On one reading of Kant’s account of our original representations of space and time, they are, in part, products of the understanding or imagination. On another, they are brute, sensible givens, entirely independent of the understanding. In this article, while I agree with the latter interpretation, I argue for a version of it that does more justice to the insights of the former than others currently available. I claim that Kant’s Transcendental Deduction turns on the representations of space and time (...) as determinate, enduring particulars, whose unity is both given and a product of synthesis. (shrink)

This thesis argues that Kant is able to maintain the distinctiveness of his position in opposition to Hume's naturalism (contrary to the arguments of R. A. Mall and L. W. Beck) without invoking premises which are question begging with regard to Hume's scepticism. The argument of Kant's Transcendental Deduction of the Categories, as presented in the second edition of the Critique of Pure Reason, is considered in relation to the two sets of criticism that have been levelled at it from (...) its publication up to the present day, both of which aim to demonstrate that synthetic a priori judgements are subjectively necessary but without objective validity. The first set of criticisms involves problems raised with regard to the status of transcendental arguments. The difficulties identified here (by B. Stroud, M. S. Gram, and others) are that the Deduction can either, at best, show that it is necessary for experience to be regarded in a certain way without demonstrating anything as to the nature of experience as such, or the argument is circular in that it begins by making assumptions regarding the nature of our experience. Alternatively, if the Deduction is taken to establish the objective nature of concepts via an analysis of the conditions under which it is possible for us to have some knowledge of ourselves, then incoherence is said to arise because this requires either an implausible reflective theory of consciousness (according to D. Henrich) or that we have knowledge of the subject-in-itself (as held by J. G. Fichte and other contemporaries of Kant). Through a consideration of both the historical and contemporary manifestations of these criticisms, the thesis advances an interpretation of the Deduction, with special attention paid to the role and nature of the subject, which does not fall prey to the alleged incoherence. As such, the thesis defends both the distinctiveness and legitimacy of transcendental philosophy. (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses (...) worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions. (shrink)

Kant's first antinomy uses a notion of infinity that is tied to the concept of (finitary) successive synthesis. It is commonly objected that (i) this notion is inadequate by modern mathematical standards, and that (ii) it is unable to establish the stark ontological assumption required for the thesis that an infinite series cannot exist. In this paper, I argue that Kant's notion of infinity is adequate for the set-up and the purpose of the antinomy. Regarding (i), I show that contrary (...) to appearance, the Critique can even accommodate a modern notion of infinity without consequences for the antinomy; and regarding (ii), that the ‘ontological’ consequence indeed follows once its covertly epistemic character is adequately understood. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)