thereof,1I with the notable difference that here Kant makes use of his recently devised doctrine that time is the "form of inner sense" in order to justify his extrapolation from the constitution of representations "in the mind" to the constitution of phenomenal objects. Kant sums up this argument by saying that "the cause of the law of continuity is time" (28:201). Thus, the doctrine that space and time are forms of sensibility, and that therefore our objects must be thought of as phenomenal objects, is the doctrine Kant uses to justify the agreement between the form of our representations and the form of their objects. Specifically, this agreement consists in a correspondence of certain formal features, including the quality of continuity or infinite divisibility: as our representations are always divisible, so are their objects. Now, if we were to phrase Kant's doctrine of space and time as forms of sensibility in the Inaugural Dissertation in the terms Leibniz employs to formulate his law of continuity, we could plausibly refer to our representations as the "data" and to their objects as "that which is sought for" in this case. Then, at least for this particular groundconsequence relation, we may see how Kant's innovation in the Inaugural Dissertation could provide him with a new argument for the Leibnizian law of continuity." ,. Cf.: "Thus what is in space and in rime is infinitely divisible; no pan is the smallest. neithet in space nor in rime. The law of continuiry thus rests on the continuiry of space and of time .... All experiences happen through the senses; thus. we can srill anticipate appearances through the understanding. and comprehend a priori the conditions of objects" (18:205). " Cf. Section 4.1. " This reading takes the Immgural Dissertation to advocate a kind of phenomenalism. since. although Kant takes our immediate objects to be appearances of independent things rather

The Magnitude of Reality This helps us alleviate the concern raised previously, namely, that in our brief overview of his references to the law of continuity in the pre-Critical period Kant seems to describe the law of continuity exclusively in terms of the no-leaps formulation, even though he implicitly relies on the law's pertinence (Q the ground-consequence relation in order to get around the paradox of the moment of change. And although Kant eventually abandons some of the most central doctrines of the Inaugural Dissertation, the association of the law of continuity with the ground-consequence relation persists in Kant's thought in subsequent stages of his development, as the pure concept representing this grounding relation - the category of realitybecomes the context of Kant's most sustained treatment of the law of continuity in the CPR.

S.3 The Law of Continuity's Place in the Table of Categories In some sense, something like the law of continuity as Kant comes to understand it in the Inaugural Dissertation should be equally relevant to all forms of objective judgment represented in the CP/(s table of categories. On this understanding, the law of continuity follows from the insight that the forms of sensibility govern all of our experience; in some sense, therefore, since in the CPR the forms of sensibility constrain the way all the categories are applied, each schematized category should have a version of the law of continuity as a corollary. In other words, Kant shows for each category how its application in a judgment can be described in spatio-temporal terms (thus proving that the category can be applied to constitute spatio-temporal objects), and thereby he also shows that the quality of continuity applies to any objective aspect expressed by a category. Quantities, qualities, relations, and modalities should all be continuous in one way or another. And indeed we find clear textual evidence of this, e.g. in the following Reflexion (dating from 1794 to 1795) that appears to be Kant's attempt to cast

than ideas (" Phaenomena proprie sint rerum species. non Ideae" (§II. 2:397), in the arguments we have examined Kant analyzes the structure of our representations within in order [0 infer the structure of objects without, as if we are only directly aware of our representations. and only derivatively of their objects. In later stages of his thought, Kant comes to view this epistemological picture as susceptible [0 skepticism. We return to comment further on the picture of the Inaugllral Dissertation in which these Kantian arguments for the law of continuity are couched. and the way it differs from the subsequent picture of the CPR. in Sections 5.4 and 6.1.

The Category ofReality and the Law of Continuity his own earlier classifications oflaws of continuity (which we examined in Section 5.1) into an "architectonic" structure, by formulating a law of continuity for each of the four headings of the table of categories: On the possibility of things in accordance with all of the preceding categories, insofar as the concepts of them are to have objective reality ... r) The geometrical law of continuity: space and time, therefore spatial and temporal quantities arc continuous, i.e., each of their parts in a homogeneous whole is itself a quantity. Any part of them is a sum ofhomogeneous parts: discrete quantities in them are contradictory, except in the sense that any space is a sum of homogeneous parts. E.g., a vessel full of fruit is not a quantity of fruit, except in abstraction from the intervals between the materials of the fruit which fill the space. - A discrete quantity is a multitude. 2) The dynamical law of continuity. The momentum of accelerative forces is a continuous quantity; e.g., it is always possible to assign a smaller one which will not be uniform with the given acceleration. 3) The mechanical law of continuity: No change in the state of rest or motion of a body or in its speed or direction is possible except in an interval of time, through infinitely smaller differences from the initial state, which gradually lead to the latter, e.g., in any change no degree is the smallest, there is always another which precedes or succeeds it. 4) The cosmological law of continuity. The continuum of forms. There are no diverse species in nature between which there are not some intermediate species. - Mistake. 1his is true of possibilities, not actualities. (Refl. 6338a, 18:664-5, Kant, Notes and Fragments, p. 381)

However, Kant does not emphasize these correspondences in the CPR. Although he endorses each of these four laws of continuity, and even acknowledges some correspondence between them and the four headings of the table of categories, such a list is not made there explicitly, and can only be roughly reconstructed from scattered remarks. Instead, significantly, Kant chooses to associate continuity and the laws of continuity with one heading in particular: he places the CPR's most sustained and general discussion of this topic in the Anticipations of Perception, which is part of his treatment of the heading of quality, and especially the category of reality. Thus, it is only within the Anticipations that we can glean a partial parallel to the Ref/exion just quoted, in the following paragraph, where the "geometrical," "dynamical," and "mechanical" laws of continuity are all mentioned, each with a hint to its corresponding category:

86

The Magnitude of Reality All appearances whatsoever are accordingly continuous magnitudes, either in their intuition, as extensive magnitudes, or in their mere perception (sensation and thus reality), as intensive ones ... the proposition that all alteration (transition of a thing from one state into another) is also continuous could be proved here easily and with mathematical self-evidence. (AI7o/B212)IJ

These several aspects of the continuity of appearances - viz_ "in their intuition, as extensive magnitudes"; in "their mere .. _ sensation and thus reality"; and in their "alteration (transition of a thing from one state into another)" - naturally fit into the architectonic scheme of the categories, progressing from quantity, through quality (specifically, reality), to relation (specifically, causation). By placing his most general discussion of the law of continuity in the Anticipations, then, Kant ties it especially with the category of reality and its corollaries. This special tie is also evident, for example, in Mttaphysik Mrongovius (1782-3), where the law of continuity is counted as one of four "negative principles," and is again tied specifically with the categories of quality: These negative principles are four, according to the number of the four types of categories: (I) concerns quality ... ; There is no leap in the world ... This proposition could also be expressed so: everything is connected according (0 the law of continuity . (Metaphysik Mrongovius 29:862-3)" Later in the same lecture, Kant derives several more specific laws of continuity from the general law of continuity, in the familiar fourfold pattern, but still includes all of them in his extended account of the principle "there is no leap in the world," thereby effectively associating them with the general heading of the categories of quality: Space and time are continuous quanta , the real in these is also a quantum ... Every alteration has its degree as well. No body can

ShorrIy following rhis passage, Kant adds a curious reservation to his apparent endorsemenr of the law of the continuity of alteration. We pass over this complication here, but discuss it at some length in Chapter S. •• Kant. Lectures on MetaphysiCS. p. lIS. For a parallel text cf. A12S-9/Bl8C>-2: "We could easily represent the order of these four propositions (in mundo non datllr hiatus, non datur saltus, non datur casus. non datur fotum) in accordance with the order of the categories. just like all principles of transcendental origin. and show each its position. but the already practiced reader will do this for himself or easily discover the clue to it" (A1l9/Bl82). The second irem in the list. which accords with the categories of quality. is. of course, the law of continuity: "non datur saitu,.'· 'J

lhe Category ofReality and the Law of Continuity transfer from one state into another without passing through all the intermediate states, or intermediate degrees ...

This law of nature can also be applied to the kinds and species of things ... : no kind or species is so closely relared to another that another intermediate kind or intermediate species might not be able to occur between them ... [This law] is called the cosmological. (29:921)

If we take Kant's organization of this material to have some architectonic significance - as I believe we should - then his choices in the CPR suggest that, while each category has its own law of continuity attached, the general idea of a law of continuity is somehow especially associated with the category of reality. It may not be entirely transparent why the notion of a law of continuity in general should be especially associated with reality and the categories of quality. This is all the more puzzling since, arguably, a more natural choice for Kant would have been to associate it with the categories of quantity: Kant often refers to the categories of quantity as the categories of magnitude,'1 and continuity is the single distinctive feature of magnitudes as such.'6 But the reason for this association becomes easier to see once we recognize the primary role of the category of reality in Kant's system. As we shall see in greater detail in Section 5-4, the concept of reality is primarily the concept of the grounds of our perception of appearances what corresponds to sensation in the object, as Kant puts it. Thus, while the continuity of all appearances as magnitudes is indeed implied by the validity of the categories of quantity, we should recall that the law of continuity rather expresses a further claim, viz. that the continuity of the consequences indicates the continuity of the grounds; therefore, it claims specifically that reality, as the grounds of our sensation of appearances, has the same continuous structure as that to which it gives rise. But the import of the law of continuity according to Kant is precisely in drawing a formal correspondence between empirical experience as a consequence and reality

'I

,6

For example, in the Metaphysik Mrongovius, 29:922 (Kant, Lectures on MetaphysiCS, p. 221), and throughout. See also e.g. BIll, AI41/B181, AI61/B10I; B20), etc. The notion of "magnitude" and the notion of "quantiry" are not quite interchangeable, although Kant might be using the term Grose to denote both. Cf. editors' note c in CPR p. 286. "we can cognize Q priori of all magnitUdes in general only a single '1uaUty, namely continuiry" (AI76/BlI8).

88

The Magnitude of Reality

as its ground. Thus, the association of the law of continuity with the category of reality becomes clearer. In proposing this reading of the CPR, I have in mind the interpretation I offer of Kant's treatment of the law of continuity in the Inaugural Dissertation, according to which the law of continuity pertains primarily to the relation of sensations and their grounds. But there is something potentially misleading about this proposal, to the extent that it threatens to import toO much of the metaphysical picture of the Inaugural Dissertation into the CPR. In Section 5.4, I argue that the manner in which Kant sees the validity of the law of continuity in connection with the category of reality not only differs from the view of the Inaugural Dissertation, but is indeed the crux of the difference between the proto-Critical framework of the Inaugural Dissertation and the Critical framework of the CPR.

