ABSTRACT One of the core issues where interpreters of Kant disagree concerns his alleged Noumenalism—the claim that the objects of our experience, which are in space and time, are underpinned by entities that are not spatio-temporal and that non-spatio-temporally cause our representations of empirical objects. Although there is much textual evidence in favour of Noumenalism, non-Noumenalists have also gathered a significant number of philosophical and exegetical challenges to such a reading of Kant. I present a novel way of understanding the (...) Noumenalist view, which characterises the distinction between appearances and things in themselves as the distinction between referents and truthmakers. I show that, on this interpretation of Kant, the most pressing problems for the Noumenalist reading are primarily based on equivocations between features of reference and features of truthmaking. (shrink)

By considering the semantic footings of the so-called antinomies of pure reason, this article contributes to the debate about whether Kant was committed to semantic realism or anti-realism. That is, whether verification-transcendent judgements are truth-apt (realism) or not (anti-realism). Against the (empiricist) semantic principle that Strawson, and others, have ascribed to Kant as the “principle of significance,” the bedrock of my article is what I call Kant’s Real Principle of Significance: an extension-based and normative principle stating that a judgement can (...) have no “significance” or “objective validity” (truth-value) without a universally recognizable norm for verifying it. This principle entails semantic anti-realism. I argue that we can extract the principle from the antinomy chapter of KrV, since in there Kant concludes that judgements of the form “the world as such is x” are without “significance” (lack a truth-value) in virtue of being unverifiable as a matter of principle. I propose that Kant’s reference to some of the antinomical judgements as “false” is not incompatible with this anti-realist reading because he operates with two distinct world-concepts: an illegitimate transcendental realist one and a legitimate transcendental idealist one. In contrast to most anti-realist Kant-interpretations, it is furthermore argued that any satisfactory anti-realist construal of Kant’s view must be compatible with his assertion that the thesis in the third antinomy about freedom “can be true.” That requires a thicker conception of “significance” or “objective validity” than what is often ascribed to Kant, which is encapsulated by the Real Principle of Significance. (shrink)

This paper draws out and connects two neglected issues in Kant’s conception of a priori knowledge. Both concern topics that have been important to contemporary epistemology and to formal epistemology in particular: knowability and luminosity. Does Kant commit to some form of knowability principle according to which certain necessary truths are in principle knowable to beings like us? Does Kant commit to some form of luminosity principle according to which, if a subject knows a priori, then they can know that (...) they know a priori? I defend affirmative answers to both of these questions, and by considering the special kind of modality involved in Kant’s conceptions of possible experience and the essential completability of metaphysics, I argue that his combination of knowability and luminosity principles leads Kant into difficulty. (shrink)

I thank the editors for inviting me to contribute to this issue on critical views of logic. Kant invented the critical philosophy. He fashioned its doctrines (Understanding versus Reason, synthetic...

ABSTRACT This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant’s ‘Critical Philosophy’. Part I reviews some old work of mine that applies these models to provide a reading of Kant’s second antinomy about the divisibility of matter and to answer several attacks on Kant’s antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant’s second antinomy claim that matter is divisible ‘ad infinitum’ and (...) his first antinomy claim that empirical space extends only ‘ad indefinitum’. Secondly, in conformity with the ‘assertability’ heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant’s two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts to resolve a tension in Leibniz’s philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant’s signature critical doctrines, and it shows how Kant’s critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. (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 ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which (...) last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy. (shrink)