kant on marks and the immediacy of intuition

The Philosophical Review, Vol. 109, No. 2 (April 2000)

Kant on Marks and the Immediacy of Intuition

Houston Smit

The distinction between concept and intuition is of the utmost importance for understanding Kant's critical philosophy. For, as Kant himself claimed, all the distinctive claims of this philosophy rest on, and develop out of, a detailed account of the way all our' cognition of things requires both intuitions and concepts.2

Unfortunately, interpreting Kant's distinction between concepts and intuitions remains a vexed matter. The locus classicus for these controversies is the Critique of Pure Reason's famous taxonomy of representations (called the Stufenleiter, or "step-ladder"):

The genus is representation in general (representatio). Under it stands representation with consciousness (perceptio). A perception [Perception] which relates solely to the subject, as the modification of its state, is

I am grateful, above all, to Tyler Burge for his extensive and incisive criticisms of all of the many drafts this paper has undergone. This paper has also benefited greatly from Robert M. Adams's and Charles Parsons's insightful comments and expert advice. Torin Alter provided generous and judicious comments on the penultimate draft. I am also grateful to the following people for helpful discussions and comments on earlier drafts: Rogers Albritton, Tim Bayne, Thomas Christiano, Suzanne Dovi, Bill Fitz- patrick, Sean Foran, Eckart Forster, Daniel Guevara, Thomas Hofweber, Andrew Hsu, Michael Jacovides, David Kaplan, Keith Lehrer, Frank Me- netrez, Marleen Rozemond, Daniel Sutherland, Joseph Tolliver, Carol Voeller, and Eric Watkins. Finally, I am indebted to two anonymous referees for the Philosophical Review for invaluable criticisms and suggestions.

"Our' in 'our cognition' is shorthand for 'human', a practice I will follow throughout the present essay.

2See the Amphiboly chapter of the Critique of Pure Reason, especially A 269 / B 325f., where Kant presents his realization that concepts and intuitions are different in kind as key to his advancing beyond his predecessors. In particular, he traces the shortcomings of the systems of Locke and Leib- niz to their failure to appreciate the true nature of this distinction: the former made the mistake of assimilating concepts to intuitions, the latter, the reverse mistake; their conflations blinded them to the distinctive con- tribution each makes to our cognition of things. Passages from the first critique will be cited in this, the usual, fashion: the first (1781) edition pagination following 'A,' and the second (1787) edition pagination following 'B'. All other citations from Kant's works will be from the standard German edition of his works, Kants Gesammelte Schriften, edited by the Royal Prussian Academy of Sciences (Berlin: Georg Reimer, later Walter de Gruy- ter, 1900- ), with volume and page numbers separated by a colon.

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sensation (sensatio). Objective perception is cognition [Erkenntnis]. This [Diese, so objective perception3] is either intuition or concept. The former relates to the object [bezieht sich auf den Gegenstand] immediately and is singular, the latter, mediately, by means of a mark [Merkmal] which several things may have in common. (A 320 / B 376- 77)

Kant's distinction between concepts and intuitions turns, then, on

two points of contrast: intuitions are immediate and singular, con-

cepts, mediate and general. The import of both of these points of

contrast, and their relation to each other, continue to be a subject

of debate among Kant scholars. In particular, there is still much

disagreement over the import of the immediacy criterion that Kant

sets for intuition.4

I will argue that this debate has been hampered by misunder-

standing of Kant's notion of a mark. Examining the account of

marks he develops in his writings on logic leads to a new reading

of the criterion of immediacy he sets for intuition.

I begin in section 1 by briefly reviewing three interpretations of

the immediacy criterion offered in the recent secondary litera-

ture.5 I then identify a crucial misunderstanding common to all

parties to this debate: the assumption that the immediacy of an

intuition consists (at least in part) in its not relating to its object

by means of marks. In section 2, I sketch the interrelated senses

in which Kant uses 'object', 'objective perception', and 'cognition'

in the Stufenleiter, bringing out their connection to his notion of a

really possible object of thought. In section 3, I elucidate Kant's

definition of a mark as a part of his essentially Leibnizian concep-

tion of predication. In section 4, I examine his pivotal, yet almost

3'This' translates 'diese, and thus refers back to 'eine objective Perzeption' a point for which I am indebted to an anonymous referee for the Philo- sophical Review. As this referee also pointed out, Kant allows for cognitions-for example, practical ones, or the ones had in general logic-that are not objective perceptions. In section 2, I explain how, in the sense in which Kant employs 'cognition' in the Stufenleiter, these cognitions are not objective perceptions.

4The term 'immediacy criterion' is due to Charles Parsons; see his "Kant's Philosophy of Arithmetic," originally printed in Philosophy, Science, and Method, ed. S. Morganbesser, P. Suppes, and M. White (New York: St. Martin's Press, 1969) and reprinted, with a postscript, in his Mathematics and Philosophy (Ithaca: Cornell University Press, 1983), 110-49.

5My overview of these three readings is indebted to Parsons's incisive discussion in his postscript to "Kant's Philosophy of Arithmetic."

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entirely overlooked, distinction between intuitive and discursive marks. In section 5, I connect the foregoing to the debate over Kant's distinction between intuitions and concepts, and offer a new reading of the mediacy of concepts and the immediacy of intuition.

1. Three Readings of the Immediacy Criterion on Intuition

The authors who have recently proposed and defended different readings of the immediacy criterion agree on the import of the contrast between the singularity of intuitions and the generality of concepts. What divides them is their understanding of the contrast between the immediacy of intuitions and the mediacy of concepts.

Jaakko Hintikka ascribes to Kant the view that an intuition is simply a singular representation, the counterpart of a singular term in the latter's system of representations.6 On Hintikka's reading, the generality and the mediacy of a concept amount to the same thing, namely, a concept's relating to its object through marks, where a mark is construed as a property at least potentially had by more than one thing. Hintikka thus holds that the immediacy of an intuition consists in its not relating to an object through marks and that the immediacy criterion on intuition is merely a logical corollary of the singularity criterion.

Charles Parsons agrees with Hintikka that, in being singular, an intuition is the analogue of a singular term. But he contends that the immediacy of an intuition consists, not merely in its not relating to its object through marks, but also in its being a cognition in which the object is "directly present to the mind, as in perception." Parsons maintains, then, that the immediacy criterion is not merely a logical corollary of the singularity criterion, but an independent constraint. What is more, Parsons holds that, on Kant's view, this direct presence has a certain epistemic import: due to its immediacy, intuition is "a source, ultimately the only source, of

6For Hintikka's most detailed defense of this reading, see "On Kant's Notion of Intuition (Anschauung) ," in Kant's First Critique, ed. T. Penelhum and J. J. MacIntosh, (Belmont, Calif.: Wadsworth, 1969), 38-53. The assumption that the relation of intuitions to objects can be understood on the model of the reference of singular terms has not gone unchallenged. See Manley Thompson's classic article, "Singular Terms and Intuitions in Kant's Epistemology," Review of Metaphysics 26 (1972) and Kirk Wilson, "Kant on Intuition," Philosophical Quarterly 25 (1975).

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immediate knowledge of objects." Parsons goes on to remark that, given his construal of the immediacy criterion, the fact that mathematics is based on intuition implies that it is "immediate knowledge and, even though synthetic a priori, does not require the elaborate justificatory arguments which the Principles do (A87=B120)."7

Robert Howell takes a middle course between Hintikka and Par- sons. He agrees with Hintikka that A 320 / B 376 is to be read as claiming that the immediacy of intuition consists simply in its not relating to its object through marks.8 This he takes to be Kant's strict definition of the immediacy of intuition. But he agrees with Parsons in holding that the immediacy of intuition is not a mere corollary of its singularity. Moreover, he suggests, Kant comple- ments his strict definition of intuition's immediacy with a positive conception of this immediacy, analogous to the contemporary notion of the direct reference had by demonstrative terms.9

All three commentators, then, hold that the immediacy of intuition consists at least in part in its not relating to objects, as concepts do, through marks.10 Call this the standard minimal reading of the immediacy criterion. This reading is mistaken. Examining Kant's notion of a mark, and his account of the way we cognize things through marks, will show that concepts are not the only objective perceptions that relate to objects through marks: our intuitions, being sensible, are also objective perceptions that relate to objects through marks." What distinguishes sensible intuitions

7"Kant's Philosophy of Arithmetic," 112; see also the postscript, 144- 46.

8"Intuition relates immediately to its object simply in that the relation is not (as is that of concept and object) mediated by marks or characteristics" ("Intuition, Synthesis, and Individuation in the Critique of Pure Reason," Noius 7 (1973): 210f.).