5.4 The Ground of Sensation in the Inaugural Diuertation and in the CPR In the Inaugural Dissertation, Kant sets out to develop a conception of the object of experience as a phenomenal object that cannot be reduced to a mere idea, even though it depends on our own faculties of cognition for its fundamental properties. To achieve this, Kant envisages a faculty of sensibility that can be affected or impinged upon by independent things to generate representations, and that, at the same time, imposes on these objective representations its own characteristic form, namely, the form of a spatio-temporal order. This way of generating objects of experience, or phenomena, is supposed to allow Kant to maintain that our objects exist independently of us, while guaranteeing that the sensible attributes we ascribe to them are valid. Kant makes this point most clearly in §II: In so far as [phenomena] are sensory concepts or apprehensions, they are, as things caused, witnesses to the presence of an object [ceu causata testantur de praesentia obiecti], and this is opposed to idealism. Consider, however, judgements about things which are sensitively cognised. Truth in judging consists in the agreement of a predicate with a given subject. But the concept of a subject, in so far as it is a phenomenon, would only be given through its relation to the sensitive faculty of cognising, and it is in accordance with the same relation that predicates would be given which were sensitively observable. It is, accordingly, clear that representations of a subject and a predicate arise according to common laws; and they thus furnish a foothold for cognition which is in the highest degree true.

The Category of Reality and the Law of Continuity

89

Close to the surface of this passage we can discern further conditions that make Kant's view "opposed to idealism": the "presence of an object" is called for, since phenomena must be "things caused" by something other than phenomena. To accommodate these conditions of "presence" (i.e. existence) and causal efficacy, Kant stipulates a faculty of understanding (or "intelligence," intelligentia) alongside the faculty of sensibility. The understanding ascribes to the very same things that affect sensibility a variety of nonsensible properties and relations, which includes "possibility, existence, necessity, substance, cause etc.• together with their opposites or correlates" (2:395). Crucially, Kant takes these nonsensible characteristics to apply to objects not as they appear but as they are in themselves.'? It is not entirely clear how the pertinence of such properties to things in themselves is supposed to be established - and indeed Kant soon concludes that the Inaugural Dissertation in fact fails to establish it - but it is clear that the need to distance himself from idealism is paramount among Kant's motivations for insisting that the concepts of the understanding do pertain to things in themselves. It is clear because one of these nonsensible concepts in particular, namely, the relation of ajfectingor causing that holds between objects and sensibility, is the very relation that is supposed to make phenomenal objects real rather than ideal; this arises naturally from such comments as "phenomena ... arl" as things caused, witnesses to the presence of an object, and this is opposed to idealism" (2:397. my emphasis), once we note that "cause" and "presence" (or "existence") are concepts of the understanding. The picture becomes considerably more complicated as the metaphysical framework shifts from that of the Inaugural Dissertation to that of the CPR. While in the Inaugural Dissertation a certain concept of affecting, causing, or grounding is regarded as valid independently of the forms of sensibility, and thus intelligible and applicable to things in themselves, in the CPR the affecting of sensibility can no longer be construed in those terms. This shift in Kant's views is famously documented in a letter to Marcus Hen on February 2I, 1772,,8 where Kant worries that, since the concepts of the understanding neither are caused by objects (as the understanding is an active rather than a passive faculty) nor are the cause of " "Intelligence (rationality) is the faculty of a subject in virtue of which it has rhe power

to represenr dungs which cannot by their OWn quality come before the senses of that subject ... that which contains nothing but what is to be cognised through the inrelligence is inrelligible. In the schools of the ancients •... the larcer [is called] a noumenon. '" things which are inrellectual are represenrations of things as thry are" (2:392). " Kant, Cormpondmce, pp. 132-7.

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objects (on pain of surrendering to idealism), the Inaugural Dissertation fails to demonstrate their applicability to objects at all (10:130). The primary role of the concept of causation or affection in the Inaugural Dissertation's notion of objectivity entails its primacy for the skeptical challenge Kant poses to himself in the letter to Herz. Thus, although the letter identifies the failure of the Inaugural Dissertation as the failure to justify the validity of the pure concepts of the understanding in general, the fundamental, crucial problem is specifically with the concept of affection, as the cause of phenomena "in so far as they are sensory concepts or apprehensions." This is because it is this concept in particular whose invalidity pulls out the foundation from under Kant's distinction between phenomenal objects and mere ideas, and makes it impossible to justify the objectivity of sensible representations. This is why the failure of the Inaugural Dissertation cannot be remedied simply by reassigning the concepts of the understanding from being a priori features of things in themselves to being a priori features of our cognitive powers, similarly to space and time. Merely extending the list of elements that make up the form of experience so as to include conceptual conditions alongside the sensible ones would not do, because the new problem that Kant discovered is not that of complementing the sensible structure of our cognitive powers with a representation of its conceptual structure, but rather that of representing the very receptivity of sensibility on which his conception of objectivity relies.'9 " This reading bears on the issue of locating the crucial influence of Hume on Kant'S development. namely, the influence that Kant famously describes as resulting in his awakening from a "dogmatic slumber" in Prolegomena (4:260). Leaving aside the question of identifying the relevant source of Kant's acquaintance with Hume (i.e. whether it was the passages from Hume's Treatiu of Human Nature included in the 1772 translation of Beattie's Essay on the Nature and Immutability of the Truth, or the [760'S translation of Hume's Enquiry Concerning Human Understanding), the crucial Humean inlluence seems [0 me to be neither the notion that there is a distinction between logical and real grounds, which Kant already makes in Negative Magnitudes (2:202), nor the notion that pure concepts of the understanding require a demonstration of their objective validity, as Kant came to reali2e by the time he wrote the letter to Hen. The first option is ruled out (pau De Pierris and Friedman, "Kant and Hume on Causality") since Kant makes this very distinction between logical and real grounds already years prior to the Inaugural Dissertatitm, whereas his so-called awakening rook place only after the Inaugural Dissertation. This dating of Kant's awakening is based on the fact that he describes the dogmatic oudook from which he awoke in a way that is plainly apt for the views he still maintained in 1770: "everyone [including Kant himself) confidently made use of Ihese concepls [i.e. concepts such as causation] without asking what their objective validity is based on" (4:260). Thus, although Kant'S distinction between logical and real grounds might very well have been influenced by Hume, it cannot be rhe crucial inRuence Ihat brought about his awakening. The second option (proposed, e.g. by Beck, "A Prussian Hume and a Scoltish Kant," elc.) is much

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While the Inaugural Dissertation's version of the view that our sensibility is affected by things in themselves is untenable in the CPR, it is not entirely abandoned, but rather transformed in ways that are investigated in the following chapters. The direct descendant of this early concept in the CPR is the category of reality. Reality, as I suggest in Section 5.3, represents the notion that sensibility is affected by something entirely independent of our cognition and its forms; it is the way we represent most generally the thing that affects sensibility. This is strongly suggested, for instance, by the following Rejlexion dating from the 1790S: "the awareness of the presence of an object is perception. The subjective part of perception is sensation, whereas the objective part, that is, the concept of the sensed, is reality [Realitiit)" (Rejl. 6333, 18:654, my emphasis). A similar idea is expressed in the CPR definition of reality: Reality is in the pure concept of the understanding that to which a sensation in general corresponds ... That which corresponds to the sensation in these is the transcendental matter of objects, as things in themselves (thinghood [Sachheit], reality). (A.r43/BI82)

The fact that Kant uses the phrase "things in themselves" in this context is a powerful indication that the category of reality is indeed a descendent of the Inaugural Dissertation's doctrine of affection, so much so that the use of the phrase might be mistaken to be an illegitimate remnant of Kant's preCritical views. Of course, the position that the category of reality somehow allows us to make any kind of objective judgments about things as they are in themselves, in the dogmatic fashion, would be out of place in the more plausible, since it characterizes the same transition from the Inaugural Dissertation to the CPR that Kant hirnself designates as the rnoment of the awakening in the Prolegomena. But it is still incornplete: it does not fully capture the problern that in fact rnotivated this transition, as it is reported in the letter to Herz. According to Kant, it is not sirnply that the concepts of the understanding lack a proof of their objective validity, but rather it is specifically that the undermining of the concept of causation (or the ground-consequence relation) casts the entire rnethod of the Inaugural Dissertation into disarray. The crucial Humean influence on Kant, therefore, seems to me to consist in Hume's further realization that the concept of causation is the basis of the very idea that our representations apply co objeCts at all. This realization is found in both the Treatise and the Enquiry (which is why my proposal does not bear on the issue of identifying the precise textual source of Kanr's acquaintance with Hume): "Here then ir appears, that of those three relations. which depend not upon rhe mere ideas, the only one, thar can be trac'd beyond our senses, and informs us of existences and objects, which we do not see or fed. is causation. This rdarion, therefore, we shall endeavour (Q explain fully before we leave the subject of the understanding" (Treatise l.iii,2); also: "All reasonings concerning maner of facr seem to be founded on the relation of cause and effect. By means of that relation alone we can go beyond rhe evidence of our memory and senses" (Enquiry IV.I).

The Magnitude of Reality

CPR.20 Nevertheless, this reference to things in themselves (which remains unchanged in both the A- and B-editions) is not an oversight on Kant's part, but a genuine expression of the subtle role, and the subtle status, assigned to the idea of the thing in itself in the CPR. Although I cannot offer a very comprehensive treatment of it in this study, I shall have more to say on the topic as I examine Kant's treatment of the category of reality in further detail in the following chapters .

•0

This is why some commentators even suggest to amend Kant's "as things in themselves" to read "not as things in themselves,· as Kemp-Smith does in his translation, explaining that he is "reading. with Wille, nicht die for die. This seems, on the whole, preferable to taking, with Erdmann, the second pan of the sentence as "that in the objects [as things in themselves] which corresponds to sensation is the transcendental matter" (in Kemp-Smith's translation of Kant's Critique of Pure RrIlJOfl.

p. 184 n. I).

