It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

While Kant’s position concerning human freedom and divine foreknowledge is perhaps the least Molinist element of his multifaceted take on free will, Kant’s Molinism (minimally defined) is undeniable when it comes to the threat ensuing from the idea of creation. In line with incompatibilism and with careful qualifications in place, he ultimately suggests regarding free agents as uncreated. Given the limitations of our rational insight, this assumption is indispensable for granting that finite free agents can acquire their intelligible characters by (...) themselves. Nonetheless, Kant concedes that creation may, as a matter of fact, be compatible with what for Molina is the pre-volitionality of the counterfactuals of freedom. (shrink)

The eighteenth-century German rationalist tradition is, broadly speaking, committed to (what I call) ‘the principle of rational cognition’: the grounded must be rationally cognizable from its sufficient ground. Whereas the prevailing view takes the fundamental challenge to rationalist paradise to stem from the principle of sufficient reason, I argue that it instead stems from this principle: How is it possible to rationally cognize anything at all from its ground? By investigating the opposing responses of two of Leibniz’s most influential immediate (...) successors, Christian Wolff and Christian Crusius, we find no easy way to remain in rationalist paradise. (shrink)

Kant’s published arguments for the non-spatiotemporality of things in themselves have not been well received. I argue that Kant has available to himself an argument for the non-spatiotemporality of things in themselves that is premised upon a disparity between the compositional structure of the intelligible world and the structure of space and time. I argue that Kant was unwaveringly committed to the premises of this argument throughout his career and that he was aware of their idealistic implications. I also argue (...) that this argument is consistent with Kant’s restrictive mature epistemology. If my argument is successful, then even if Kant’s published arguments for transcendental idealism fail, we need not regard his ambitious metaphysical project as a failure. (shrink)

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in this collection. I first examine the more general questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the (...) question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy of mathematics. (shrink)

The paper examines Kant’s views on divine foreknowledge of contingent truths, in particular truths concerning free actions of creatures. It first considers the shape this traditional philosophical problem takes in the transcendental idealist context. It then situates Kant’s views relative to three competing theories of foreknowledge discussed by Leibniz. These are Molina’s theory of middle knowledge, the Thomist theory of foreknowledge through divine predeterminations, and Leibniz’s own ‘possible worlds’ theory. The paper concludes that no consistent theory of divine foreknowledge emerges (...) in Kant’s philosophy. His discussions alternate between two inadequate and incompatible models. One is a post-volitional model suggested by his conception of the intuitive intellect’s relation to creation. Extended to creaturely free action, it is incompatible with his commitment to the relative autonomy of free action. The other is a version of Leibniz’s possible worlds solution; it cannot underwrite certain foreknowledge of determinate outcomes in a libertarian setting. (shrink)

Much recent attention has been paid to Kant’s account of the unity of space in the Critique of Pure Reason, not least because of the significant implications of that view for other key critical-period doctrines. But far less attention has been paid to the development of Kant’s account of the unity of space. This paper aims to offer a systematic account of Kant’s pre-critical account of the unity of space. On the view presented herein, Kant’s early account of the unity (...) of space is deeply rooted in his pre-critical cosmological views. In particular, I argue that Kant sees the unity of space as grounded in the cosmological unity of the world of substances, which is itself rooted in the divine conservation of all substances in relations of mutual causal dependence. I contend that the seeds of this view are present in the late 1740s and 1750s, but that this view receives its fullest and most complete expression in the 1770 Inaugural Dissertation. The final section of the paper considers the fate of Kant’s pre-critical account of the unity of space. I contend that the theory is excluded from the Critique of Pure Reason in light of the strict epistemological strictures adopted in that text. But considerable textual evidence shows that Kant continues to aver the theory throughout the 1770s and 1780s in the looser epistemic context of his lectures. I contend, then, that this theory is not abandoned at all. Rather, like Kant’s 1763 proof of the existence of God, it is epistemically demoted: it is Kant’s preferred view, but one that falls short of the demanding epistemic standards of the critical philosophy. (shrink)