9Howell, "Intuition, Synthesis, and Individuation in the Critique of Pure Reason," 211-22. Others had already proposed that Kant's notion of intuition should be understood on the model of demonstratives; see, for instance, Wilfrid Sellars, in Science and Metaphysics (London: Routledge and Kegan Paul, 1968), 3-8.

10In a recent article, Charles Parsons takes Kant's claim in this passage and elsewhere that intuition relates to an object immediately to mean "at least that it does not relate to an object by means of marks" ("The Tran- scendental Aesthetic," in The Cambridge Companion to Kant, ed. Paul Guyer (New York: Cambridge University Press, 1992), 64).

1'On Kant's conception of intuition, it is (at least logically) possible that

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from concepts is that they are objective perceptions that relate to objects through singular, as against general, marks. It is neither a part, nor a logical consequence, of Kant's notion of intuition that an intuition does not relate to its object through marks. Seeing how concepts are objective perceptions that relate to objects through general marks will clarify both the mediacy of concepts and the immediacy of intuition.

2. 'Object' and 'Cognition'

Before turning to Kant's notion of a mark and his account of how all our objective perceptions relate to objects through marks, I will discuss the relevant and highly interrelated senses of 'object', 'objective perception', and 'cognition'.'2

Near the outset of the Second Analogy of Experience, Kant draws a distinction between two senses of 'Objekt':

Now one can, to be sure, call everything, and even every representation, insofar as one is conscious of it, an object [ Objekt], only what this word is to mean in the case of appearances, not insofar as they are (as representations) objects [Objekte], but rather only insofar as they designate an object [Objekt], requires a deeper investigation. Insofar as they are, only as representations, at the same time objects [Gegen-

there are intuitions that do not relate to objects by means of marks. Con- cepts, in contrast, relate to objects by means of marks as a matter of logical necessity. Intuitions that do not relate to objects by means of marks would be intuitions had by a being with intuitive understanding, an understanding that does not cognize objects through concepts and thus does not cognize things through marks (intuitive as well as discursive) at all. Kant's notion of an intuitive understanding, though notoriously difficult, is one that plays a central role in his critical philosophy. Such an understanding would be archetypal: it would create the things it cognizes, through its cognition of them. It is thus akin to the kind of understanding (at least of created things) traditionally ascribed to God. I say a little more about Kant's notion of intuitive understanding in section 3, as well as in note 48; one of the advantages of the account of marks developed in section 3 is that it serves to clarify this notion.

12Any plausible reading of these notions needs to address complex and still unresolved interpretive problems posed by a myriad of extremely difficult texts, and is thus apt to prove controversial. The one I offer is orig- inal, and consequently in need of extensive development and defense. In the present section, however, I will merely state the reading in outline, citing a few crucial supporting passages. The outline should serve to orient the reader for subsequent sections, which will provide, among other things, the needed development and defense of this reading.

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stdnde] of consciousness, they do not differ from their apprehension, that is, from their being taken up into the synthesis of the imagination. (B 234-35 / A 189-90)

The first sense of 'Objekt' is that of anything insofar as one is conscious of it, the notion of what is consciously represented. What makes something an Objekt in this sense is its making up the content of a conscious representing. In this passage Kant uses 'representation' in his customary sense to mean 'represented'. And in claiming that "everything, even every representation," can, "insofar as one is conscious of it," be called an Objekt, he implies that anything that is consciously represented, so including something whose esse is not percipi, is as such an Objekt in the first sense. The proviso "insofar as one is conscious of it" in introducing his first sense of 'object' must not be read in a sense that renders all objects ideal-that is, as specifying that objects can exist only in being consciously represented.

Kant's second sense of 'Objekt restricts the first, by specifying further that an Objekt be something that a perception designates and so something distinct from that representation. For example, one can have a mental image of a tree in such a way that one is conscious, not only of this image, but also thereby of that tree, something distinct from that image. What we are conscious of, in being conscious of the tree, is an Objekt, not only in the first, but also in the second sense. An Objekt in the second sense is what we are conscious of through a representation.

Let's consider the Stufenleiter in light of this distinction between Kant's two senses of 'Objekt'. On pain of its being redundant, 'objective' in 'objective [objektive] perception' must be a cognate of 'Objekt' in the second sense: since Kant defines 'perception' as "representation with consciousness," all perceptions are as such Objekte in the first sense.13 This suggests that what makes a perception objective is its being a representation of which one is conscious in such a way that one can thereby be conscious of an Objekt in the second sense. A sensation, in Kant's sense, is a representation (a represented) that is an Objekt in the first sense: this is why the Stu-

13Kant also takes 'Objekt' in the more restrictive sense when he uses its cognates in the phrases 'objective validity', and 'objective reality'. For a representation to have objective reality is for it to characterize the reality of a thing, that is, the quality of its activity as it exists outside of being represented.

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fenleiter classifies sensations as a species of perception, representation with consciousness. What makes them subjective is not that they are Objekte only in the first sense and not in the second. What makes them subjective is that they are representations of which we are conscious in such a way that we cannot thereby also be conscious of them so that they designate an object. They are perceptions that can be related to the subject, but only as its representations: as Kant puts it, a sensation "relates solely to the subject, as a modification of its state." The concept of a sensation, in contrast, is a representation that relates to other representations of the subject. It designates an object, and this is what makes it an objective perception.'4

But at B 234-35 / A 189-90 Kant employs another term stan- dardly translated with 'object'-' Gegenstand'. A Gegenstand in Kant's sense is a thing insofar as it is consciously represented and so constitutes an Objekt.'5 And a thing (Ding res) in the relevant sense is, in turn, not just anything, but something real (etwas reales): something whose esse is not percipi but has its being, so that it can exist, outside of being represented. Kant holds the Aristotelian view that what makes something a thing is its being the subject of activity. Numbers, figures, concepts-all on Kant's view are ideal, not (even empirically) real.'6

Something that is not a Gegenstand can be an Objekt in the second sense: for example, the geometric figure of which we are conscious in doing geometry is, on Kant's view, not real, and so not a Gegen- stand; however, it is an Objekt that one's geometric concepts and intuitions designate. Moreover, Kant's remark that "appearances,

*14Note that the same material representational content-that common to the sensation of pain and the concept of pain-can constitute different representations, in Kant's sense of 'representation'. I will develop this point further in section 4.

'5Keep in mind that B 234-35 / A 189-90 implies that a thing can be an Objekt in the first sense.

16I provide textual grounds for these readings of 'Dinge and 'Gegenstand' in an unpublished manuscript, "What Can We Know about Things in Themselves?" The connection between these two notions is evident in Kant's claim that we can give content to our concepts of a Gegenstand only by relating them to contents given in our sensibility, where sensibility is "the capacity (receptivity) to acquire representations through the way in which we are affected by objects [Gegenstdnden]" (A 19 / B33); he makes this claim, for example, at B147, in an important passage that I discuss in note 20, below.

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insofar as they are, merely as representations, at the same time, Gegenstdnde of consciousness, do not differ from their apprehension" implies that a Gegenstand can be an Objekt in merely the first of the two senses Kant distinguishes. So considered appearances are contained in consciousness "merely as representations" and do not stand for an Objekt, so considered, appearances, like sensations, relate "only to the subject as a modification of its state." What makes appearances so considered, nonetheless, Gegenstdnde

of consciousness is that in this consciousness we are conscious of our own activity in uniting them.

Notice that in the Stufenleiter Kant contrasts concepts and intuitions in respect of the ways in which they relate to a Gegenstand, a thing insofar as it constitutes an Objekt. Moreover, the Gegenstand Kant has in mind is an Objekt in the second sense, for it is the Gegenstand to which an objective perception relates, and so the Gegenstand it designates. In light of what we have seen about Kant's use of these terms, I propose that a perception is objective, in the sense of the Stufenleiter, if it is one in which the subject is conscious of a content that she can predicate of a thing in cognizing it: it is a representation that can make up the content of an act of cognizing a thing.'7 Unless I specify another sense, I will hereafter use 'object' to refer to a Gegenstand that is an instance of an Objekt in the second sense.'8

We can clarify what makes a perception objective by looking at Kant's conception of what it is to cognize (erkennen) a thing. In the Logic he characterizes cognizing as a degree of the "objective content" of our cognition:

The third: kennen is to represent something in comparison with other things in respect of identity as well as diversity. The fourth: erkennen, kennen with consciousness. (Logic, Introduction ?8; 9:64-65)

17Note that what makes any perception an objective one, is only the possibility of its constituting, perhaps only with other representations, a Ge- genstand. In geometry, we employ the concept triangle to think, not about a thing, but about the figure. This concept is, nonetheless, an objective perception, because we can use it to think of a triangular thing.