CHAPTER

6

Objectivity and the Quantification ofReality

The category of reality is the concept we use to represent the grounds of sensation and so, in a way, to capture the notion that our experience is grounded in something other than itself, that it is objective in some rudimentary sense of the term. But in order to be a part of our experience, whatever we conceive through the category of reality must conform to the conditions of experience in general, including the conditions set by the forms of sensibility. Considering these two features of the category of reality together is enough to reveal a tension essential to the concept, between its role as the representation of the "outer," independent grounds of experience, on the one hand, and its subordination to the "inner," innate form of sensibility, on the other. It is not easy to express this tension in a precise, tractable way, because it is not easy to characterize precisely what it means for an object to be "outer" or independent in the relevant sense within the framework of Kant's transcendental idealism. In this chapter, I present Kant's ingenious manner of articulating this tension as a genuine philosophical problem - the problem of quantifying qualities. The chapter begins by following Kant's growing realization that the failure to establish the validity of the concept of quality, or of the category of reality, constitutes the crux of the Inaugural Dissertation's shortcoming. Kant brings this out by contrasting the problem of validating the concept of quality with the relatively unproblematic validity of the concept of quantity, first in the letter to Herz and again in the CPR (Section 6.1). The contrast rests on the fact that the categories of quantity apply directly to the fonn of sensation and only indirectly to the objects given through it, whereas the categories of quality are supposed to represent the matter of sensation. The fact that quantity and quality correspond, respectively, to the form and matter of sensation, indicates that quantity is to be brought to bear on quality, somehow, just as the .()rlll sensation is supposed to bear on its matter (Section 6.2).

or

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However, there is an essen rial dittil.:ulry in applying the concept of quantity to quality - or, rather, reality - hecause reality seems to lack the appropriate structure, lhe hnal Sl'l'I ion of' this chapter spells out this difficulty and examines Kant's preliminary comments on it in the Anticipations of Perception, A detailed collsideratioll of Kant's main discussion of the category of reality in a short passage of the Anticipations reveals little by way of a satisfactory argument to address this difficulty. Rather, the Anticipations contain only a statement of what such an argument would require (Section 6,3). This has led some readers to doubt that Kant has a satisfactory argument at all. However, I maintain that such an argument is available, but mostly developed in the subsequent Second Analogy, and in certain parts of the MFNS, which are the topic of Chapter 7,

6.1 Objectivity and the Concepts of Quality In the CPJ(s A-edition, the Axioms of Intuition state that "appearances are, as regards their intuition, extensive magnitudes" (AI6x). This is to say that every object of experience "takes up," in some sense, a region of space and time of a determinate, measurable size, and is thereby subject to the concepts that serve in the general procedure of measurement, namely, the pure concepts of quantity. This principle is based in part on Kant's (notoriously obscure) view that space and time themselves must be amenable to the concepts of quantity, since these very same concepts are somehow essentially involved in generating space and time as pure representations. One might say that, insofar as Kant succeeds in establishing the validity of the Axioms, he thereby achieves the kind of objectivity or qualified realism that he pursued in the Inaugural Dissertation, namely, the kind of realism that consists in the view that spatio-temporal order, in virtue of being the form of sensibility, applies not only to ideas or figments but also to objects of experience (or "appearances," in the language of the CPR) given in sensibility. However, this achievement depends on an adequate defense of the notion that there are indeed objects given in sensibility - the notion that there is something to which sensations correspond. Considered independently of such a defense, all that the Axioms could possibly show is that the formal aspect of appearances, which is innate, is an extensive magnitude, without securing any further commitment to an object underlying our sensations. Something like this view of the Axioms is already suggested in the 1772 letter to Hen discussed in Section 5+ There, Kant entertains the possibility that the pure concepts of quantity are somehow privileged, and might

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alone be spared the difficulty that he raises for the validity of other pure concepts, since the objects before us are quantities and can be represented as quantities only because it is possible for us to produce their mathematical representations (by taking numerical units a given number of times). Hence the concepts of the quantities can be spontaneous and their principles can be determined

a priori. (10:131, Kant, Correspondence, p. 134)

Already at the earliest stages of his Crirical thought, then, Kant believes that the concept of quantity is special: it can be gleaned in what is "before us" and, crucially, from the a priori element of what is before us, whereas other pure concepts of the understanding, for example cause, are not discernable in experience in the same way. In other words, Kant argues that, even if, per impossibi/e, all we had to consider were figments or mere ideas, we could still demonstrate that the pure concepts of quantity are indispensable to them, and so guarantee that these concepts, and the universal judgments they imply, have a valid application; the validity of other pure concepts, by contrast, cannot be estahlished in the same manner. In the more fully developed terms of the CPR, K;tnt upholds a descendant of this view for the reason that, as he puts it in the Axioms, the consciousness of the homogeneous manifold in intuition in general [through which the representations of a determinate space or time are generated) is the concept of a magnitude (Qlllmti). (Ar61/B202-3)

This later development of the view enhances the earlier one with the Critical doctrine that the categories of quantity are not only involved in producing the mathematical representation of space and time but are also more fundamentally involved in the very synthesis of space and time themselves. In both stages in the development of this view, the unique, privileged relationship between the pure concepts of quantity and the pure forms of intuition remains essentially intact. It is precisely in order to emphaSize this point that Kant makes a slight revision to the statement of the Axioms between the A-edition and Bedition of the CPR: the Axioms in the A-edition state that "appearances are, as regards their intuition, extensive magnitudes" (AI6I), whereas the B-edition simply reads: "intuitions are extensive magnitudes" (B202, my emphases). In the B-edition, then, Kant chooses to omit the reference to appearances. This certainly does not mean that he abandons the A-edition Axioms' claim that appearances are extended in space and time, or the

The Magnitude of Reality claim that the Transcendental Deduction establishes the applicability of the categories of quantity to appearances. Rather than represent a shift in Kant's views, this revision is made simply to emphasize that the Axioms directly describe a feature of the pure form of intuition, and only thereby, indirectly, describe appearances or objects. The categories of quantity, then, are seen to pertain to appearances only when supplemented by an account of how sensations are grounded in objects. As I have already suggested in Section 5.4, this issue of grounding, which is the primary import of the categories of quality, is what the Inaugural Dissertation crucially fails to address, and what ultimately undermines it in Kant's eyes. Accordingly, we find evidence that the concepts of quality (rather than the concepts of quantity) are the source of Kant's concern already in the letter to Hen, where he describes his reason for undertaking the work that will become the CPR: The concepts of the quantities can be spontaneous and their principles can be determined a priori. But in the case of relationships involving qualities - as to how my understanding may, completely a priori, form for itself concepts of things with which concepts the facts should necessarily agree, and as to how my understanding may formulate real principles concerning the possibility of such concepts, with which principles experience must be in exact agreement and which neverrheless are independent of experience this question, of how the faculty of the understanding achieves this conformity with the things themselves is still left in a state of obscurity. (10:131, Kant, Correspondence, p. 134)

Kant makes a similar point in the CPKs Anticipations, where he finds another way to describe this important difference between the concepts of quantity and those of quality. Kant remarks that in some broad sense of the word, not only the Anticipations but also the Axioms deserve to be called "anticipations" insofar as they anticipate - i.e., in the broad sense, represent a priori - some features of appearances. But it is helpful, Kant says, to reserve the term "anticipations" for another, narrower sense, to refer only to the anticipation, or a priori representation, of certain features of the properly empirical aspect of appearances. This narrow sense is helpful since it brings out just how remarkable it is that any feature of the empirical aspect of appearances can be anticipated at all: One can call all cognition through which I can cognize and determine a priori what belongs to empirical cognition an anticipation ... But since there is .~ome(hing in the appearances that is never cognized a priori, and which hence also constitutes the sensation (as matter of perception), it follows that

it is really this that cannot be anticipated at all. On the contrary, we would

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call the pure determinations in space and time, in regard to shape as well as magnitude, anticipations of appearances, since they represent a priori that which may always be given a posteriori in experience. But ifit were supposed that there is something which can be cognized a priori in every sensation, as sensation in general (without a particular one being given), then this would deserve to be called an anticipation in an unusual sense, since it seems strange to anticipate experience precisely in what concerns its matter, which one can draw out of if. And this is acwally how things stand. (Ar67/B209)

Kant's aim in this passage is, again, to highlight an important difference between the concept of quantity and the concept of quality (and between their respective principles): whereas it is prima facie easier to show how pure concepts can validly describe the pure element in intuition, it is difficult to show how the same could be done for the empirical element of intuition. This difference, then, is one of the core differences between the Inaugural Dissertation (where Kant is content to show only the former) and the CPR (where he sets out to show the latter as well).

6.1 Why Qualities Should Have Quantities While this passage from the Anticipatiolls Sl'tS the concepts of quantity and quality apart, it also suggests a manlier in which they are inextricably joined, inasmuch as it identifies the pure ami empirical elements of appearance - to which these concepts correspond - with the "form" and the "matter" of appearance, respectively, thus indicating that the former is somehow applied to or brought to bear upon the latter. The Anticipations represent "experience precisely in what concerns its matter" or the "matter of perception," and the Axioms, presumably, represent the form thereof Now, to say that the Axioms and the Anticipations are related to one another as principles of form and matter is to make a somewhat delicate point, since Kant employs the terminology of form and matter in several different senses throughout the CPR, and more than one of these senses is relevant here. Thus, for example, both principles - merely in virtue of their transcendental status - are formal in the sense that Kant takes his transcendental idealism to be a "formal idealism" (B519 n.),' i.e. in the sense that they are elements of the general form of any possible cognition. Also, as transcendental principles of the understanding, they are formal in the sense in which the spontaneous, active faculty of the understanding , Also in the Prolegomma, 4:337, 37\.

The Magnitude of Reality informs or determines the receptive, passive faculty of sensibility: as Kant puts it in §26 of the B-Deduction, "the understanding determines the sensibility" (B161 n.)! But the primary, most direct sense in which the formmatter distinction is relevant here is the sense in which the Axioms and the Anticipations are, respectively, the conceptual representations of the form and the matter of appearances in general. Kant first distinguishes a formal and a material element in appearances in the Transcendental Aesthetic: I call that in the appearance which corresponds to sensation its matter [die Materiel, but that which allows the manifold of appearance to be intuited as ordered in certain relations I call the fonn [die Forml of appearance. (A2o/B34)

Although Kant does not name any of the categories in this passage, it is easy to recognize the category of reality in the description of the matter of sensation, viz. as "that in the appearance which corresponds to sensation," since, in the Anticipations, reality is identified in the very same terms: "[appearances] contain in addition to the intuition the materials [die Materien] for some object in general ... , i.e. the real of the sensation" (AI66IB207). Similarly, the Axioms are supposed to pertain to the formal aspect that all appearances have in virtue of being given in intuition: Kant says that "all appearances contain, as regards their form, an intuition in space and time" (AI62/B202), and it is dear that this "intuition in space and time" is the form of appearance in exactly the same sense that he has in mind in the Aesthetic, i.e. as what "allows the manifold of appearance to be intuited," because he goes on to explain that appearances can be intuited, or "taken up into empirical consciousness [only] through the synthesis of the manifold through which the representations of a determinate space or time are generated" (AI62IB202).J , Maner and form are identified with the determinable and the determining, respectively, in the Amphiboly: "the [matter] signifies the determinable in general, the [form] its determination" (AJ.66/ S322).

, I n the M FNS, the metaphysical concept of matter as the real in sensation is shown to be closely related to the empirical concept of matter, i.e. the concept of "an extended, impenetrable being" that is topic of "the doctrine of bodies" (A)SJ). The former concept is presented as the explication of the latter concept's relationship to the faculty of sensibility: If I am to explicate the concept of matter ... only by relation to that cognitive faculty in which the representation can first of all be given to me, then evety object of the outer srom is matter, and this would be the merely metaphysical explication thereof... Matter, as opposed ro form, would be that in the outer intuition which is an object of sensation, and thus the properly empirical element of sellSible and outer intuition, because it can in no way be given a priori.

