In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

I argue that Kant’s distinction between the cognitive roles of sensibility and understanding raises a question concerning the conditions necessary for objective representation. I distinguish two opposing interpretive positions—viz. Intellectualism and Sensibilism. According to Intellectualism all objective representation depends, at least in part, on the unifying synthetic activity of the mind. In contrast, Sensibilism argues that at least some forms of objective representation, specifically intuitions, do not require synthesis. I argue that there are deep reasons for thinking that Intellectualism is (...) incompatible with Kant's view as expressed in the Transcendental Aesthetic. We can better see how Kant’s arguments in the first Critique may be integrated, I suggest, by examining his notion of the 'unity' [Einheit] of a representation. I articulate two distinct ways in which a representation may possess unity and claim that we can use these notions to integrate Kant’s arguments in the Aesthetic and the Transcendental Deduction without compromising the core claims of either Sensibilism or Intellectualism—that intuition is a form of objective representation independent of synthesis, and that the kind of objective representations that ground scientific knowledge of the world require synthesis by the categories. (shrink)

Among the extensive literature on the first Critique, very few commentators offer a thorough analysis of Kant's conception of inner sense. This is quite surprising since the notion is central to Kant's theoretical philosophy, and it is very difficult to provide a consistent interpretation of this notion. In this paper, I first summarize Kant's claims about inner sense in the Transcendental Aesthetic and show why existing interpretations have been unable to dissolve the tensions arising from the conjunction of these claims. (...) Secondly, I present my own reconstruction of Kant's model of inner sense, relying essentially on Kantian considerations found in the B-version of the Transcendental Deduction. My main idea is that inner sense, for Kant, is a passive faculty that gets affected by the understanding performing its figurative synthesis on material given in outer sense. In the remainder of the paper, I highlight a few consequences of my interpretation and outline ways to deal with some objections. (shrink)

I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why Kant (...) takes geometrical constructions in the style of Euclid to provide us with an a priori framework for physical space. I attempt, along the way, to shed new light on the relationship between Kant’s theory of space and the debate between Newton and Leibniz to which he was reacting, and also on the role of geometry and spatial intuition in the transcendental deduction of the categories. (shrink)

James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, and it suggests (...) an interesting reason why the rewriting might have been thought necessary. (shrink)

Are the pure intuitions of space and time, for Kant, dependent upon the understanding's activity? This paper defends the recently popular Self-Affection Thesis : namely, that the pure intuitions require an activity of self-affection—an influence of the understanding on the inner sense. Two systematic objections to this thesis have been raised: The Independence objection claims that SAT undermines the independence of sensibility; the Compatibility objection claims that certain features of space and time are incompatible with being the products of the (...) understanding's activity. I show that the resources to rebut these objections can be found in Kant's account of causal influence. (shrink)

It's well-known that Kant believed that intuition was central to an account of mathematical knowledge. What that role is and how Kant argues for it are, however, still open to debate. There are, broadly speaking, two tendencies in interpreting Kant's account of intuition in mathematics, each emphasizing different aspects of Kant's general doctrine of intuition. On one view, most recently put forward by Michael Friedman, this central role for intuition is a direct result of the limitations of the syllogistic logic (...) available to Kant. On this view, Kant's reasons for introducing intuition are taken to be logical or mathematical, rather than philosophical. The other tendency, which I shall try to develop here, emphasizes an epistemological or phenomenological role for intuition in mathematics arising out of what may loosely be called Kant's ‘antiformalism.’This paper, which focuses specifically on the case of geometry, falls into two parts. First, I consider Kant's discussion of intuition in the Metaphysical Exposition of the concept of space. (shrink)

:Space is not an empirical concept that has been drawn from outer experiences. For in order for certain sensations to be related to something outside me , thus in order for me to represent them as outside and next to one another, thus not merely different but as in different places, the representation of space must already be their ground. Thus the representation of space cannot be obtained from the relations of outer appearance through experience, but this outer experience is (...) itself first possible only through this representation. 1Abstract:Der Raum is kein empirischer Begriff, der von äußeren Erfahrungen abgezogen worden. Denn damit gewisse Empfindungen auf etwas außer mir bezogen werden, imgleichen damit ich sie als außer und neben einander, mithin nicht bloß verschieden, sondern als in verschiedenen Orten vorstellen können, dazu muß die Vorstellung des Raumes schon zum Grunde liegen. (shrink)

Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method 'ideation'. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern (...) mathematics. This view leads naturally to different types of spatial ontologies and it can be used to shed light on Husserl's general claim that there are different ontologies in the eidetic sciences that can be systematically related to one another. The paper is rounded out with a consideration of the role of ideation in the origins of modern geometry, and with a brief discussion of the use of ideation outside of pure geometry. (shrink)

In interpretations of the "Transcendental Aesthetic" section of the first Critique, there is a widespread tendency to present Kant as establishing that the representation of space is a condition for individuating or distinguishing objects, and to claim that it is on this basis that Kant establishes the apriority of this representation. The aim of this paper is to criticize this way of interpreting the "Aesthetic," and to defend an alternative interpretation. On this alternative, questions about the formation of the representation (...) of space figure more centrally, and the anti-Leibnizian character of Kant 's argument can be properly appreciated. (shrink)