18This sense seems close to the sense of 'object' that Strawson dubs 'weighty'; see The Bounds of Sense (New York: Routledge, 1989), 73. Straw- son, however, does not distinguish Objekt and Gegenstand, and so does not specify that the sense he has in mind has the force of being ontologically weighty.

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Notice that being conscious merely of an object in general (as we are when we represent a thing merely in the categories) does not amount to cognizing a thing. To cognize a thing, one must be conscious of a thing in respect of its determinate identity, so as to distinguish it from (some) other things. Moreover, as Kant's con- trasting a thing's identity with its diversity from other things suggests, to cognize a thing is to distinguish it from other things, not merely negatively, in respect of what it is not, but also positively, in respect of what it is. The objective content of our cognition thus consists in content through which, in cognizing a thing, we are conscious of that thing in respect of some aspect of its distinctive intrinsic constitution. It follows, moreover, that Kant's notion of an objective perception is broader than that of an objective content. For the categories are objective perceptions, insofar as they constitute content that we can-and indeed must-predicate of objects in any act of cognizing them (this is why the Stufenleiter includes them as instances of objective perceptions). However, as our concepts of an object in general, they do not themselves constitute objective content.

The thing the identity of which one is conscious in cognizing it is the object that one thereby cognizes. Consider an example of an intuition, one species of objective perception. An experienced birder and I both get a clear look at a bird. The birder identifies it as a Hudsonian Godwit, and I, merely as a shorebird. Nonethe- less, our intuitions are the same-we both see the various identifying properties of the Hudsonian Godwit (the curved bill, the markings, and so forth). And, Kant would say, we both have the same cognition (considered in respect of its objective content), despite the difference in the manner in which we have it: I have a mere intuition of the Hudsonian Godwit, whereas the content of the birder's cognition is at the same time both an intuition and a concept of the Hudsonian Godwit.19

19Consider Kant's contrast between the cognition had in looking at a house by, on the one hand, a savage lacking the concept of a house, and, on the other, by someone who has that concept (Logic, Introduction ?5; 9: 33). Kant says that both have "the same object before him" and thus "the same cognition, in respect of its matter," but that in the savage this cognition is a mere intuition, whereas in the latter the cognition is "intuition and concept at the same time."

Moreover, the consciousness of an objective content had in an objective perception needn't be one of that content as an objective one. Indeed, on

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It may be surprising that Kant draws his distinction between concepts and intuitions as one between two species of objective perceptions-perceptions that we can relate to things in cognizing those things. After all, there are concepts (for instance, that of the faculty of thought or the categorical form of judgment) that are not concepts of a Gegenstand. But Kant often uses 'concept' in a restrictive sense, on which a concept is a general representation through which one can cognize, not just any subject matter, but a thing. Indeed, more generally, throughout the first critique Kant typically uses 'cognition' to refer to objective perception.20

Kant's account, the same holds of the consciousness had in cognitions that are concepts, or even both "concepts and intuitions at the same time." The cognition had in geometry is one in which one is conscious of an objective content-the content triangle, for instance, is one through which one can be conscious of the identity of a body in an act of cognizing it. But Kant is a conceptualist about geometric figures, and denies that figures are things: not being possible existents, they cannot exist outside of being represented (see next note). Since in doing geometry one is concerned merely with the figure, and not with triangular things, it follows that in doing geometry one has cognition, despite not being conscious of objective contents as objective contents.

20In the B edition Transcendental Deduction we find a crucial case of such usage, one concerning mathematical concepts:

Through the determination of pure intuition we can acquire a priori cognition of objects [Gegenstdnden] (in mathematics), but only in regard to their form, as appearances; whether there can be things which must be intuited in this form, is still left undecided. Mathematical concepts are not, therefore, of themselves cognition, except on the supposition that there are things which allow of being presented to us only in accordance with the form of that pure sensible intuition. Now things in space and time are given only in so far as they are perceptions (that is, representations accompanied by sensation)-therefore only through empirical representation. Consequently, the pure concepts of understanding, even when they are applied to a priori intuitions, as in mathematics, yield cognition only in so far as these intuitions-and therefore indi- rectly by their means the pure concepts also-can be applied to empirical intuitions. (B 147)

Kant uses 'cognition' in a sense in which mathematical concepts constitute cognitions only in virtue of being contents that can be related to things in cognizing (and not mere thinking) them-so are cognitions of objects. But it is only insofar as these a priori intuitions make up the form of empirical intuitions (objective perceptions that relate to an object in an experience of that object) that mathematical concepts constitute representations of things. This is why Kant makes it a condition of mathematical concepts constituting cognitions that a priori intuitions are partially constitutive of experience. Indeed, the second step of the B edition Deduction is, in part, devoted to establishing that this condition holds-a point I intend to develop elsewhere.

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In the rest of the paper, I will follow Kant in using 'concept' and 'cognition' in this restrictive sense. A mark, in the sense with which we will be concerned, is an identifying property through which we can cognize a thing; Kant's notion of a mark, then, is that of a property through which we can cognize, not just any subject matter, but things.2'

Before I turn to Kant's account of a mark, however, I need to introduce a further distinction between two senses in which he employs the term 'cognition'. What it is to cognize a thing in the sense I have explicated thus far must be distinguished from an epistemologically more restrictive sense on which the first critique focuses. In particular, Kant holds that cognizing a thing requires more than merely thinking of it (B xxvi n.). Merely thinking of a thing requires only that one not contradict oneself in forming

Kant holds that the Objekte of pure intuition (geometric figures and numbers) are not things: they are ideal, and not real, because not capable of existing outside of being represented. Mathematical concepts are predicable of Gegenstdnde, and so constitute cognitions, only in virtue of the fact that the syntheses they signify are ones that proceed in accordance with the axioms of intuition and the anticipations of perception. For, in according with these principles of pure understanding, mathematical concepts constitute contents that are predicable, through the categories of quality and quantity, of Gegenstdnde. Thus, Kant claims that mathematical concepts do not, of themselves, constitute cognitions-that is to say, simply in virtue of the use to which we put them in (pure) mathematics- "except insofar as one presupposes that there are things that can be presented to us only in accordance with the form of that pure intuition."

I am grateful to Tyler Burge for pointing out how I had been misreading B 147. The present observations about Kant's conception of mathematical concepts develop a point made originally by Thompson ("Singular Terms and Intuitions in Kant's Epistemology," 338-39) and discussed instructively by Parsons in his postscript to "Kant's Philosophy of Arithmetic" (147-48). Friedman puts this point as follows: the objective reality of mathematics depends on the possibility of applied mathematics, and this possibility is established not in mathematics, but a priori in transcendental philosophy, through the arguments for the mathematical principles of the pure understanding (note: not empirically, on the grounds adduced in applying mathematics in experience). See Friedman's Kant and the Exact Sciences (Cambridge: Harvard University Press, 1992), 102. The first two chapters of this book contain a lucid and insightful discussion of Kant's theory of concepts and intuitions, as well as an important new interpretation of the nature and motivation of Kant's theory of mathematical construction.

21See, for instance, Kant's remark in the introduction to the first critique that necessity and universality are marks of a priori cognition (B 3); here 'mark' is used in the broader sense, which will not be in question in the definitions we will be examining.

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one's concept of that thing, and he refers to this, the possibility of the concept of a thing, as "merely logical possibility" (ibid.). And he maintains, further, that the nature of things might not permit the existence of what one consistently thinks of in a concept of an object, so that not every possible concept need have a "corre- sponding object in the sum-total of all possibilities" (ibid.). In other words, what one thinks of as a possible thing needn't be a possible thing. So, for instance, on Kant's view, although the thought of a thing that is both round and square is possible, no such thing is possible: we can see that the common nature shared by all the phaenomena of our outer sense (the nature of matter) does not permit the existence of such a thing. And although the concept of God as the most real being is possible, Kant argues that we cannot adjudicate the possibility of such a being itself (at least on theo- retical grounds). In order to cognize a thing, as against merely think of it, we must be able to establish the possibility of that thing (ibid.). Let's call thoughts of things that satisfy this epistemic condition 'genuine cognitions'.