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To sum up our brief consideration of the comparison Kant draws between the pure concept of quality and the pure concept of quantiry. we may note two characteristics of qualities in general: first, insofar as particular qualities are taken to be the contributions made to our experience by things independent of us, the general concept of a quality as such can be taken to express the general notion that such a contribution occurs at all. Therefore, any attempt to make use of the pure concept of quality should press us to ask how the very idea of such a contribution could be validated or, as Kant does in the letter to Herz, "how my understanding may, completely a priori, form for itselfconcepts of things" (10:131). Second, Kant associates qualities with the "matter" of appearance, thereby implying that qualities are subjected to the structural properties he associates with the "form" of appearance, as expressed by the concepts of quantity. Therefore, the pure concepts of quality also lead us to ask how qualities could be subjected to the pure concepts of quantity. By placing these two characteristics side by side we can begin to make sense of Kant's somewhat curious decision that the transcendental principle of reality should be the proposition that reality has a quantity or a magnitude (AI66/8208). This decision is curious because, if the CPR is supposed to address the skeptical challenge regarding qualities that Kant originally sets for himselfin the letter to Herz successfully,4 then the principle of the Anticipations - being the lesson to be learned from the fact that reality is an objectively valid concept - should simply be a straightforward statement of this success. We may expect, therefore, of the Anticipations to be a statement to the effect that, indeed, sensations are grounded in reality and are thus more than mere figments, much as the principle of the concept of causality, for instance, is a statement to the effect that, indeed, events have causes, i.e. that "alterations occur in accordance with the law of the connection of cause and effect" (B232). Instead, we find that the Anticipations consist in the seemingly unrelated proposition that reality has a magnitude, i.e. that the concepts of quantity apply to qualities: in the A-edition, the Anticipations state that "in all appearances the sensation, and the real, which corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, i.e.,

We return to examine this further developmenr of the relationship of reality ~nd "1;111,·,. ill Section 7.2 . • Or rather a more refined version of this skeptical challenge, since in his Critical period "-lilt wOlild be wary of defending objectivity by claiming without qualification that "the unucr"t""dilll-: .\, hi,'v,', ... conformity with the things themselves," as he does in that letter.

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a degree" (AI66); the revised formulation of the B-edition, designed, as we have seen with the Axioms, to bring out more clearly which aspect of appearances is discussed, states that "in appearances the real, which is an object of the sensation, has intensive magnitude, i.e., a degree" (B208). Even if we put aside for the moment certain unclarities regarding the meaning and justification of this claim, we may still wonder what led Kant to designate it as the principle of Reality and - if we follow the thread leading back to the letter to Hen - as a crucial step in solving one of the core problems that led Kant to compose the CPR in the first place. In other words, we may wonder how the claim that reality has a magnitude (or that qualities have quantities) is supposed to help make sense of the claim that our sensibility is somehow affected by something independent of it. An answer to this question will only emerge from a detailed investigation of the procedure by which qualities can be given determinate quantities. The remainder of this chapter explains the fundamental challenge facing such an investigation. The following chapter then outlines how qualities are supposed to be quantified, showing that quantifying qualities cannot be accomplished without recourse to the general concept of dependence - and more specifically, causality - as Kant understands it. In drawing this connection it will become clear that showing how reality can be quantified is Kant's way of showing how what affects our faculty of sensibility can be conceived. 6.3 Intensive Magnitudes and the Anticipations of Perception In the Axioms, Kant states that the concept of a magnitude in general is "the consciousness of the homogeneous manifold in intuition in general, insofar as through it the representation of an object first becomes possible" (B203). Thus, the application of the concept relies on its object being composed of mutually exclusive homogeneous parts. Now, in the Anticipations Kant states that the concept of magnitude applies to reality, but, insofar as we take reality to represent the qualitative content of a sensation, it is not obviously the sort of thing that can be quantified at all. This is because qualities do not appear to be homogeneous manifolds, as they do not consist of an aggregate of external parts. While we may be inclined to say, for example, that the brightness of the sun is greater than that of the moon, as one does in comparing magnitudes, we cannot discern several "moon-brightnesses" aggregated within the sun's brightness in the way that we can discern several moon-sized volumes within the sun's volume. This structural difference between the property of

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brightness and the property of volume is the difference between intensive and extensive magnitudes: All magnitudes (quantitates) can be considered in two ways: either intensively or extensively. There are objects in which we distinguish no multitude of homogeneous pam; this is intensive magnitude. This magnitude is the degree. The objects in which we distinguish a multitude of homogeneolls parts have extensive magnitude. (Metaphysik L2 , 28:562)'

This definition brings the problem to the surface: how can we be conscious of a homogeneous manifold in what has no distinguishable multitude of homogeneous parts? The priority of extension over intension with regard to the concept of magnitude is also evident in the fact that the Axioms, which are supposed to treat the concept of magnitude in general, are actually concerned only with extensive rather than intensive magnitudes. Kant explains this by noting that the most fundamental application of the categories of quantity occurs in the synthesis of the manifold of pure intuition, i.e. the manifold contained in space and time as a priori forms of sensibility. Therefore, extensive magnitude is primarily a property of space and time, and only secondarily of appearances, merely in virtue of their being spatio-temporal: "the appearances are all magnitudes, and indeed extensive magnitudes, since as intuitions in space or time they must be represented through the same synthesis as that through which space and time in general are determined" (B203). Intensive magnitudes, on the other hand, are not extended in space and time; an intensive magnitude is a measure of something at an instant and at a point: "the real in appearance always has a magnitude - but one which can only be met with in apprehension in so far as it takes place by means of mere sensation in an instant, and does not proceed from parts to the whole; it thus certainly has a magnitude, but not an extensive [magnitude]" (AI68/BlIO). The problem of intensive magnitudes, then, is the problem of finding a principled way to "extract" a multiplicity of parts from something available only as a unity, and arrange them according to the forms of space and time to which the categories of quantity fundamentally apply. As Kant succinctly states in a Reflexion from I780, "every intensive magnitude must, ultimately, be brought to the extensive [AIle intensive GroBe muB doch zuletzt auf extensive gebracht werden]" (Rejl. 5590; 18:242). Thus, we find

\ Kant.

L~ctures

on MetaphYSiCS. p.

r~6.

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at the center of the Anticipations a line of reasoning that seems designed to address this problem: Apprehension. merely by means of sc:nsation, fills only an instant (if I do not take into consideration the succession of many sensations). As something in the appearance, '" it therefore has no extensive magnitude; the absence of sensation in the same moment would represent this as empty, thus = o. Now that in the empirical intuition which corresponds to the sensation is reality (rtalitas phaenomenon); that which corresponds to its ahsence is negation = o. Now, however, every sensation is capable of a diminution, so that it can decrease and thus gradually disappear. Hence between reality in appearance and negation there is a continuous nexus of many possible intermediate sensations, whose difference from one another is always smaller than the difference between the given one and zero, or complete negation. That is, the real in appearance always has a magnitude. (AI67-S/B209-10) 6

On the assumption that any given sensation, as a state of inner sense, "fills" or occupies an instant in time, the argument appears to proceed along the following lines: (a) any given sensation implies the possibility of an infinite variety of other sensations (or variations of the same sensation) forming a continuous series; we can imagine going through this series of possible sensations in sequence over an extent of time, beginning with the given sensation. Now, (b) we are able to associate any point in this extent of time with the corresponding possible sensation that would "fill" it, i.e. the possible sensation we imagine just as we reach that point in time in going through the sequence in imagination. And since we can determine in principle how long it takes to reach each point in time throughout this process (as shown in the Axioms), we can further associate each possible sensation with a determinate quantity, as a function of how long it would take to reach it: the intensity of each sensation we encounter through the process

, The schema of the category of reality consists in an almost parallel argument: Reality is in the pure concept of the understanding that to which a sensation in general corresponds ... Now every sensation has a degree or magnimde. through which it can more or less fill the same time. i.e., the inner sense in regard to the same representation of an object, until ir ceases in nothingness (= 0 = negatio). Hence there is a relation and connection between. or rather a transition from realiry [Q negation, that makes every reality representable as a qUAntum, and the schema of a reality, as the quantity of something insofar as it fills time, is just this continuous uniform generation of that quantity in time, as one descends in time from the sensation that has a certain degree to its disappearance or gradually ascends from negation to its magnitude.

Objectivity and the Quantification ofReality

r03

of imagining the diminution of the original sensation would be a magnitude in some proportion to the length of time separating it from the beginning of the process. Thus, in virtue of this relation of sensations with the form of time, we can say that every sensation has an intensive magnitude. Finally, since there is some kind of correspondence between sensation and reality, this procedure for assigning quantities to sensations is supposed to have a corresponding procedure for assigning quantities to reality. This reconstructed line of reasoning, as it stands, is not very compelling. I believe, however, that Kant does not intend for the Anticipations to contain a complete argument for its principle. Rather, the chapter contains an outline whose details are fleshed our in subsequent chapters, especially in the Second Analogy. In the remainder of this section, I point out two ways in which the Anticipations falls shorr of fully demonstrating its principle, in both steps (a) and (b), with the intention of showing how these shortcomings are rectified elsewhere in the CPR in the following chapters. One conspicuous shortcoming is in step (a). where Kant associates sensations with extensive magnitudes by asserting that sensations can be varied in imagination. In this passage, Kant makes no anempt to prove this assertion, and yet it is hardly self-evident. On the contrary, while Kant ostensibly takes it to be a priori, since the Principles are supposed to be "these whose relation to possible experience must constitute all pure cognition of the understanding a priori" (AI48/Br87), the implication that we possess a capacity to imagine a continuous order of possible sensations for any given sensation seems doubtful and, even if true, essentially a matter of empirical psychology. 7 It is true that Kant does not explicitly provide a reason to think that every sensation implies an ability to represent or imagine a sequence of its possible variations, but we can better appreciate his position by noting that Kant does provide a reason to think that every sensation implies an ability to represent or imagine its complete absence: the ability to represent time independently of what "fills" or occupies it, i.e. the ability to "take the appearances away from time," is a crucial part of , Thus. Jonarhan Bennerr. commeming on Kane's claim rhar sensarions can be diminished gradually in imagination, complains rhar "rhis, however. merely says rhat our sensarions are like that: it states an empirical facr. and has no place in Kant's appararus of a priori principles" (Bennen. Kants Analytic. p. 171); Paul Guyer raises a similar complaint: "the principle of intensive magnitudes seems [0 lack any a priori basis. let alone a clear place in Kant's theory of time-derermination or even in the official schematism of rhe caregories" (Guyer. Kant and th. Claims of KnowlLdge. p. 104); cf. Wolff. Kant's Theory ofMental Activity. pp. 135-6. for similar criricism. But see Warren. Reality and Impmetrability i" Kant's Philosophy ofNalllr•• p. 18 n. 26.

