Translation of Paul Guyer's "Kant’s Deductions of the Principles of Right".

Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have `intuitive content' in order to show that both (...) Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. -/- Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (shrink)

In this paper, I argue, first, that Hegel defended a version of the analytic/synthetic distinction—that, indeed, his version of the distinction deserves to be called Kantian. For both Kant and Hegel, the analytic/synthetic distinction can be explained in terms of the discursive character of cognition: insofar as our cognition is discursive, its most basic form can be articulated in terms of a genus/species tree. The structure of that tree elucidates the distinction between analytic and synthetic judgments. Second, I argue that (...) Hegel has an interesting and so far unexplored argument for the analytic/synthetic distinction: Hegel argues that the systematic relationship between concepts expressed in a genus/species tree can only be expressed through synthetic judgments. Third and finally, I explore some of the implications that the arguments in the first two parts of the essay have for understanding the way in which Hegel differs from Kant. I argue that Hegel accepts Kant's point that discursive cognition cannot be used to cognize the absolute. However, Hegel thinks that we can, nevertheless, cognize the absolute. I explore the character of this non-discursive cognition and argue that we can understand Hegel's glosses on this form of cognition—as simultaneously analytic and synthetic and as having a circular structure—through contrasting it with his account of discursive cognition. As a consequence, I argue that we must give up on attempts to understand ‘the dialectical method’ and ‘speculative cognition’ on the model of discursive cognition. (shrink)

I present an argument for an interpretation ofKant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations ofKant's views on cognitive content, which ascribes toKant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading ofKant put forward byMcDowell and others, according to whichKant embraces a version ofRussellianism, I argue thatKant's views on this topic are of a much moreFregean bent than has (...) traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp ofKant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non‐conceptual content. (shrink)

Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have 'intuitive content' in order to show that both (...) Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (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)