The overarching project of the first critique is to articulate the nature of our understanding, our capacity to cognize objects, insofar as it constitutes a faculty of genuine cognition. Kant uncovers the origin of our various a priori concepts of objects, and the roles they play either in constituting our experience or in regulating our pursuit of empirical cognition. And he does all this in the service of explaining the grounds on which we may legitimately accord real possibility to our concepts of objects and thereby determining the bounds of our capacity to have insight into the natures of things.22 So it should not be surprising that the first critique tends to employ 'cognition' in the epistemically restrictive sense. The

Stufenleiter, however, uses 'cognition' and 'objective perception' in the epistemically permissive sense, to refer to the content of a cognizing that need not constitute any more than a mere thinking of a thing. For it counts ideas among objective perceptions, and thus as cognitions (A 320 / B 377), and ideas are concepts, such as

22To be sure, the Transcendental Deduction of the Categories provides an account of how we can grasp the nature of our faculty of mere thought, by explaining the origin and the status of our grasp of the rules and principles that constitute this nature (see B 133-34 n.). But it does so in the service of explaining how the categories have a valid a priori applicability to objects in genuine cognition.

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those of God, freedom, and immortality, the real possibility of which we cannot adjudicate, and which thus do not constitute genuine cognitions. The Stufenleiter, we might say, offers a taxonomy of mere representations as such (the highest genus it specifies is, after all, "representation in general"), and thus abstracts from whether representations meet the conditions required for them to constitute genuine cognitions.

3. Kant's Notion of a Mark

Kant's notion of a mark, along with his notions of object, thing, and cognition, makes up an integral part of his Leibnizian conception of predication.23 Examining Kant's notion of a mark, and his claim that all our objective perceptions relate to objects through marks, will help clarify this conception of predication. No student of Kant's critical philosophy can afford to ignore this conception. For, as Allen Wood has pointed out, Kant retained this conception of predication throughout his transcendental turn, and develops his critical account of genuine cognition in terms of it.24

I will structure my discussion around the Logic's definition of a mark, the only one of Kant's to be published in his lifetime:

A mark is that in a thing [Ding] which makes up part of its cognition,

23The texts on marks on which I will be relying in this and the following sections are drawn mainly from Kant's Reflections on logic, private notes that Kant kept for his lectures on logic (which he gave at least once a year over the course of his long teaching career). He kept these notes in his copy of the text he used, G. F. Meier's Auszug aus der Vernunftlehre. They have been edited, compiled, and dated by Adickes, in volume 20 of the Academy Edition of Kant's works. Questions could be raised about relying too heavily on these notes: Kant did not, after all, intend them for publication, and since he kept them over the course of several decades, they naturally evince some development in his thinking. Nonetheless, I take them to be quite reliable: Kant's practice was to revise them constantly, and it is a measure of the care he took in doing so that, when he entrusted his student Gottlob Jasche with the task of preparing his lectures on logic for publication, he gave Jasche his Reflections on logic to work from. The Reflections that develop Kant's account of marks are a series that Adickes compiles as R 2275 through R 2288. Adickes dates R 2275 through R 2279 to the 70s, and R 2280 through R 2288 to the 80s and 90s. The texts on marks from Jdsche's Logic (to which I have referred, and will continue to refer, simply as "the Logic") are largely paraphrases of these Reflections.

24See his Kant's Rational Theology (Ithaca: Cornell University Press, 1978), 40-41. The present section is indebted to his helpful discussion of the relevant passages from the first critique.

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or-what is the same-a partial representation so far as it is considered as ground of cognition [Erkenntnisgrund] of the whole representation. (Introduction ?8; 9:58)

Here Kant uses 'cognition' and 'representation' in his customary way, to refer to the content of a cognizing or representing. And he uses 'thing' in his standard sense, in which a thing is to be contrasted with a mere representation: as we will see, a thing, un- like a mere representation, is wholly determined in respect of every possible predicate of things. Recall that to cognize a thing, in Kant's sense, is to represent it positively in respect of its determinate identity, where one does so in consciousness.25 Such representing consists in being conscious of a thing as determined in respect of possible predicates of things. So, as a first approximation, we can gloss the passage's first characterization of a mark as follows. A mark is "that in a thing which makes up part of its cognition" (italics mine), because it is an identifying property of a thing. It makes up only a part of a thing's cognition, because in being conscious of a thing as having that property, one cognizes it only partially, not wholly-that is, through some, but not all, of the predicates that apply to that thing.

What is initially most puzzling about the Logic's definition is that it treats a mark not only as an objective property ("that in a thing"), but also as its representation ("part of its cognition" and "partial representation"). Nor is this definition an anomaly. In some texts Kant clearly counts properties as marks: in the first critique, he speaks of "a property [eine Beschaffenheit] which, as a mark, can be met in some place [irgendwoan angetroffen]" (B 133 n.); and in his lectures on logic, he remarks that having a hand, or having a perishable body, are marks of a human being. On the other hand, Kant repeatedly counts representations as marks: he holds that every mark "can be considered as a representation in itself" (Logic Introduction ?8; 9:58; cf. R 2285; 16:299); and he classes concepts as marks, writing, "All our concepts are marks and all thought representation through them" (R 2287; 16:300). In- deed, Kant even speaks of the properties of body as constituting our intuitions of a body: "All the properties which constitute the intuition of a body [impenetrability, for example] belong merely to appearance" (Prolegomena ?13; 4:289).

25See, again, Logic, Introduction ?8; 9:64-65.

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This puzzle reflects the way Kant operates, as do many other early modern philosophers, within a broadly Aristotelian conception of cognition. On this conception, one cognizes a thing by having its distinguishing properties in one's intellect. This conception turns on the idea that-to use Aquinas's terminology-a property can enjoy intentional, as well as natural, existence. This broadly Aristotelian conception of cognition is implicit in the Leibnizian G. F. Meier's Auszug aus der Vernunftlehre, a text Kant used for his lecture courses on logic. Consider, in particular, the definition of a mark that Meier offers in this work:

A mark, a character [Kennzeichnen] of cognition and the thing [nota, character cognitionis et rei], is that in the cognition or the thing, which, when it is cognized, is the ground on which we are conscious to our- selves of it. (?115; 16:296-97)

The definition suggests that a mark is a property that can exist, not just in a thing, but also in our cognition of that thing. Indeed, it suggests that the characteristic function of a mark requires that it be a property that can exist intentionally, as well as naturally. Kant, too, adapting Meier's notion of a mark, thinks of cognition as formal assimilation, and of marks as the mediating element in this assimilation. This explains why, in the passages cited above, Kant uses 'property' in such a way that a property of a thing can make up "part of its cognition": those that can, by existing intentionally in our representation and being related to a thing in a cognition, are marks. As his remark that every mark "can be considered as a representation in itself" indicates, he takes potential intentional being in some kind of representation as essential to a mark: to consider a property as a mark is to consider it, not in itself, but as the content of a possible representing.26

In order to bring out the Leibnizian conception of predication implicit in it, I want next to examine the Logic's second characterization of a mark: "a partial representation so far as it is considered as ground of cognition of the whole representation." Consider first

260n Kant's view, what makes a property a mark is our being able to be conscious of it as a property of a thing, and it is only by way of its existing in our representation that we are able to be conscious of it as such a property. Moreover, marks may be represented, without thereby being reg- istered in consciousness, so as to serve as grounds of cognition, as R 2275 makes clear: "In consciousness there are marks. But where marks are represented, there is not always consciousness" (16:296).

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the technical Leibnizian terminology ("ground of cognition," "partial and whole representation") that this characterization employs. As his speaking of a mark as "that in a thing which makes up its cognition" indicates, what is in question is cognition of an object, and thus a ground on which one can cognize a thing, as against a mere representation. In short, the ground of cognition in question is a representation on which one can ground the identi- fication of a thing in cognizing it (compare Meier's definition of a mark). But a thing, as against its representation, must on Kant's view be concrete, fully determined in respect of all possible predicates of things: in the "Ideal of Pure Reason" of the first critique, he claims that every possible thing-as opposed to a concept-is determined in respect of all possible predicates of things.27 This suggests that the whole representation in question is one of a thing, a suggestion confirmed by Kant's other characterizations of a mark. In his Reflections on Logic he writes that a mark is " [w] hat is considered as belonging as a part to the whole (possible) representation of a thing" (R 2280; 16: 298). And later in the Logic, he remarks that " [e]very mark may be considered from two sides: first, as a representation in itself; second, as belonging as a partial concept to the whole representation of a thing, and thereby as a ground of cognition of this thing itself' (Introduction, ?8; 9:58).28 The Logic's second characterization of mark, then, invokes a notion of a whole representation that is a descendant of the Leibnizian notion of a complete concept: the notion of a representation that determines a thing in respect of all possible predicates of things.29

27To be sure, Kant adapts the Leibnizian conception of predication to his critical philosophy by distinguishing between predicates of appearances, which apply to things as they appear to us in our experience, and predicates of things in themselves. Our concept of a thing as it appears is the concept of something fully determined in respect of all the possible predicates of appearances, and our concept of a thing as it is in itself, a concept of something fully determined in respect of all the possible predicates of things in themselves (see A 581-82 / B 610).