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Kant's proof that time is a form of intuition, and it is already supposed ro be established a priori in the Transcendental Aesthetic (A3I/B46). With this a priori distinction between the representations of empty time and "filled" time, all that is missing in order to arrive at Kant's assertion in step (a) is to show a priori that any transition between empty and "filled" time must be gradual or continuous. In other words, what is needed here is an a priori argument for some kind of a necessary continuity of alteration. Clearly, such an argument would not be concerned with the psychological-empirical claim that, given an actual sensation, we can "visualize" a variety of possible sensations in the "mind's eye," any more than the Transcendental Aesthetic is concerned with the absurd psychological-empirical claim that we can "visualize" what empty space "looks like." This is evident in Kant's description in the Anticipations of the gradual alceration as one between empirical and pure consciousness, rather than between two states - say, "full" and "empty" - of empirical consciousness: Now from the empirical consciousness to the pure consciousness a gradual alteration is possible, where the real in the former entirely disappears, and a merely formal (a priori) consciousness of the manifold in space and time remains.

Does Kant believe he has an a priori argument for the continuity of alteration? We have already encountered Kant's earlier, pre-Critical endorsement of the principle that all alteration is continuous or gradual, e.g. in Section 5.2, and he turns his attention back to this same principle on several occasions in the Critical period. In the Anticipations chapter itself, for example, Kant acknowledges some conceptual connection between the proposition that all alceration is continuous and the proposition that reality and sensation have intensive magnitudes, when he says that the latter prima facie implies the former: "if all appearances ... are continuous magnitudes, then the proposition that all alteration (transition of a thing from one state into another) is also continuous could be proved here easily and with mathematical self-evidence" (AI7I/B2I2). Kant quickly qualifies this endorsement of the continuity of alceration, but only to reassert it in greater detail in the Second Analogy (A207/B253). The issue is raised yet again in the MFNS General Remark to Mechanics, where Kant distinguishes between a "metaphysical" and a "mechanical" law of continuity of alteration (4:552-3). This is already enough to suggest that Kant's attitude

Objectivity and the Quantification of RealiLy

10 5

toward the continuity of alteration is complex and in some ways pu,/..,.Iing. and so I shall take up this issue in greater detail in Chapter 8. In addition to the shortcoming in step (a), the argument seems dChcit'lll in step (b) as well, in at least two respects: first, even if the Anticipations successfully shows that any given sensation contains or presupposes sOllie manifold of variations that can only be represented through the form of time - thereby establishing that something seemingly without extensioll is essentially tied to an extensive magnitude - the chapter still lacks an account of how these variations may be ordered according to their respective intensities, i.e. how we are £0 determine which of two varieties of a given sensation is the more intense. There is nothing, it seems, in the sensation of red to indicate that it is a hue of lesser intensity than blue; and there is nothing about the way lukewarmth feels that puts it between heat and cold. But without a general procedure for such ordering, step (b) does not go through since such an ordering is part of the very concept of magnitude. Second, even if the order of the variations is established, Kant does not provide a way to determine the distance between any two possible variations of a sensation along the time in which it is generated. In other words, no procedure is given to determine the rate at which the intensities are supposed to vary. Taken together, these deficiencies in step (b) show that Kant's argument as it stands in the Anticipations is still missing an account of how the law that governs the change - i.e. the representation of the rate of change - is to be established. Therefore, the argument does not fully provide a way to order and compare different degrees or intensities, as it purports to do. 8 These considerations show that the argument of the Anticipations does not offer a complete demonstration that sensations, and reality, have magnitudes. The implication, however, is not that the Anticipations chapter fails to do so, but that it is not intended to do so. Rather, it is meant as a preliminary step in such a demonstration, which consists in explaining what it would mean for reality to have a magnitude at all. The point of the Anticipations, in other words, is just to show that the notion that sensations have magnitudes leads directly to the problem of generating and ordering sensations along a continuous scale, since, according to the

B

It bears repeating here that. just as with step (a). the problem with step (b) is not thar Df llnllTill~ and estimating the stages of some empirical, subjective process whereby we inwardly expeli"",,, .1 given sensation diminishing to nothing, since the Anticipations do not stipulate the p,ycll(1I"I~i"rI possibiliry of such a process.

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schema of magnitude (A.I42/Br82), all magnitudes as such have metric properties. Now, this problem is reminiscent of the problem of objective timedetermination treated in the Analogies of Experience, inasmuch as the problem of time-determinations is the problem of ordering possible states of inner sense on a one-dimensional continuum, i.e. according to the form of time. And so, as with the issue of the continuity of alteration mentioned previously, we may hope to find the steps missing from the outline provided by the Anticipations in the ensuing Analogies, where Kant continues to pursue the goal of representing reality as a magnitude.

CHAPTER

7

Reality, Causation, and Motion

The Anticipations chapter claims that our sensations are generated (transcendentally, not psychologically) through a succession of intermediate states according to the form of inner sense, i.e. time. The significance of this claim is that it gives us a way to think about reality as a magnitude: if this claim were substantiated, it would reveal a manifold of intuition implicit in every sensation, which in turn would help render sensation amenable to the categories of quantity. As empirical sensations are supposed to be grounded in reality, their implicit structure is supposed to represent the structure of their grounds and would show that reality can be quantified and thus apprehended. However, the Anticipations chapter does not establish that sensations indeed contain an implicit manifold to be ordered in succession, nor does it have the resources to determine the succession of the elements in such an implicit manifold if it exists. For Kant, the way to correct these shortcomings is to enrich our concept of reality with the conditions for representing grounds and consequences in general, conditions that are naturally relevant here because reality is the concept of the grounds of sensation in the object. The first section of this chapter gathers several passages - most importantly, from the Second Analogy - where Kant outlines this strategy and summons his analysis of the concept of causation in order to treat reality as a magnitude (Section 7.r). The Second Analogy contains a highly abstract method of measuring the magnitude of causation, which, Kant argues, is an articulation of the sense in which reality is a magnitude. This abstract method seems at odds with its purported instantiation in the more concrete method of measuring the degree of illumination, contained e.g. in the MFNS. This apparent tension, however, is reconciled once Kant's account of simultaneous causation is taken into consideration (Section 7.2). But Kant's task is not complete with taking reality to be a ground or a cause in general; reality must fundamentally be a cause of motion in particular. The priority of motion in this context, I believe, emerges in 107

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the MFNS Phoronomy chapter. The Phoronomy is concerned with the determination of the magnitude of motion, or velocity, and to that purpose tackles a version of the problem of quantifYing something that lacks external parts, first encountered in the Anticipations (Section 7.3). Finally, I consider the difficulty in aSSimilating the procedure of measuring velocity into the broader problem of measuring reality, in view of the prima facie discrepancy between the formal, noncausal nature of motion and the material, causal nature of reality (Section 7-4).

7.1 Reality and Causation The Anticipations of Perception and the Second Analogy, associated with the categories of reality and of causation, respectively, include closely parallellines of reasoning: the former suggests that reality is measured by gradually altering the sensation to which it corresponds through a manifold of intermediate variations in imagination, and relying on this manifold in order to apply the categories of quantity; the latter similarly argues that a cause is measured by the gradual alteration of an object through a manifold of intermediate states over time. Such similar procedures are called for in both cases because, just as reality is given as a unity at an instant, so a cause is present in its entirety at each instant throughout the duration of its action. Clearly, there is considerable agreement between the a priori structures of reality and causation. It is natural to expect such an agreement because the category of reality, as what corresponds to sensation in the object, is taken to represent the ground of experience, and the concept of grounding is just the category of causation in its unschematized form. Therefore, causation is the proper concept to summon in articulating the way reality figures in experience. Accordingly, we find that in several places Kant takes intensive magnitude, i.e. the kind of magnitude appropriate to reality, to be the magnitude of grounds. In the Metaphysik von SchOn, for example, Kant says that "that which is the object of sensation, we call degree; for example, the degree of heat, cold, light. Why do we attribute a magnitude to it? Because we represent the magnitude of a ground through it," in such a way, moreover, that the magnitude of the ground is proportional to the magnitude of the sensation; a ground of great magnitude, Kant continues, is said to "have caused a great sensation" (28:502). Similarly, in certain Reflexionen, Kant claims that "the magnitude of an (intensive) ground does not demonstrate any composition from smaller [elements]" (Ref!. 4183; 17:448); and

Reality, Causation, and Motion

10 9

that "the magnitude of a whole is extensive," whereas "the magnitlllil- (If a ground is intensive or degree" (ReJl. 4411; 17:536). In the CPR itself, toward the end of the Anticipations, Kant dearly states that reality can be taken as a ground or a causal power - specif1cllly as the power to generate sensations, and generally as the power to gencratl· any sensible effect - in a passage that exhibits the similarities in both futll:tion (i.e. grounding) and structure (i.e. intensity) between the two concepts: If one regards this reality as cause (whether of the sensation or of another reality in appearance, e.g., an aiteration), then one calls the degree of reality as cause a "moment," e.g., the moment of gravity, because, indeed, the degree designates only that magniwde the apprehension of which is not successive but instantaneous. But I touch on this here only in passing, for at present I am not yet dealing with causality. (AI68-9 /B2IO ).

After touching on this "only in passing" in the Anticipations, Kant eventually explains this passage in the Second Analogy, where the significance of the connection between Reality and causation is clarified. As I argue in Section 6.3, the Anticipations chapter does not by itself complete the task of associating reality with a manifold: the process it seems to suggest (viz. of imagining a sensation gradually diminished to nothing, and then extrapolating from that manifold of gradations to a corresponding manifold in the underlying reality) fails to establish a manifold that is continuous and ordered (as a magnitude must be). But the analysis of the concept of cause in the Second Analogy tackles both issues by offering the following template for a procedure that associates a cause with a manifold: A cause does not produce its alteration suddenly (all at once or in an instant), but rather in a time, so that as the time increases from the initial instant a to its completion in b, the magnitude of the reality (b - a) is also generated through all the smaller degrees that are contained between the first and the last. All alteration is therefore possible only through a continuous action of causality, which, insofar as it is uniform, is called a moment. The alteration does not consist of these moments, but it is generated through them as their effect. (A20S/B254)

The idea here seems to be that "the magnitude of the reality," or of the cause, is generated throughout the duration it takes for it to bring about a certain change in an object. Kant seems to assume that the change occurs gradually and uniformly, and so that it inherits the structural features of the time it takes, thereby acquiring the nature of a magnitude. Thus,

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whereas a causal power itself has no distinguishable parts, its effects can be extended through parts of space and time. Assuming it is possible to measure the extension of those effects, they can be used to estimate the intensive magnitude of the underlying cause in proportion to the extensive magnitude of the effect. The way in which Kant's concept of causation fulfills its role vis-a-vis the measuring of reality can be gleaned from several illustrations that Kant provides to highlight the fact that, whereas a causal power has no distinguishable parts, its effects can be extended through parts of space and time. Since it is possible to measure the extension of those effects, they can be used to estimate the intensive magnitude of the underlying cause in proportion to the extensive magnitude of the effect. For example, the intensity of heat can be measured by the extent to which it causes mercury to move up the marks of a thermometer's scale:' One cannot say, e.g., that heat consists of lukewarmths, one therefore determines its magnitude not according to the parts which it contains, but rather according to the effects which it produces, e.g., that it expands a body. And one can thereby ascribe to it not a genuine magnitude [presumably, an extensive magnirudel. but rather a degree [Le. an intemive magnitude].

