«ABSTRACT I argue that Kant’s distinction between the cognitive roles of sensibility and understanding raises a question concerning the conditions ...»
2.1 Step One: Pure Intuition and Unity Kant argues in the Metaphysical Exposition of the Transcendental Aesthetic (A24–25/B39–40, A41–42/B47–48) for our non-conceptual or intuitive grasp of space (and mutatis mutandis time). These arguments are worth quoting in full.
Space is not a discursive or, as we say, universal concept of things as such; rather, it is a pure intuition. For, ﬁrst, we can represent only one space; and when we speak It is true that the second edition added new headings (such as “Metaphysical Exposition”) and changed some of the wording and argument. Nevertheless, the A-edition clearly argues that, for example, space is given as inﬁnite, something that we would not be capable of grasping in a purely conceptual manner independent of intuition (A25).
two kinds of unity in the CRITIQUE OF PURE REASON of many spaces, we mean by that only parts of one and the same unique space. Nor, second, can these parts precede the one all-encompassing space, as its constituents, as it were (from which it can be assembled); rather, they can be thought only as in it. Space is essentially one; the manifold in it, and hence also the universal concept of spaces as such, rests solely on [our bringing in] limitations. It follows from this that, as far as space is concerned, an a priori intuition of it (i.e., one that is not empirical) underlies all concepts of space. (A24–25/B39; my emphasis) Space is represented as an inﬁnite given magnitude. Now it is true that every concept must be thought as a representation that is contained in an inﬁnite multitude of different possible representations (as their common characteristic) and hence the concept contains these representations under itself. But no concept, as such, can be thought as containing an inﬁnite multitude of representations within itself. Yet that is how we think space (for all parts of space, ad inﬁnitum, are simultaneous). Therefore the original representation of space is an a priori intuition, not a concept. (B39–40; my emphasis) The ﬁrst argument indicates that space is given or presented to the mind as a single whole. Its “parts” are actually limitations. Therefore the representation of space (and time) is “prior” metaphysically to its represented parts, which are dependent upon this whole. It is partially because the representation of space as a whole cannot be built up out of a previous representation of its parts (particular spaces) that Kant considers it as having the status of an a priori representation.19 The second argument indicates that our representation of space cannot be fundamentally conceptual, for if it were, we would need to grasp the totality of conceptual parts or “marks” (Merkmale) that constitute its content or intension.20 Since this would mean grasping an inﬁnite set of marks (conceptual marks of each individual space or location), it would be impossible for any ﬁnite being. Hence, space is not something originally grasped conceptually.21 In contrast to this account, compare the accounts of spatial representation in the British empiricists. Locke argues that spatial representation is based on the representation of distance between bodies that we immediately perceive and then join and multiply in order to get an idea of an all-encompassing space (Essay, Book II, chapter iv, sections 3–4; cf. II.xiii.1–14). Berkeley construes three-dimensional spatial representation as the construction of distance via the association of visual and tactile impressions (Theory of Vision, LX–LXII). Hume construes space as the manner in which colored points are distributed, and extended space as simply a greater distribution of such points (Treatise, Book I, chapter iii, sections 2–5). According to Hume, the representation of depth, in a manner similar to Berkeley’s view, is had in virtue of associations between visible and tangible points.
All three empiricist theories construe the representation of space as involving construction via additive or other combinatorial operations of the mind.
The primacy of our aesthetic representation of space is, however, compatible with holding that we do in fact have a conceptual grasp of individual spaces (e.g. in analytic geometry). Kant’s main point is that our grasp of geometric space, which can involve the arbitrary addition or subtraction of spatial magnitudes, is parasitic upon a non-conceptual grasp of a single uniﬁed and all-encompassing space in which such subtraction or addition takes place. For discussion of Kant’s theory of concept extension and intension and its signiﬁcance for the argument of the Metaphysical Exposition, see Friedman, Exact Sciences; Posy, “Immediacy and Reference”; Anderson, “It Adds Up”; Anderson, ‘Wolfﬁan Paradigm”;
Janiak, “Kant’s Views on Space and Time.” One might object to this interpretation on the basis that it makes a psychological claim regarding the kinds of concepts that a ﬁnite discursive being can apprehend. It might seem better to simply read Kant as asserting that concepts cannot have an inﬁnite number of marks and arguing for the existence of an intuition of space and time from this assertion. Dialectically, however, this seems to put Kant’s argument at a disadvantage, for one of his key opponents (Leibniz) did think that concepts 88 journal of the history of philosophy 53:1 January 2015 Recall premise (2) of the Intellectualist’s argument. It says that both intuition and judgment have a common source of unity—namely, discursive activity. If this premise were correct then our cognitive grasp of space and time as pure forms of intuition would depend on a discursive form of uniﬁcation, and thus on the combination of their many parts into a unity.22 This is what it means to say that the unity of intuition depends on a discursive unity.23 This view entails that our conception of space as an inﬁnite whole would be logically constructed from our grasp of the discrete spaces composing it (whether these spaces are perceived or mathematically grasped). However, this seems to be precisely what Kant denies discursive intellectual activity is able to accomplish.24 Kant suggests instead, in the above quotations from the Metaphysical Exposition, that our cognitive grasp of space is holistic. We grasp the whole of space ﬁrst, and it is in virtue of this that its parts, as limitations of the inﬁnite whole, are conceptually grasped and cognized discursively.25 One might attempt to avoid this objection by arguing that it only applies to positions that interpret the forms of intuition as uniﬁed by their conceptual content.
Such an interpretation, it might be granted, indeed runs afoul of Kant’s arguments.