28Compare the parallel text in Kant's Reflections on Logic "A mark is considered, first, as a representation in itself, and second, as belonging as a partial representation to another representation and thereby as a ground of cognition of a thing" (R 2285; 16:299).

29Kant usually avoids calling such a representation a concept, since such a representation is singular, and he holds that all concepts, by definition, are general (cf. Logic 1, ?1.2; 9:91).

The notion of the whole representation of a thing in question is help- fully illustrated in the following passage from the introduction to the first

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The notion of a partial representation this characterization employs is also one of the representation of a thing, a representation that as such is a part of this whole representation, not of just any representation that contains it. And this characterization reflects a Leibnizian conception of predication on which to predicate a representation of an object is to regard it as belonging to a possible whole representation of that thing.

We can now begin to see why Kant specifies that a mark is "a partial representation so far as it is considered as ground of cognition [Erkenntnisgrund] of the whole representation." As we saw, Kant holds that we can consider a mark "as a representation in itself"-that is, apart from the relation it bears to a thing as a part of its possible whole representation. But to consider it in this way is to consider it, not as a mark-and so as a content that is predicable of an object-but rather as a mere representation (see section 2). Moreover, what makes a partial representation a mark is not merely its being a partial representation, a representation that makes up part of the whole representation of a thing. To consider a partial representation as a mark is to consider it as "ground of cognition of the whole representation," and we can, according to Kant, at least conceive of a mode of cognition in which a partial representation does not serve as the ground of that cognition. An

critique. Having claimed that all synthetic judgments demand, in addition to the concepts of the logical subject ("A") and the logical predicate ("B"), some third element ("X") on which its justification rests, Kant writes:

In the case of empirical judgments, judgments of experience, there is no dif- ficulty whatsoever in meeting this demand. This X is the complete experience of the object which I think through the concept A-a concept which makes up only one part of this experience. For though I do not include in the concept of a body in general the predicate "weight," the concept nonetheless designates the complete experience through one of its parts; and to this part, as belonging to it, I can therefore add other parts of the same experience. (A 8; see B 12)

The "complete experience of the object" is a representation that determines an object in respect of all possible predicates of appearances and thus as a phenomenon. On Kant's account, such an objective content would be infinite and thus one that we, having finite minds, cannot have. Our concept of such a "complete experience" is, thus, a problematic concept, an idea: its object (like that of the cosmological idea of the world) cannot be given to us. Nonetheless, Kant holds that this idea is our idea of a thing as it appears, of a thing that is determined in respect of all possible predicates of appearances.

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intuitive understanding, he maintains, would be one that grounds its cognition of a thing on the whole representation of a thing, not a partial representation, and thus a faculty that does not cognize things through marks. Grounding one's cognition of things on partial representations of those things is a mode of cognition distinctive of a discursive understanding-a faculty of cognizing things in representing them through concepts. Thus, to consider a partial representation as a ground of cognition is to consider it, not insofar as it is predicable of an object in just any mode of cognition, but specifically insofar as it is predicable of an object in the mode of cognition distinctive of discursive understanding. This is why Kant says that to consider a representation as a mark is to "consider it as belonging as a partial concept to the whole representation of a thing and thereby as a ground of cognition of that thing itself" (italics mine): what makes a partial representation a mark is its being a representation on which a discursive understanding can ground its cognition of that thing, by representing that partial representation through concepts as a part of a possible whole representation of a thing.

Fully appreciating Kant's conception of a mark would require examining his account of the nature of discursive understanding. And that is a task that I will have to defer for another occasion. And I will thus also have to defer explaining why Kant infers from our understanding's being discursive that "we cognize things only through marks" (Logic, Introduction ?8; 9:58). But for present pur- poses, it will suffice to have a first approximation of his conclusion-namely, that we can be conscious of things in respect of their determinate identities only in taking partial representations of those things as the grounds of their cognition. It follows from this conclusion that all the objective content of our cognition, content through which we cognize things, must consist of marks-representations that we can legitimately regard in this way as a part of a possible whole representation of a thing, and in such a way that they function as grounds of that thing's cognition. In particular, insofar as our intuitions are objective perceptions through which we can cognize objects, they constitute objective content of our cognition, and thus consist of marks. Indeed, it follows that all of our objective perceptions-including the categories, which as our concepts of an object in general do not themselves constitute objective content-relate to things only through marks. The catego-

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ries constitute objective perceptions, contents predicable of objects in cognition, only insofar as they can be realized in possible marks as the form of our cognition of any possible object in general. Fi- nally, to understand the relation that our objective perceptions bear to an object is to understand either how they themselves consist of partial representations that we can legitimately regard as parts of a possible whole representation, or how they are concepts whose em- ployment is constitutive of so regarding partial representations.

In predicating an objective perception of an object-even where that predicating constitutes a mere thought, not a genuine cognition-we represent that object as a possible thing. But, as we saw (section 2), even where such a predicating satisfies the general condition set by the law of noncontradiction, the object may not, for all we know, be a possible thing: not just any such predicating constitutes a genuine cognition. In order to constitute a genuine cognition of a thing, our predicating an objective perception of an object must meet the further, epistemic, condition specified above, namely, that we can establish that the thing so represented is possible. Nonetheless, the Leibnizian conception of predication implicit in Kant's characterization of a mark provides a partial specification of what it is for one of our representations to relate to an object as the ground of its genuine cognition. For it specifies the logical conditions on doing so properly, ones set by the nature of discursive understanding. Providing the rest of this specification- in the case of our a priori cognition, by articulating the relation this cognition bears to possible experience-so as to explain fully the way these perceptions constitute grounds of our genuine cognitions of objects, is the task of Kant's transcendental philosophy. A central tenet of this philosophy is that our thoughts meet the conditions of constituting genuine cognitions only insofar as they relate to possible experience, and thus that the scope of our genuine cognition is limited to possible objects of experience-a claim that breaks sharply with the Leibnizian tradition. But Kant's task of specifying this condition is framed by his Leibnizian conception of predication, a conception on which the first critique builds. Thus, although the Leibnizian conception of predication I have sketched in this section is to be distinguished from Kant's account of genuine cognition, it partially specifies the relation that any of our objective perceptions bear to an object in a genuine cognition of that object.

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4. Intuitive versus Discursive Marks

We have seen that Kant defines a mark as "that in a thing which makes up part of its cognition." We have also seen that intuition and concepts are two types of objective perceptions. It should come as no surprise, then, that Kant distinguishes between two types of marks, intuitive and discursive: an intuitive mark is a property as it makes up a thing's (partial) cognition in intuition (that is, a property as it is represented, and thus has intentional being, in intuition), and a discursive mark, a property as it makes up a thing's (partial) cognition in a concept (that is, a property as it is represented, and thus has intentional being, in a concept).

Consider the following Reflection on logic, which to my knowledge is the only place in which Kant distinguishes explicitly between intuitive and discursive marks:

A mark is a partial representation (which), as such (is a ground of cognition). It is either intuitive (a synthetic part): a part of intuition, or discursive: a part of a concept, which is an analytic ground of cognition.30 (R 2286; 16:299-300)

An intuitive mark is "a part of intuition" because it is a partial representation of a thing had in intuition. An example of an intuitive mark is the content rectangle in your perception of this page: that is, this rectangular shape, which you relate to the page as its property in intuiting it as a rectangular thing.3' Notice that what makes this content singular (that is, predicable of only one thing and thus intuitive) is not its characterizing a thing in respect of all possible predicates of things (it is, after all, a partial representation), but rather its being a partial representation that is contained in intuition ("a part of intuition"). A discursive mark, by contrast, is "a part of a concept" because it is a partial representation of a thing as it makes up-either a part or the whole of-a concept.32

30The parentheses indicate Kant's later emendations. Adickes dates this Reflection to sometime between 1780 and 1789.

31So by "this rectangular shape," I mean the property of the page-not the page itself, nor the shape merely as the object of pure intuition.

32The present reading accounts for Kant's holding that " [c] oncepts are marks of general use" (R 2281; 16:298). I take his point to be that the properties of objects insofar as these properties are represented in concepts, so as to constitute these concepts (wholly or partially) in respect of their matter, are "of general use" in that they may be predicated of more than one thing.