(Refl. 5663; 18:322)' Kant's paradigmatic example of this strategy is the estimation of the degree of illumination. In introducing the Analogies, Kant alludes to the procedure for measuring illumination, when he explains that the Axioms and the Anticipations pertained to appearances with regard to their mere possibility, and taught how both their intuition and the real in their perception could be generated in accordance with rules of a mathematical synthesis, hence how in both cases numerical magnitudes and, with them, the determination of the appearance as magnitude, could be used. E.g., I would be able to compose and determine a priori, i.e., construct the degree of the sensation of sunlight out of about 200,000 illuminations from the moon. (AI78/B22I)

, I take this to be one of Daniel Warren's poinrs in section 1.5 of his Reality and Impenetrability. Warren identifies a requiremem for a metric of intensities in the argumenr of the Anricipations, and claims that Kanr inrends co fulfill this requiremenr by creating reality as a causal power: "my claim is that, for Kanr. sensible qualities - those properties of an object on account of which it falls under the category of reality - can only be quantified in the full sense insofar as they are regarded as causal powers" (Warren, Reality and Impenetrability, p. 25). , This {ranslacion is by Warren, Reality and Impenetrability, p. 26.

Reality, Causation, and Motion

III

In the MFNS, Kant says more on how he thinks the illumination of sunlight may be constructed as a composition of less intense illuminations: Light, for example, diffuses from 7 Proposition 2 singles out circular motion as the kind of motion that can be objectively attributed to a material body in the most straightforward fashion. 28 What " "Every motion, as object of a possible experience, can be viewed arbitrarily as motion of the body in a space at rest, or else as rest of the body, and, instead, as motion of the space in the opposite direction with the same speed" (4:487). C£ Section 7.3. " For a more comprehensive account of Proposition 2 of the Phenomenology, and of rhe rheme of distinguishing actual from apparent motions in Kanr, see Friedman, Kams Construction ofNaturt, especially pp. 460--509. " "The circular morion of a matter, as disrinct from the opposire motion of the space, is an actual predicate of rhis marter; by contrast, the opposite motion of a relative space, assumed instead of the

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makes circular motion (or, indeed, any curvilinear motion) objective in this sense is the availabiliry of a procedure for discovering the presence of circular motion in the absence of any observable change in the relative positions of bodies. This means that the attribution of circular motion through this procedure does not essentially depend on the relative (and, in Kant's sense, subjective) motions of reference frames. The procedure Kant has in mind is mentioned in the Remark to Proposition 2. There, Kant refers to Newton's Scholium, where Newton raises a similar problem of distinguishing actual motions from apparent motions in the absence of any direct empirical experience of absolute space, on which, for Newton, this distinction depends. 29 In his solution to the problem, Newton shows that the assumption of a specific attractive force and the validity of the law of inertia can be used together in order to conclude that a rotating system must involve a certain centrifugal endeavor of its elements away from the center of rotation. The gist of the procedure is finding a point within the system such that, if it is taken to be the center of rotation, the actual empirical properties of the system turn out to conform with the effects of the centrifugal endeavor that would arise in a rotating system held together by the presupposed specific attractive force. In this way, these empirical properties become indications of actual rotation that are, moreover, detectable within the system itself, rather than with regard to its motions relative to anything outside itself. JO Thus, to take Newton's examples, the rotation of a system consisting of two balls connected by a string can be detected by a centrifugal tension in the string itself, once the string's e1asticiry is presupposed.)! Analogously, the rotation of the system consisting of the parts of the earth can be detected by noting how opposite parts along its equator are drawn away from one another by

motion of the body, is no actual motion of the latter, but, if taken to be such, is mere semblance" (4:55 6-7) . .. "It is certainly very difficult [0 find out the trUe [i.e. actual] motions of individual bodies and actually [0 differentiate them from apparent motions, because the parts of that immovable space in which the bodies truly move make no impression on the senses. Nevertheless, the case is not utterly hopeless. For it is possible to draw evidence partly from apparent motions, which are the differences between the true motions, and partly from the forces that are the causes and effects of the true motions" (Principia 414). )0 "Newton's Scholium [0 the Definitions he has prefixed to his Principia may be consulted on this subject, towards the end, where it becomes clear that the circular motion of twO bodies around a common central point (and thus also the axial rotadon of the earth) can still be known by experience even in empry space, and thus without any empirically possible comparison with an exur1liJi space; so that a marion, therefore, which is a change of external relations in space, can be empirically given. even though this space is not itself empirically given, and is no object of experience" (4:557-8).

" Prillcipia 414.

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The All of Reality

centrifugal endeavor while being held together by gravitation, creating a bulge along the equatorF For Kant, who has the additional burden of reconciling Newtonian physics with a relationist conception of space and motion, this same procedure offers a way to characterize a delicate notion of a reference frame that is tentatively - but not arbitrarily - regarded as absolute. This is the reference frame defined by the purported center of the rotating system: since it is verified empirically (and is not merely a pure phoronomical construction), but independently of any observable change in the relative positions of the system's pares, it can be the basis of a meaningful, objective attribution of actual (circular) motion to bodies. The characterization of this notion, then, accomplishes the first stage of the Phenomenology argument. The second stage of the argument, to which we now turn, begins with noting that this procedure depends on the presupposition of some specific moving force of attraction pulling the bodies in the system together. Indeed, it is this presupposition that makes the choice of a reference frame nonarbitrary. In bringing this procedure to bear on the axial rotation of the earth, for example, or on the various lunar and planetary orbits in the solar system, the force presupposed is specifically the force of universal gravitation. Therefore, in order to adjust Newton's procedure for his own theoretical framework, and employ it for his own purposes, Kant must tie his attempt to characterize an objectively valid distinction between actual and apparent motion with the attempt to establish the validity of the inversesquare law of universal gravitation. In Section 11.5, we consider how this second stage of Kant's argument relies on the transcendental principles of reason as described in the Transcendental Ideal and the Appendix.

11.5 Kant on Genus-Species Subordination and Newtons Derivation of Gravitation For Newton, as we have seen in Section II.3. the derivation of gravitation involves a principled transition through a series of reference frames, which gradually leads to greater conformity between the implications of the inverse-square law of universal gravitation and the record of actual astronomical measurements. Having examined Newton's typical argumentative " Book III Proposition 18 Theorem 16: "If it were not for the daily circular morion of the planets. ,hen. because the gravity of their partS is equal on all sides. they would have to assume a spherical figure. Because of that circular motion it comes about that those parts. by receding from the axis. endeavor to ascend in the region of the equator" (Principia 821); cf. Friedman. Kantr Construction of Nature. p. 465.

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approach in Principia Book III, we can also note that Kant's example in the Appendix, which is a schematic portrayal of Newton's derivation, highlights those steps in the derivation that have the following features: (a) they involve curvilinear celestial motions represented in simplified or idealized form; (b) they involve analyses of these motions on the presupposition that the inverse-square law of gravitation holds (showing that the represented motions can be made to conform to the presupposition); and (c) they collectively form a series of finite encompassing reference frames, culminating in the ideal, all-encompassing reference frame of absolute space. In Section 11.4, I suggest that these features are valuable for Kant in his attempt to draw a meaningful distinction between actual and apparent motion while maintaining his relationist commitments. Following Friedman, I explain that in his attempt, Kant adapts a procedure from Newton's Scholium to show that, in considering rotating systems, the presupposition of universal gravity makes it possible to ascribe motion to a body in a manner that does not depend on a change of position relative to other bodies, effectively treating the reference frame of the rotating system in isolation, as if it were that of absolute space. It is easy to see, then, how features (a) and (b) of Newton's derivation serve this procedure. Now, for Kant's attempt to go through, feature (c) is also necessary: the treatment of a reference frame as if it were absolute must be a step in a series of similar treatments of other reference frames toward an ideal, genuinely absolute reference frame. This last feature, insofar as it involves an indefinitely iterable series aimed at an ideal goal, is just the sort of feature that characteristically falls under the faculty of reason in the Kantian framework. My purpose in this final section, then, is to explain the role of reason in scientific inquiry by elucidating the relationship between the series of encompassing reference frames aimed at an ideal absolute reference frame, on the one hand, and the series of generalizations and specifications aimed at an ideal genus-species hierarchy, on the other. The CPR makes it clear that it is the latter series that represents the proper role of the faculty of reason, and the MFNSs Phenomenology argues that the former series is indispensable to the book's central project. Therefore, byelucidating the relationship between the two series and their respective regulative ideas we can better understand the unified role of reason that relates the CPR and the MFNS. The key to understanding this relationship is, again, Kant's example in the Appendix, since it ostensibly illustrates the latter series in terms of the former. Disconcertingly, however, in the MFNS Kant seems to justifY the position that absolute space is an idea of reason with an argument that has little

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The All of Reality

to connect it with the proper role of reason as it is described in the CPKs Transcendental Ideal and the Appendix to the Dialectic: in the General Remark to Phenomenology Kant explains that [absolute space] cannot be an object of experience, for space without matter is no object of perception, and yet it is a necessary concept of reason, and thus nothing more than a mere idea. For in order that motion may be given, even merely as appearance, an empirical representation of space is required, with respect to which the movable is to change its relation; but the space that is to be perceived must be material, and thus itself movable, in accordance with the concept of a matter in general. Now, to think of it as moved, one may think it only as contained in a space of greater extent, and take the latter to be at rest. But the same can be done with the latter, with respect to a still further extended space, and so on to infinity. (4:559)

According to this passage, absolute space has a necessary regulative role as an idea of reason because anything in space must be ipso facto movable, as Kant already assumes in the preface to the MFNS (4:476),33 and therefore any finite reference frame tentatively regarded as absolute must also be represented as movable relative to a wider reference frame. Thus, any reference frame tentatively regarded as absolute always occurs within "a still further extended" reference frame, to infinity - or, in other words, to an ideal infinite reference frame. This account may raise some concern insofar as it may seem to trade on nothing more than the phoronomicaL fact that for any reference frame there is always a pure construction of a further relatively moving reference frame, in accordance with the Phoronomy's Principle of relativity (4:487). If this is indeed the case, then the mere pure form of motion is supposed to give rise to absolute space as an idea of reason. And, indeed, in introducing the passage quoted previously, Kant states that the concept of absolute space is the basis for "the concept of motion in reLative (movable) space (4:558), i.e. the basis for precisely this phoronomic concept of motion. l4 This is a concern because the faculty of reason in its proper, transcendental use is dedicated to the regulation of series of real grounds and consequences,'! whereas a pure - and essentially arbitrary - phoronomical construction

" Cf. Section 7.3 . .. The manner in which motion phoronomically conceived relies on absolute space is discussed earlier in the MFNS, in Phoronomy, Explication I, Remark 1 (4:481). " .. Reason demands ... in accordance with the principle: If the conditioned is given, then the whole sum of conditions, and hence the absolutely unconditioned, is also given, through which alone the conditioned was possible" (A409/B436).