However, the suggestion goes, there is an alternative means of construing the dependence of the forms of intuition on the activity of the understanding (or its operation in imagination). According to this alternative, the unity of the forms of intuition depends upon a pre-conceptual synthesis whereby the understanding (speciﬁcally, the capacity to judge) acts upon the faculty of sensibility and in doing so provides for the synthetic uniﬁcation rather than the actual content (propositional or otherwise) of intuition. So it is not the case that the form of (e.g.) space is uniﬁed by a conceptual grasp of each of its elements (i.e. individual spaces).
Instead, the form is uniﬁed according to a rule provided by the understanding in the gathering-together or “comprehension” (Zusammenfassung) of the given “manifold.” The most inﬂuential contemporary version of this thesis is offered by Béatrice Longuenesse.26 She argues that §26 of the B-deduction entails a “rereading could contain an inﬁnite number of marks, even if they could not all be cognized by ﬁnite beings;
cf. Discourse, §8. This allows Kant to avoid begging the question against Leibniz while allowing him to press the point that if concepts are to play their requisite theoretical role in explaining cognition, which requires that they be susceptible to cognitive processing, then they cannot be of the very same representational kind as those representations that God uses to cognize the world. Along with his arguments considering God as an intuitive intellect, Kant can thus give a substantive reply to the Leibnizian, without simply presuming the denial of the Leibnizian position. Thanks to an anonymous referee for encouraging clarity on this point.
Note that the awareness of space and time as inﬁnite wholes is pure or a priori in nature and therefore not speciﬁcally perceptual. I discuss below the signiﬁcance of this point for the understanding of perception as empirical intuition.
See e.g. McDowell, “Hegel and the Myth,” 79. McDowell emphasizes that the unity is a logical one, but this is compatible with describing it as discursive—viz. as the combination of disparate elements into a uniﬁed complex whole.
Others have noticed this problem as well. Cf. Falkenstein, Kant’s Intuitionism, 139; Messina, “Kant on the Unity of Space”; Onof and Schulting, “Space as Form of Intuition and as Formal Intuition.” For alternative perspective on the holistic nature of the forms of intuition that emphasize phenomenological themes, see Aquila, “Holistic Intuition” and “Inﬁnitude.” Longuenesse, Capacity to Judge, ch. 8. See also Land, “Prescribing Unity” and “Kantian Conceptualism.” For further discussion of Longuenesse’s reading and the French reception of that reading, particularly by Michel Fichant, see Onof and Schulting, “Space as Form of Intuition and as Formal Intuition.” two kinds of unity in the CRITIQUE OF PURE REASON of the theory of space and time propounded in the Aesthetic” resulting in a “reinterpretation of the manner in which things are given to us.”27 The rereading requires that we see the understanding, in the guise of the productive imagination, as synthesizing the manifold of the sensory given in such a way as to make possible the unity of the forms of space and time.28 A key text that Longuenesse cites as central to her rereading comes in the dense footnote to §26, B161. Kant says, Space, presented as object (as we are actually required to represent it in geometry), contains more than [the] mere form of intuition—viz. it contains also the gatheringtogether [Zusammenfassung] of the manifold given according to the form of sensibility, in an intuitive representation—so that the form of intuition gives us merely a manifold, but formal intuition gives us unity of representation. In the Transcendental Aesthetic I had merely included this unity with sensibility, wanting only to point out that it precedes any concept. But this unity indeed presupposes a synthesis which does not belong to the senses, through which all concepts of space and time ﬁrst become possible. For through this unity (inasmuch as understanding determines sensibility) space or time are ﬁrst given as intuitions, and hence the unity of this intuition belongs a priori to space and time, and not to the concept of understanding (see §24). (B161n) According to Longuenesse, the footnote demonstrates Kant’s reinterpretation of his discussion of a priori intuition in the Transcendental Aesthetic in order to bring it in line with the argument of the Deduction. Her claim is that via an act of the understanding on the faculty of sensibility, which Kant terms a “ﬁgurative” synthesis or “synthesis speciosa,” the pure intuitions of space and time are generated.
This “determination” of sensibility by the understanding, which generates the pure intuitions of space and time, is nevertheless importantly pre-conceptual, and thus does not entail (so Longuenesse argues) any conﬂict with the account Kant gives in the Aesthetic of the intuitive nature of space and time.29 This is why, says Longuenesse, Kant can claim in the note quoted above both that the unity of intuition presupposes a synthesis that “does not belong to the senses” while also claiming that the unity of intuition belongs to space and time and “not to the concept of the understanding.” The problem with the rereading Longuenesse proposes—and, more generally, with any proposal that attempts to avoid my objection via an appeal to preconceptual synthesis—is that it does not ﬁt with Kant’s general view of the nature of our ﬁnite intellectual activity. According to Kant, intellectual activity in ﬁnite Longuenesse, Capacity to Judge, 208–9, 213.
There is some debate as to whether the imagination should be understood as part of the understanding’s activity or part of sensibility’s receptivity. For example, Hanna (“Kant and Nonconceptual Content,” 249) argues for sensibility as itself being spontaneous in virtue of having a productive imagination. However, Kant is quite explicit in the B-edition of the Critique that the productive imagination is merely the understanding under another name (B162, note). One advantage of my argument is that it avoids the issue of whether the imagination is part of the understanding or sensibility. Instead, my argument depends only on the idea that the activity characteristic of human cognitive activity, whether imaginative or explicitly intellectual, cannot bring about the requisite unity of the forms of intuition, given Kant’s characterization of those forms in the Metaphysical Expositions and his characterization of human cognitive activity as structured via a dependence relation of whole on part. For this reason, I will continue to talk interchangeably of the understanding or its activity via the imagination, since the same fundamental form of structuring activity takes place in both cases.
Cf. Longuenesse, Capacity to Judge, 216.
90 journal of the history of philosophy 53:1 January 2015 beings such as ourselves always proceeds from part to whole (CJ 5:407; cf. B72;