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The concepts rectangle and body, thus, are examples of discursive marks. For they are partial representations of things that, as concepts, are general: they subsume under themselves, and so can be related in different possible judgments to, more than one rectangular body.

Kant's distinction between a discursive and an intuitive mark is, thus, parallel to that between a universal property and a singular instance of a universal property-what, in twentieth-century metaphysics, has variously been called an abstract particular or a trope.33 And, like more recent trope theorists, Kant privileges tropes in his metaphysics. For, on his view, things-albeit merely as they appear- consist of appearances. And so regarded, appearances are tropes: as the constituents of empirical intuitions, they are the singular instances of the predicates through which we determine these things in experiencing them. In doing transcendental philosophy, we learn that these tropes can be regarded either empirically, insofar as they are real, or transcendentally, insofar as they are mere representations (see section 2). Because tropes are real (if only empirically), Kant develops his account of what makes a property a trope in the course of developing his transcendental theory of experience. But his account of universals is, in effect, a variant of

Notice that on this reading, the import of the phrases "a part of intuition" and "a part of a concept" is to distinguish between a partial representation (so a part of a whole representation of a thing) as that part is had in intuition and as it is had in a concept. Its import is not to distinguish between a representation that makes up part of an intuition and one that makes up part of a concept. Against this second reading, notice that Kant says "a part of intuition," not "a part of an intuition." Not noticing the possibility of the first reading, Stuhlmann-Laeisz adopts the second reading, taking it to be definitive of a discursive mark that it is a representation that makes up a part of a further concept, then goes on to show the dif- ficulties that result (see Kants Logik (Berlin: Walter de Gruyter, 1976), 73f.). On the reading I propose, in contrast, a partial representation of a thing can be considered in such a way that it constitutes a concept simply of itself, and not only as a part of another (more determinate) concept.

33For a seminal discussion of this idea of an abstract particular, see G. F. Stout, Proceedings of the Aristotelian Society, supp. vol. 3 (1923), especially 114, where he introduces a notion of "character" quite similar to the notion of an intuitive mark that I am ascribing to Kant, as "abstract particulars which are predicable of concrete particulars." See, too, Donald C. Wil- liams, The Principles of Empirical Realism, (Springfield, Ill.: Charles C. Thom- as, 1966), 74ff. especially 78, where Williams originates this use of the term trope'.

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Aristotelian abstractionism: universals are nothing but contents of certain acts of understanding. They are thus not real, even in the empirical sense. And, because of its radically new conception of metaphysics, and thus of what should head the metaphysical agen- da, the first critique does not give the kind of prominence to the distinction between intuitive and discursive marks that one might expect. Nonetheless, Kant uses this distinction to pose and pursue the distinctive questions of his new metaphysics.

Notice that on the reading I propose, Kant's distinction between intuitive and discursive marks is one between two ways the same partial representation of a thing (for example, the content rectangle) is predicable of a thing and thus constitutes a mark. This point is implicit in Kant's hylomorphic analyses of intuitions and concepts. According to Kant the form of intuition34 and the form of a concept are what, respectively, render the same partial representation either an intuitive or a discursive mark. So what makes the content rectangle in your perception of this page an intuitive mark-an objective content that is singular, predicable of only one object-is its being contained in the forms of our sensible intuition, that is, in the unbounded individuals, space and time. But the same partial representation can also take on the logical form of a concept-that is, generality (Logic 1, ?2; 9:91)-and thereby constitute a discursive mark, (the matter of) the concept rectangle.35

Let's take an initial look at Kant's account of the logical form of

34 am using 'form of intuition' in the sense of the Transcendental Aesthetic, in which space as form of intuition is not distinguished from space as formal intuition. It is only in the course of the B edition Deduction that Kant comes to distinguish between these two, remarking that in the Aesthetic he had for simplicity's sake treated the latter as merely sensible, though it actually presupposes a synthesis and thus the activity of the understanding (B 160-61 n.). Henry Allison provides a helpful summary of recent discussions of this important distinction in chapter 5 of Kant's Tran- scendental Idealism (New Haven: Yale University Press, 1983), especially 94- 98; more recently, Longuenesse has suggested an interesting reading of this distinction in chapter 8 of her important Kant and the Capacity toJudge (Princeton: Princeton University Press, 1998), especially 218 n. 12.

35In taking Kant's distinction between intuition and concept to turn on his accounts of the form of intuition and the form of a concept, I am in agreement with Kirk Dallas Wilson. See his interesting "Kant on Intuition," Philosophical Quarterly 25 (1975). However, my accounts of these forms, and especially of the way they ground Kant's distinction between intuition and concept, differ sharply from Wilson's.

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a concept.36 Kant maintains that this form is the product of our cognitive activity: we make a representation general through certain "logical acts" of comparison, reflection, and abstraction. For example, I produce the concept tree by (a) comparing a fir, a willow, and a linden so as to notice the respects in which their trunks, branches, leaves, and so forth, differ; (b) reflecting on just what they do have in common, "the trunks, branches, and leaves themselves"; and (c) abstracting from other respects in which the objects differ (their size, shape, and so forth) (Logic 1, ??4-6; 9:93- 94). In the act of reflection, we consider a partial representation as a property potentially common to more than one object, and the very act of so considering the partial representation makes it one common to more than one object. In short, reflection is an act that makes a mark discursive, one predicable of more than one object.37 This explains why Kant defines a concept as "a general (representat. per notas communes) or a reflected representation (representat. discursive)" (Logic 1, ?1; 9:91).

Seeing that, on Kant's view, the generality of a concept is its consisting of, and relating to an object by means of, one or more discursive marks sheds light on his discussions of this generality. Consider the Logic's initial characterization of the generality of a concept:

Concept is to be contrasted with intuition; for it is a general representation, or a representation of that which is common to a plurality of objects and so a representation insofar as it can be contained in various ones [Verschiedenen].8 (Logic 1, ?1.1; 9:91)

36Keep in mind that logical form, for Kant, is a property of thoughts. It is not, as most since Frege have held, a property of propositions or sentences (as is, for instance, their capacity to be true), or of their ele- ments.

37The reflection that makes a mark discursive is a specific instance of what Kant terms 'logical reflection' (B 318-19 / A 262). But what makes a discursive mark a mark, a content predicable of a thing as one of its properties, is a different sort of reflection, which Kant terms 'transcendental'; for it is transcendental reflection that constitutes the relation of objective perceptions to an object (B 319 / A 262). The form of a concept does not suffice, of itself, to constitute an objective perception's relation to an object, any more than does the form of intuition. I discuss the difference between these two sorts of reflection in "The Role of Reflection in Kant's Critique of Pure Reason," Pacific Philosophical Quarterly 80 (1999). Beatrice Longuenesse has developed a reading of Kant's account of reflection that is, in many important respects, along the same lines. See chapters 5 and 6 of her Kant and the Capacity to Judge.

38The passage leaves it open whether "the various ones" refers to ob-

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A parallel passage is to be found in the first critique, one that invokes the notion of a common, that is, discursive, mark:

Now one must indeed think of every concept as a representation which is contained in an infinite number of different possible representations (as their common mark). (B 40)

As B 40 confirms, what is referred to in the Logic passage as "a representation of that which is common to a plurality of objects" is a discursive mark, a partial representation that relates to objects as a property common to them. And, recall, we relate a representation to an object as its identifying property in a cognition, by regarding that representation "as belonging as a partial concept to the whole representation of a thing, and thereby as a ground of cognition of this thing itself." Moreover, what makes a representation one "of that which is common to a plurality of objects" is our taking it as a representation that makes up part of the whole representations of each of those different objects-as a representation contained in, and thus common to, all these different whole representations.39 Kant thus concludes that a concept is a repre-

jects or to representations. But, given the readings of 'representation' and 'object' offered in section 2, nothing hangs on this choice: Kant's notion of an object is one of a representation (though not a mere representation); a possible object is a possible representation.

39Thus, though on Kant's view a concept can be contained in other, more determinate concepts (for instance, the concept animal is contained, as a part, in the concept human), what makes a concept an objective perception is its being contained in the whole representation of a thing, for that is what makes it a ground of cognition of a thing. It is in light of this point that Kant's contrast between the intension and extension of a concept should be understood:

Every concept, as a partial concept, is contained in the representation of a thing; as ground of cognition, that is, as mark, these things are contained under it. In the first respect, every concept has a content; in the other an extension (Umfang). (Logic, 1 ?7; 9:95)

The first sentence presupposes Kant's view that all concepts (of objects) are partial-that is, that no concept is a whole representation: a whole or complete concept is an oxymoron, because such a concept would be a singular representation, and generality is definitive of a concept. Moreover, the first sentence implies that a concept's being partial consists in its being contained in-making up a part of-the whole representation of a thing. It is in respect of being so contained that a concept has an (objective) content, because the (objective) content of a concept is what, in grasping that concept, one regards as contained as a part in the whole representation of a thing. Moreover, Kant implies that every concept is a ground of

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sentation "insofar as it can be contained in various ones." In contrast, an intuition, as a representation predicable of only one object, is a representation insofar as it cannot be predicated of more than one object.