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20 3

cannot be the ground of anything at all. Moreover, if this passage truly relies only on the form of pure phoronomical constructions in order to establish a proper role for the faculty of reason in experience, then it is entirely disconnected from the picture described in the Appendix to the Dialectic, and supposedly illustrated in Kant's example in the Appendix, whereby the progression toward an ideally extended spatial region is somehow an upshot of the fundamental role of reason in determining an ideal hierarchy of empirical concepts. J6 This concern is related to our earlier concern in Chapter 7, where we ask how Kant could claim in the MFNS preface that "only [by motion] can these senses be affected" (4:476), i.e. how Kant could claim that motion itself is a ground of sensation (or a reality), if it is conceived phoronomically as pure construction in intuition. J7 The answer I give there is that motion cannot be represented properly - i.e., represented as a magnitudeexclusively in phoronomical terms, because any change at all must be represented as caused in order to mitigate the opposing properties at the very moment of change. l8 In the case of change in motion in panicular, this is because the moment of change, according to Kant, requires us to represent a body as moving in opposite directions simultaneously within one and the same space or reference frame, which is only intelligible if the opposite motions are infinitesimal. The representation infinitesimal motions, in turn, requires us to think of them under some specific law of motion or some specific concept of cause. J9 A closer look at the concern regarding the status of absolute space as an idea of reason, I believe, reveals similar notions at work. One way in which causal grounding must be an element in the determination of motion is evident in the role that the law of gravitation plays in the procedure of attributing motion to objects, as we have seen in Section II.4. Also, the law of gravitation itself is determined as a causal law through an iterative process involving the repeated expansion of reference frames after the "Newtonian style," as we have seen in Section 11.3. By drawing these themes together, we can see that the objective attribution of motion is indeed based on the series of encompassing reference frames,

" In Section 9.3. I have already noted the difference between the operation of reason in the context of the mathematical antinomies. where it has a determinate use grounded entirely in the a priori form of intuition, and its transcendental role in regulating the subordination of concepts. where it lacks a determinare use. 17 Cf. Section 7.3" Cf. Secrion 7.2 . .. Cf. Secrion 7+

20 4

The All of Reality

JUSt as Kant intends it to be in the General Remark to Phenomenology,40 but only indirectly: it is an auxiliary process in the service of determining a specific concept of a cause - namely, universal gravitation - that is the more direct basis for objective motion. Thus, we can explain that the basic role of the faculty of reason is not simply to guide the series of pure reference frame expansions toward the idea of an absolute space, but rather thereby to pursue the grounds of appearances by gradually bolstering the empirical evidence for the validity of the inverse-square law of gravitation. 4' On this reading, then, the series regulated by reason is primarily the series of approximations of the law of gravitation rather than the series of reference frame expansions, and the regulative idea of reason is primarily that of a perfect conformity between the theory of gravitation and available observations rather than that of absolute space. This reading has the advantage of establishing that the faculty of reason is indeed somehow engaged in the determination of real grounds, and also begins to clarify the connection between the role of reason according to the MFNS and the role of reason as it is illustrated in Kant'S example in the Appendix, since in both places reason is taken to regulate the same process of deriving the law of gravitation. But this account is still not entirely satisfactory as it stands, since it does not explain how the Newtonian procedure of deriving gravitation, as it is construed by Kant, is supposed to be a process of articulating relations of "containment" or subordination among species and genera, or of" [reducing] given, apparently different forces to a smaller number of forces," as he puts it in the General Remark to Dynamics (4:534), and thus it does not yet identify the proper, transcendental use of reason.4' In other words, insofar as Newton's derivation is guided by reason, on the reading offered earlier, its successive steps appear to be concerned with gradually accruing evidence for one single empirical concept rather than with gradually bringing systematic unity to different empirical concepts. Therefore, it does not seem to be an example of what the Transcendental Ideal and the Appendix to the Dialectic characterize as the fundamental, proper use of reason.

,0

"[Firsr,] the concept of motion in r~lative (movable) space, second, rhat of motion in absolute (immovable) space ... The concepr of absolute space is the basis for all of rhem" (4:H8-9). " These considerations suggesr a way in which the iterative procedures Kant examines in the mathematical Antinomies might be essentially involved in the rranscendental procedure of determining the hierarchy of empirical concepts. This indirect transcendental significance might explain why the Antinomies generate inevirable ideas of reason (such as the idea of absolute space), wherC'dS orher indefinirely irerable procedures do nor (as counting does not involve an idea of the "highest number") . •' Cf. Section II.!.

Reality and the Derivation of Gravitation

20 5

Some progress can be made, however, by noting that the gradual determination of gravitation involves a structure that can be made to fit these requirements. The progression from step to step in the derivation typically involves an analysis or a division of the motion within the considered reference frame into two components: one, main component of the motion that is due to the influence of gravitation among the bodies within the system, and another, subsidiary component that is the perturbation of the first due to an influence from without the system. The relation between the composite motion and its main component, I propose, is how Kant envisages the relation between a specific empirical concept and its genus, or between a given moving force and a more fundamental moving force that explains its actions. The subsidiary component of the motion, accordingly, corresponds to the difference added to the genus, or the special conditions in which the fundamental moving force acts. For example, if we were to represent Saturn's corrected, unidealized orbit with a single rule of motion, that rule would deviate from Kepler's rules (since that rule would have to account for all the peculiar, distinctive deviations that actually stem from the influence of Jupiter, among other sources}.43 Thus, if that rule of motion were taken to be a law of nature or a representation of a cause that gives rise to Saturn's orbit, it would appear to be a peculiar, distinctive cause unlike any other to be found in the solar system. In this case it would appear, therefore, that we have found one of many "apparently different forces" or one of many distinct kinds of cause at work. However, a proper analysis of the motion of Saturn and other motions in the solar system into their respective constituents reveals that in fact they are all instances of one and the same moving force, viz. gravitation: the peculiarities that distinguish them are merely due to the fact that, for each motion, the force of gravitation is acting under different conditions that yield different perturbations. On my proposal, such an analysis is what amounts to a subordination of different species under a single genus. As we have seen in Chapter 10, the genus-species relation (along with the idea of a system organized by this relation) is seen in the Transcendental Ideal and the Appendix to the Dialectic to be a distinctively Kantian development of a Leibnizian (or perhaps Wolffian Leibnizian) tradition. One way in which Kant's view breaks with the Leibnizian tradition is based on Kant's ability to distinguish logical conceptual relations (basically, logical containment) from real ones (again, basically, real containment). For .,. Cf Section

11.3.

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Kant, relations oflogical containment, insofar as they are objectively valid, merely represent the manner in which we express real containment (somewhat analogously to the way that the table of judgments lists the manners in which we express the transcendental syntheses organized in the table of categories). Therefore, the terms oflogical containment should correspond to the terms of the relation of real containment that they are supposed to express. Now, for Kant, the relation of logical containment between genus and species is that of logical division - the genus is divided into species by the addition of marks (Merkma/e, differentiae, nota). In the framework I propose, the logical combination of a genus concept and specific marks is grounded in a real combination of motions: what we refer to as the main part of the motion (Le. the constituent motion generated by the bodies within a given system of bodies) is represented by the genus concept, whereas the perturbations (Le. the constituent motion generated by bodies outside the system) are represented as the differmtilU. Thereby, we have taken a significant step toward the proper interpretation of the logical notion of concept containment and its true import in Kant's philosophical system. The broader aim of this chapter has been to develop the view I propose in Chapter 10, that the transcendental role of reason described in the Transcendental Ideal - or reason's "proper use," as it is called in the Appendix - is to advance the project of articulating reality as a measurable force, thereby complementing the central project of the Transcendental Analytic I describe in Part II. One challenge for this view is to identify the manner in which the articulation of reality as a force, and specifically as a moving force, is served by reason's principle of systematicity. This is challenging, because Kant's notion of a moving force is the modern, Newtonian one, whereas his idea of a system is a hierarchy of genera and species in the Scholastic tradition. Kant himself, however, offers Newton's derivation of gravity as a paradigmatic example of genus-species systematization. Therefore, this chapter's analysis of Kant's example sets out to show how each step in the process of determining the force of gravitation can be seen as establishing a genusspecies relation. This analysis, relying on the details of Newton's method as they are reflected in Kant's MFNS, associates the combination of a genus and a difference into a species with the combination of one force's action and another action perturbing it into a specific motion. Thereby, this analysis reveals that each step in the process described in the example

Reality and the Derivation of Gravitation

20 7

essentially involves the combination of two motions in a single space. The problem of combining two motions in a single space, discussed in Section 7.4, is what makes the measurement of motion essenrially depend on real, moving causes, and thus crucially ties it with the categories of reality and causation. These considerations, I believe, shed light on the intricate, intimate connection between the project of articulating reality in space and time, pursued in the Anticipations and the Second Analogy, and the project of scientific inquiry, described in the Transcendental Ideal and the Appendix.

Conclusion

Books about the central themes of Kant's philosophy typically include an apology: so much has been said that saying more needs justifying. This book is somewhat in the contrary predicament, since relatively little atten~ tion has been given to its theme. It is, nevertheless, a central theme, and this book's approach aims to bring it to the fore. The interpretative approach of this book is based on the assumption that Kant's category of reality, often dismissed or neglected, is introduced in the CPR to represent a central problematic, i.e. as the concept of a prob~ lem that animates the Critical project from its historical inception, and at its systematic core. Thus, in a sense, much of the confusion and obscurity that attend this concept, and that have led commentators to dismiss or neglect it, are in fact proper to it, and attest to the Significance and depth of the problem it represents. Also, some of the murkiness surrounding several other elements of Kant's philosophy can be cleared once they are understood to be in the service of resolving the problem of the category of reality. The problem is that of treating sensible objects in quantitative terms. Broadly considered, it is natural to find such a problem quite central to Kant's thought, since the mathematization of nature is a characteristic con~ cern of his intellectual epoch in general, and of his Critical philosophy in particular. The distinctive contribution that this book aims to make begins with recognizing the category of reality as the locus of these concerns, both in the historical aspect and in the systematic aspect of Kant's thought. With these brief concluding remarks, I wish to gesture at some of the widerranging advantages and challenges that this recognition entails. I have chosen to emphasize here certain features, already expressed or implied in the main body of the book, that depend on its overall interpretative approach more than on its details. My hope is that even the reader who has reached this book's Conclusion without being swayed by its argument will have seen some value in the exercise nonetheless. 208

C()ncluJion

20 9

One advantage of this approach lies in providing a deeper sense of the historical roots of Kant's Critical philosophy in the Early Modern tradition, especially in Leibniz's philosophy. 'Ihis advantage stems from the observation that the category of reality is in some ways a Kantian descendent of the traditional concept of J'ubJ'tllntiai form. This is a rich, important connection because the concept of substantial form is pivotal in Early Modern thought: for Suarez, it helps accommodate a modern attitude to natural philosophy within a traditional, Scholastic framework; for Descartes, it keeps natural philosophy mired in tradition, and deprives it of the intelligibility of mathematics; for Leibniz, it fixes natural philosophy on firm metaphysical ground, and bestows on it the intelligibility of traditional logic. Once we establish a connection between the concepts of reality and substantial form, then, we can locate Kant's ideas in this (somewhat whiggish, but instructive) retelling of the intellectual history. The basic metaphysical assumptions that compel Leibniz to stipulate substantial forms as the ultimate, perfectly unified, and hence dimensionless grounds of phenomena make it difficult for him to account for the validity of mathematical representation in natural science. I believe that Kant inherited from Leibniz similar basic assumptions, and thus confronts a similar basic difficulty in many of his works, Critical and preCritical alike. Therefore, while there are already excellent accounts of the Leibnizian, or Wolffian Leibnizian, themes in Kant's thought, I believe that this study contributes to our understanding of the nature and extent of his most fundamental Leibnizian commitments. A second advantage of this approach is the insight it provides into the historical roots of Kant's Critical philosophy within his own pre-Critical body of work. A prominent concern of the pre-Critical period, as I have noted, is the broadly Leibnizian concern to account for the relationship between mathematical representation and metaphysical grounding, an account that would decide mathematics' claim for objectivity. This concern culminates in the Inaugural Dissertation, which suggests how mathematical representation can be objective without reducing objects to mere mental entities: while mathematics is objective only insofar as it pertains to phenomenal objects or appearances, this does not mean that mathematically represented appearances are merely "imaginary" or "ideal," because they are metaphysically grounded in genuinely independent substances. However, soon after publishing the Inaugural Dissertation, Kant realized that the view suffers a fundamental flaw, in what proved to have been the crucial turn toward the Critical philosophy. Kant's realization, on this approach, is that the very same argument designed to show that

210

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mathematical representation can be objective also shows that mathematical representation is necessary for objectivity. This undermines the picture of the Inaugural Dissertation, because that picture requires some manner of objective representation that does not involve mathematical representation: the concept of metaphysical grounding as such, along with some of its corollary concepts, is supposed to be objective but not mathematizable. Thus, in the letter to Herz that documents the Critical turn, Kant presents his break from the Inaugural Dissertation as the realization of a troubling contrast between the sound objectivity of the concepts of mathematical representation - i.e., quantities - and the suddenly dubious objectivity of the concepts of the metaphysical grounding of sensations - i.e. qualities or realities. In our attempt to grasp the crucial step leading from the Inaugural Dissertation to the CPR, then, it is helpful to keep the concept of reality at the focus of our attention, as Kant himself does. A third advantage of this approach consists in that the category of reality, once it is considered as a problematic concept, sets a cenain agenda or program for the Critical system. By reading the various chapters involved in this program with regard to the roles they are meant to serve in it, some textual puzzles become easier to resolve. I have relied on this approach to address such puzzles as why the Anticipations consist simply in the claim that reality is mathematizable; why the CPJ(s main discussion of the law of continuity occurs in special connection with the category of reality; to justifY the close association - sometimes bordering on conflation - that Kant makes between the categories of reality and cause; and to explain the connection between the category of reality and the idea of the All of reality, to mention a few examples. More generally, I believe that this program highlights a certain argumentative progression within the CPR, and thereby reveals the organic manner in which some of its sections are interrelated: for instance, in the context of this program, there emerges something of an organic unity among the four headings of the table of categories. This fourfold structure is a central organizing principle of Kant's so-called architectonic - i.e. the principled construction of his metaphysical system - which recurs in different guises almost at every turn in the Critical works. A lingering suspicion regarding Kant's table of categories has long been that its composition is itself unprincipled or arbitrary, and that he gives no good reason to suppose it is either correct or complete. On this book's approach, however, we can see a single argument progressing through the headings of the table in sequence: Kant first presents the categories of quantity, then seeks to bring them to bear on quality, and turns to the categories of relation to achieve

Conclusion

2II

it. This argument, I believe, may have served as a touchstone for Kant's choice of these concepts and their order in the table, and so this approach may hold the key to the completeness of the table of categories.' This approach also reflects on another architectonic issue: the intricate relationship between the CPR and the MFNS within Kant's Critical system. To the varied considerations available in the literature surrounding the MFNS, this book adds the observation that reality can be treated as a magnitude only ifit is represented as a ground for spatio-temporal change, i.e. as a moving force. Therefore, it seems that the program set forth in the CPR cannot be accomplished without resources that are only described in the MFNS, so that Kant's general metaphysics essentially depends on the special metaphysics of force and matter. This last observation, however, raises another well-worn concern: if the MFNS describes some of the conditions required for reality to be treated as a magnitude, and so to be fit to serve its necessary role in experience, it would seem to follow that these conditions are transcendental conditions, i.e. a priori necessary conditions for the very possibility of experience. This would put them on a par with the transcendental principles of the understanding listed in the Transcendental Analytic, despite the fact that Kant is careful to demarcate the considerations offered in the MFNS from those of the CPR, insisting that only the latter belong to the transcendental part of the metaphysics of nature. This concern is an expression of a broader challenge for the view I develop in this book: by following a single thread of argument from the category of reality, through the category of causation, to the concept of force, it threatens to blur the demarcation in character and standing between the principles of general metaphysics and the principles of scientific inquiry. Yet another expression of the same broad challenge is in the tenuous status of the principle of systematicity or the uniformity of nature: on this book's approach, the applicability of the category of reality in experience seems to depend on our ability - at least in principle - to represent particular moving forces, i.e. to conceive of particular natural laws of motion

, This book does not directly discuss the fourth heading of the table of categories, namely, modality. Instead, as the argument's progress is presented in it, the discussion of the third heading, and specifically the category of causation, is followed by a discussion of causes of motion in natural science. However, I believe that an account of the categories of modality, and their development in the Postulates of Empirical Thinking, that brings out their thematic proximity to Kant's theory of natural science can hell' assign the fourth heading to a position within the argumentative progression that corresponds to its positioll in the order of the table of categories.

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successfully. But, although this appears to make the capacity to grasp laws of nature one of the conditions for the possibility of experience in general, Kant insists that we are not in a position to assert objectively that laws of nature are there to be grasped after all; instead, all we can do is subjectively assume that there are valid laws of nature, as a matter of regulative presupposition. Again, this is tenuous because, while scientific inquiry seems to be a necessary condition for experience in general, its definitive principles and presuppositions somehow fail to acquire the same objective status that is proper to other necessary conditions for experience, such as space, time, and the pure categories and principles of the understanding. To my mind, this challenge points to one of the most interesting, and daunting, ways in which the picture underlying this study is in need of further elaboration. In Chapter 9, I have suggested that the challenge might be met by extracting from Kant's writings a sense in which the concepts and judgments that define the form of our experience in general cannot themselves be regarded as constituent elements of our experience or of our body of systematic knowledge. In that sense, the pure categories and principles of the understanding neither imply nor follow from the concepts and judgments that we can claim to know - hence, Kant's reluctance to admit what appear at first to be straightforward inferences. Instead, to take the example of the Second Analogy's causal principle, the manner in which its universal validity is featured in our systematic knowledge is indirect: in the form of individual causal judgments, and, most importantly, through the regulative ideas of reason that guide scientific inquiry. Thus, in Section 10.1 n. 3 and Section 10.3 n. 30, I have suggested a tentative connection between the ideal system of all possible concepts envisioned in the Transcendental Ideal and the Appendix to the Dialectic, on the one hand, and the systematic, categorially unified experience invoked in the Transcendental Deduction, on the other. Clearly, without a detailed analysis of the Transcendental Deduction, these suggestions cannot go very far, but such an analysis exceeds the scope of what this book sets out to accomplish. This book begins with drawing attention to the questionable position of the category of reality from the standpoint of transcendental idealism: as a representation proper to appearances, or to what objects are for us, how can it also be a representation of the independent ground of appearances, or of the "transcendental matter of objects as things in themselves"? Until it is complemented with a detailed interpretation of the Transcendental Deduction, which would deepen our grasp of the Kantian notions of "appearance" and "thing in itself," our study cannot

Conclusion

2I3

fully resolve this puzzling feature of the category of reality. However, it already reveals that this puzzle cannot rest on a mere ambiguity, equivocation, or confusion. Rather, it shows that the concept's applicability to appearances essentially involves an engagement with scientific inquiry, which points toward the infinite reaches of a perfect, ideal science; precisely in order to find its place within the discursive, limited world of appearances, the category of reality must encapsulate the idea of the vanishing horizon beyond our limitations, at which would lie the thing in itself.

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Philosophisch-Historische Classe 8: 306-28, 1852.

Index

Adams. Robert M., 44n24. 41n26 affinity of forms. See law of continuity. continuity of forms Allison. Henry. 140 Anderson. R. wier. 167n22 Antognaxza. Maria Rosa. 17nl Aristotle. 157 Baumgarten. Alexander G .• 165 Bayle. Pierre. 39. 54. 56 Ikck. Lewis W.• 55m3. 80n6. 90m9. 140n2 Iknnett. Jonathan. 103n7 Ikrnoulli. Johann. 37 Bos. H. J. M .• IIn3 Boscovich, Roger Joseph. 38m4 Bouvet. Joachim. 44n24 Boyle. Robert. 28. 29 Brittan. Gordon G .• IIIn3 Brown. Gregory. 35n8 Buchdahl. Gerd. 139. III Bussotti. Paolo. 53n6 Carraud. Vincem. 21n7 Caspar. Max. 53n6 Cassirer. Ernst. 51m3 Catalan. Abbe. 38nII Cohen. Bernard I.. 195 concept subordination, 60-62. 145n7, 151-52, 157-58. 161, 165. 168. 174. 190.194. 2.03, 204-