Notice that Kant's characterizing a general representation as "a representation insofar as it can be contained in more than one" confirms the reading of R 2286 I have been developing. For this characterization implies that if we abstract from the respective forms of our concepts and intuitions and attend only to their matter, we can speak of the same partial representation (that is, an objective content) as one that, in being contained in intuition, constitutes an intuitive mark, and that, in being reflected, constitutes a discursive mark. Consider, too, R 2287, where, having stated that "I[a]ll our concepts are marks and all thought representation through them," Kant adds, "We speak here only of marks as concepts." Finally, the present reading accounts for Kant's describing a representation as both a concept and an intuition (Logic, Intro- duction, ?5; 9:33): he has in mind a case in which we reflect on an objective content that is contained in intuition, an intuitive mark, so that it simultaneously also constitutes a discursive mark. Indeed, to do so just is, on Kant's view, to subsume an intuition under a concept: to recognize an intuitive mark as a singular instance of a discursive mark.

Most of Kant's commentators have entirely overlooked Kant's distinction between intuitive and discursive marks. And, as a consequence, many give readings of his account of marks that, in effect, equate all marks with discursive ones.40 Moreover, among the few who have noted the distinction, only one discusses it in any detail, and none apply it to explicate Kant's contrast between intuitions and concepts.41 As we will now see, our understanding of

cognition, and that a concept's being a ground of cognition consists in its containing things under itself in virtue of being contained in the whole representation of those things.

40Robert Howell, for instance, holds that Kant identifies marks with general properties, in Kant's Transcendental Deduction (Boston: Kluwer, 1992), 66. Allison presents Kant's account of the generation of concepts as a process whereby "impressions become transformed into marks" (Kant's Tran- scendental Idealism, 67). But what is distinctive about this process is precisely that it produces discursive marks from intuitive ones.

41I know of three authors who note this distinction: Klaus Reich, The Completeness of Kant's Table ofJudgments, trans. Kneller and Losonsky (Stan- ford: Stanford University Press, 1992), 37 (originally published in 1932);

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this contrast has been seriously impeded by this neglect of Kant's distinction between intuitive and discursive marks.

5. The Mediacy of Concepts and the Immediacy of Intuition

Consider, once again, the way Kant contrasts concept and intuition at A 320 / B 376: "[Intuition] relates to the object immediately and is singular, [concept], mediately, by means of a mark which can be common to several things." With the distinction between discursive and intuitive marks in hand, we are in a position to see that the standard minimal reading of the immediacy criterion is based on a misinterpretation of this passage. Proponents of this reading, in effect, take the phrase "by means of a mark which can ... as appositive to the mediacy of concepts.42 And they thereby take the clause "which can be common to several things" as simply unpacking a relevant aspect of Kant's notion of a mark.

However, on the reading I have proposed the clause "which can ." is restrictive: it specifies discursive, as opposed to intuitive,

marks.43'44 Thus, the phrase "by means of a mark which can ...

Richard Aquila, Representational Mind (Bloomington: Indiana University Press, 1983), 37; and Rainer Stuhlmann-Laeisz, Kants Logik, 73. Stuhlmann- Laeisz discusses the distinction in some detail, but offers a reading very different from the one I develop. None of these three applies the distinction in interpreting Kant's contrast between concept and intuition.

42See, for example, Allison, Kant's Transcendental Idealism, 66. 43Manley Thompson also interprets the clause "which can ..." as re-

strictive. In "Singular Terms and Intuitions in Kant's Epistemology," he reads this passage as asserting that intuitions

refer to an object immediately because they somehow mark characteristics peculiar to that object alone, while empirical concepts can refer to the same object only mediately because they mark only characteristics that the object may share with indefinitely many other objects. (316)

But in speaking of an intuition as referring to an object through "characteristics peculiar to that object alone," Thompson does not have intuitive marks in mind. This becomes clear when he immediately goes on to remark: "But intuitions then appear to be simply concepts of a special sort- individual or singular rather than general concepts." Thompson thinks of a mark through which an intuition refers to its object as "peculiar" to its object not in being an individual proprietary to that object, but rather in uniquely characterizing that object, so as to distinguish it qualitatively from all other possible objects: only on this assumption would it make sense to conclude that intuitions are singular concepts.

Now, as Thompson is well aware, this conclusion is antithetical to Kant's most central critical tenets. It conflicts with his doctrine, propounded in the Amphiboly, that, pace Locke and Leibniz, intuitions and concepts are

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contrasts the generality of concepts with the singularity of intuition. The import of the phrase is to specify what the generality, not the mediacy, of a concept consists in. This reading is also suggested by the parallel structure of Kant's contrast between intuitions and concepts. And it is confirmed by the Logic, which characterizes the generality of a concept as its being "a representation through common marks [per notas communes] "-that is, through discursive marks-and refers to a concept as "a representation of what is common to more than one thing" (1 ?1.1; 9:91). Although, as we will see, it follows from an objective perception's being made up of discursive marks that it relates to its object mediately, the mediacy of a concept's relation to an object does not itself consist in its being a representation through discursive marks. In short, it is not the mediacy but the generality of a concept that consists in its being through discursive marks.

Indeed, having advanced the notion of an intuitive mark, Kant cannot consistently maintain that the mediacy of a concept's relation to an object consists in its relating to objects by means of marks. For, as we have seen, intuitive marks are, as marks, representations through which sensible intuitions-the objective perceptions whose matter they constitute-relate to an object. Thus, his

essentially different kinds of representations. Moreover, crediting us with singular concepts would contradict Kant's above-cited claim that, our understanding being discursive, all of our concepts are general. On such grounds, no doubt, Thompson regards A 320 / B 377 as a "trace" of a preliminary view Kant held of intuition, that, by oversight, survived into the first critique (315-16). But no such patchwork reading is necessary, if we read the passage as implying that some intuitions (namely, ours) refer to objects through intuitive marks.

In putting forward his reading, Thompson takes himself to be following Hintikka (316). Hintikka, however, strongly objects to being read in this vein, insisting that the immediacy of intuition consists precisely in not referring to its object through any marks. See "Kant's Theory of Mathematics Revisited," in Essays in Kant's Critique of Pure Reason, ed. Mohanty and Sha- han (Norman: University of Oklahoma Press, 1982), 214.

44Now one might object, in defense of the standard minimal reading, that if the import of this clause were restrictive in this way, Kant would surely have specified in A 320 / B 376 that intuitions relate to objects by means of intuitive marks. But there is an important reason why he doesn't: he wants his definition of intuition to be broad enough to include the intuition had by an intuitive, as against a discursive or conceptual, understanding, an intuition that does not relate to an object by means of marks (see note 11 and note 48).

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notion of an intuitive mark commits Kant to the possibility of intuitions that relate to objects by means of marks. The immediacy of an intuition's relation to an object, then, cannot consist in its not relating to an object by means of marks; and the mediacy of a concept's relation to an object cannot consist in its relating to an object by means of marks.

In what, then, do the mediacy of concepts and the immediacy of intuitions consist? Consider the following passage from the Metaphysical Deduction of the first critique:

Since no representation other than intuition goes immediately to an object, a concept is never related immediately to an object, but rather to some other representation of the same [object] (be it an intuition or itself already a concept). Judgment is therefore the mediate cognition of an object, that is, the representation of a representation of it. (A 68 / B 93) 45

What Kant explains in the passage is not the relation a concept has to its objects that constitutes the generality of that concept. This relation constitutes a concept's containing objects in its extension, in virtue of its being contained in other possible representations of those objects. It is thus a relation that concept has to all of these objects. The relation to an object in question at A 68 / B 93 is, rather, that which a concept has in being employed in a judgment as a predicate. Since this relation is one a concept has to a subset of the objects it contains in its extension, it must be distinguished from that which the concept has to all of these objects.46

45Note the implication that a concept, in relating mediately to an object by means of another representation of that object, relates immediately to that further representation of the object. And Kant's subsequent discussion makes it clear that a concept relates immediately to another concept in being employed as a logical predicate in a categorical judgment: he says that "in the judgment 'all bodies are divisible', the concept divisible is related immediately to the concept body." And a concept relates immediately to intuition (though perhaps not to a particular one) in being employed as a logical subject in a categorical judgment: so Kant says that, in the judgment just mentioned, the concept body is related immediately to "certain appearances that present themselves to us" (A 68 / B 98). Since appearances are the intuitive marks that make up the objective content of an empirical intuition (B 34 / A 20), Kant is saying that a concept is employed in a judgment so as to relate immediately to an intuition, insofar as it is related to the intuitive marks that make up the content of an intuition.

46Indeed, Kant holds that in a singular judgment, a concept is related

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Nonetheless, the same conception of mediacy-as consisting in mediation by some other representation of an object-is in play when Kant, in passages such as the Stufenleiter, characterizes as mediate the relation to an object that constitutes the generality of a concept. We saw that we generate this relation in reflection, through thinking of a partial representation as general, as one that is common to different possible whole representations of an object. But, on Kant's account, this thought is equivalent to the thought of that partial representation as the predicate of a possible judgment: so he maintains that our act of grasping a universal-which, as we saw, makes a given objective content universal-can be re- duced to the act of judging, the act of subsuming a particular under a universal. It follows that A 68 / B 93's characterization of the mediacy of the relation that a concept has to an object in its use also applies to the mediacy of the relation to an object that is intrinsic to a concept: the mediacy of a concept's relation to an object consists in its relating to an object by means of a further representation of that object.

By implication, the immediacy of an intuition can be character- ized-albeit negatively-as its not relating to an object by means of some other representation of that object.47 But to say that the im-

immediately to a particular intuition, in such a way as to come to have, in this use, a relation to a single object. In his writings on logic, Kant admon- ishes Leibnizians who divide concepts into universal, particular, and singular, on the grounds that " [n] ot the concepts themselves, but their use, can be divided in this way" (Logic, 1 ?1; 9: 91). Other remarks suggest that what Kant has in mind by this singular use is the use of a concept as the subject of a singular judgment: "Or I use the concept only for a single thing, for example: This house is cleaned in such and such a way" (Wiener Logik; 24:909; cited by Parsons, "The Transcendental Aesthetic," 64). Man- ley Thompson ("Singular Terms and Intuitions in Kant's Epistemology,") and Charles Parsons (the postscript to his "Kant's Philosophy of Arith- metic" and "The Transcendental Aesthetic," sect. 1) have both emphasized the importance of this point.

47Longuenesse proposes, in passing, something close to this reading of the immediacy of intuition: "Kant's characterization of intuition as immediate representation essentially means, I think, that intuition does not require the mediation of another representation to relate to an object" (Kant and the Capacity to Judge, 202 n. 15). However, the independence of intuition from further representations needs qualification: some of our intuitions require the mediation of some further representation to relate to an object; it is only further representation of an object that does not mediate an intuition's relation to an object. For Kant holds that an intuition is empirical if "it relates to the object through sensation" (A 20 / B 35). This does not render the intuition's relation to its object mediate,

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mediacy of intuition consists in its not relating to an object by means of any other representation of that object is not to say that an intuition does not relate to an object by means of any representation of that object. Indeed, it implies that an intuition relates to an object by means of some representation of that object. And since the immediacy of intuition consists in its not relating to an object through any other representation of that object, the only representation of an object through which an intuition can relate to an object is itself. Kant's positive characterization of the immediacy of our intuition specifies how, in virtue of consisting of intuitive marks, our intuitions relate to their objects only through themselves.

That our intuitions relate to objects through themselves should not be surprising. For it is implicit in Kant's conception of marks, and in his conception of the way in which all of our determinate objective perceptions relate to objects through marks. Recall that all of the objective content of our cognition consists of marks, where a mark is "a partial representation so far as it is considered as ground of cognition of the whole representation," and that we thus predicate this objective content of objects in considering it as consisting of marks (section 3). This is just to say that all of our determinate objective perceptions relate to objects through the marks that constitute their matter, as they constitute their matter, and so through themselves. Our determinate concepts of objects consist of discursive marks; they are objective perceptions that relate to objects by means of the discursive marks that constitute their matter, as they constitute their matter. Our intuitions constitute objective content and thus must, in an analogous vein, consist of intuitive marks; intuitions are objective perceptions that relate to objects by means of the intuitive marks that constitute their matter. What distinguishes the relation to an object had by our intuitions from that had by determinate concepts of objects is that our intuitions relate to their objects, and constitute grounds of cognition, simply of themselves and thus only through themselves.

because these sensations are not, of themselves, representations of objects (objective perceptions). It is only in conjunction with empirical intuition that sensations may be attributed (beigelegt) to an object (and even so, only relative to the subjective constitution of the particular cognizing subject) (cf. B 70 n.). Recall the Stufenleiters characterization of sensation as perception that "itself relates solely to the subject, as a modification of its state."

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Notice that on the reading I propose, the immediacy criterion is not, as on Parsons's reading, independent of the singularity criterion. What makes an objective perception singular-its being contained in the form of intuition-is also what renders its relation to an object immediate. So, though distinct, these criteria are mu- tually entailing. Indeed, the parallel point holds for concepts. What makes a concept general is also what renders its relation to an object mediate: the form of generality that renders a partial representation general (a discursive mark) also makes it a representation that only relates to an object through a further representation of that object.48

Explaining Kant's positive conception of the immediacy of intuition-the way intuition relates to an object simply through itself-would require examining his account of synthesis. For synthesis is the act of mind that produces intuitions, in a fashion analogous to the way reflection produces concepts. Unfortunately, examining Kant's account of synthesis would take me beyond the scope of the present paper. But I can close with a rough first approximation of what I believe the first critique's account of synthesis entails about Kant's positive conception of the immediacy of empirical intuition. Synthesis makes an objective perception-a representation with consciousness-an intuition in virtue of being the act of the mind that constitutes the consciousness had in this perception. In the case of a sensible intuition, this act of synthesis is the act that orders appearances into the whole representation of a single phenomenal world. But it is essential to an appearance that it be a content that is a part of such a whole representation. Thus, synthesis produces appearances in ordering them into the whole representation of a single phenomenal world. Now the relation an appearance has to all the other possible appearances contained in that whole representation is what makes it a ground of cognition of a thing as it appears. Moreover, insofar as appearances have this relation to each other, and constitute such grounds of cognition, they constitute empirical intuitions. Thus, what makes

48However, not just any kind of generality of an objective perception entails its mediacy: the synthetic universal through which an intuitive understanding cognizes objects relates to these objects immediately, despite being a general representation; it is only the generality of concepts, which consists in the analytic unity of consciousness, that entails mediacy (see Critique ofJudgment, ?77; 6:407-10; cf. B133 n.).

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an objective perception an empirical intuition is also what constitutes the relation that empirical intuition has to its object. More- over, according to Kant's transcendental idealism, this relation that empirical intuitions have to an object is what constitutes that object-the thing as it appears to which an empirical intuition relates. Thus, what makes an objective perception an empirical intuition is the sole ground on which it relates to an object. But this is just to say that an empirical intuition relates to an object simply through itself, and so immediately. This sketch explains the sense in which an appearance is an intuitive mark, a synthetic part (R 2286): it is as a part of the whole possible representation generated in synthesis that an appearance relates to an object as a ground of its cognition (see sections 3 and 4) .49

6. Conclusion

I have argued that we ought to reject the standard minimal reading of Kant's immediacy criterion for intuition. On this reading, the immediacy of intuition consists in its not relating to its object through marks. Commentators have uniformly adopted this reading, because they have overlooked Kant's distinction between intuitive and discursive marks. Intuitive marks are singular instances of properties, as they are represented in, and make up the content of, our intuitions. Discursive marks, in contrast, are general properties as they are represented in, and make up the content of, our concepts. Once one sees that Kant makes this distinction, it becomes clear that our intuitions, on his view, relate to objects through marks-in particular, through the intuitive marks that make up their contents. For it is a consequence of his view of discursive understanding that any of its cognitions-including intuition-of a thing must be through marks. The immediacy of our intuition does not, then, consist in its not relating to its object through marks. It consists, rather, in the fact that its relation to its object is not mediated by any further cognition of that object.

University of Arizona

49In other work, I develop this sketch of Kant's positive conception of the immediacy of intuition, showing how it illumines his accounts of pure sensible intuition and intellectual intuition. In doing so, I clarify how, in relation to the whole of possible human experience, empirical and pure sensible intuitions relate to objects as grounds of their genuine cognition.

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