In lieu of an abstract, here is a brief excerpt of the content:Kant on the Method of MathematicsEmily Carson1. INTRODUCTIONThis paper will touch on three very general but closely related questions about Kant’s philosophy. First, on the role of mathematics as a paradigm of knowledge in the development of Kant’s Critical philosophy; second, on the nature of Kant’s opposition to his Leibnizean predecessors and its role in the development of the Critical philosophy; and finally, on the specific role of intuition (...) in Kant’s philosophy of mathematics. One of the points that I want to make is that recognizing the importance of these first two issues is essential to giving an adequate account of the third. That is, only by appreciating how Kant uses the example of mathematical knowledge, and in particular the objections he had to previous accounts of such knowledge, can we understand the philosophical role that he ascribes to intuition in his own account of mathematics.I don’t propose to explain the details of Kant’s philosophy of mathematics, but rather to compare his views on mathematics in the pre-Critical Prize Essay of 1764 to those of the Critique of Pure Reason, with the aim of showing how Kant’s doctrine of construction in pure intuition arises out of a combination of two factors: first, his attempt to ground the distinction between the respective methods of mathematics and philosophy, and second, his concern to defend the reality of mathematical knowledge against the views of those he called ‘the metaphysicians.’ The first factor demands an account of the certainty of mathematics, the second requires an account of its content. I shall argue that there is a possible conflict between Kant’s accounts of these features in the Prize Essay, a possibility which is finally ruled out only by means of the Critical doctrine of pure intuition. So I hope to show that there is a significant philosophical role for intuition in Kant’s account of mathematical knowledge (over and above the more logical role attributed to it on readings [End Page 629] such as those of Friedman, Beth, and Hintikka1) in reconciling the content of mathematics and its certainty.2. THE MATHEMATICIANS VS. THE METAPHYSICIANSThroughout his early writings, Kant appealed to the evidence and certainty of mathematics; his attitude towards metaphysics, however, underwent a dramatic shift. In the Physical Monadology of 1756, Kant asked how metaphysics and geometry can be united,[f] or the former peremptorily denies that space is infinitely divisible, while the latter, with its usual certainty, asserts that it is infinitely divisible. Geometry contends that empty space is necessary for free motion, while metaphysics hisses the idea off the stage. Geometry holds universal attraction or gravitation to be hardly explicable by mechanical causes but shows that it derives from the forces which are inherent in bodies at rest and which act at a distance, whereas metaphysics dismisses the notion as an empty delusion of the imagination [1:475–6].2He attempted in this work to reconcile the respective positions of metaphysics and geometry regarding infinite divisibility, thereby demonstrating that “it is neither the case that the geometer is mistaken nor that the opinion to be found among metaphysicians deviates from the truth” [1:480]. But in a series of works from 1762–3, Kant reveals a markedly different attitude towards metaphysics. For example, in “The only possible argument in support of a demonstration of the existence of God,” Kant says:the mania for method and the imitation of the mathematician, who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps on the slippery ground of metaphysics. These mishaps are constantly before one’s eyes, but there is little hope that people will be warned by them, or that they will learn to be more circumspect as a result [2:71].In contrast, Kant describes the geometer as uncovering “with the greatest certainty” the most secret properties of that which is extended [2:70]. But the less conciliatory attitude to metaphysics comes out most clearly in Kant’s actual procedure in “The only possible argument.” In the Seventh Reflection, he presents an attempt to explain the origin of... (shrink)

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)

This new translation is an extremely welcome addition to the continuing Cambridge Edition of Kant’s works. English-speaking readers of the third Critique have long been hampered by the lack of an adequate translation of this important and difficult work. James Creed Meredith’s much-reprinted translation has charm and elegance, but it is often too loose to be useful for scholarly purposes. Moreover it does not include the first version of Kant’s introduction, the so-called “First Introduction,” which is now recognized as indispensable (...) for an understanding of the work. Werner Pluhar’s more recent translation, which does include the First Introduction, is highly accurate when it confines itself to rendering Kant’s German. However, it is often more of a reconstruction than a translation, containing so many interpretative interpolations that it is often difficult to separate out Kant’s original text from the translator’s contributions. Paul Guyer and Eric Matthews have provided a translation that compares to or exceeds Pluhar’s in its literal approach to the German, but that confines all interpretative material to footnotes and endnotes, so that the text itself, with all its unclarities and ambiguities, lies open to view. In addition, Guyer, as editor of the volume, has provided a great deal of valuable supplementary material. This includes an introduction with an outline of the work and details of the history of its composition and publication, and a wealth of endnotes offering clarifications of the text, background information, and, most strikingly, many references to related passages in Kant’s voluminous writings, particularly in connection with Kant’s earlier writings related to aesthetics. The edition also records differences among the first three editions of the work, and—of particular interest—erasures from and additions to Kant’s manuscript of the First Introduction. Although the introduction and endnotes reflect interpretative views that are sometimes disputable, this supplementary material makes the present edition into a valuable resource even for those able to read the text in German. (shrink)

This is a very important book. It has already become required reading for researchers on the relation between the exact sciences and Kant’s philosophy. The main theme is that Kant’s continuing program to find a metaphysics that could provide a foundation for the science of his day is of crucial importance to understanding the development of his philosophical thought from its earliest precritical beginnings in the thesis of 1747, right through the highwater years of the critical philosophy, to his last (...) unpublished writings in the Opus postumum. In the course of articulating this theme, Friedman has made extensive use of detailed historical information about their scientific and mathematical background to illuminate Kant’s texts. Over and over again, such information is used to suggest interesting and quite subtle interpretations for texts that may have seemed puzzling or just wrong-headed. (shrink)

The Duisburg Nachlaß is a bundle of Kant’s handwritten notes. These notes almost certainly go back to some time in 1775. Though very obscure, they replay issues in Kant’s early metaphysics just as clearly as they anticipate issues in the Critique of Pure Reason. This makes them an important way-station in Kant’s philosophical development—all the more important, because he published nothing in the 1770s and left no other extended writings in his own hand. A proper understanding of the Duisburg Nachlaß (...) might therefore explain some of Kant’s later ideas: their origins in his earlier thinking and their philosophical motivations. The purpose of this paper is to lay the groundwork for such an explanation—at least a partial one. I shall argue that Kant’s efforts in the Duisburg Nachlaß to correct certain difficulties in the Inaugural Dissertation of 1770 anticipate and naturally lead to the crucial claim in the Critique of Pure Reason that the understanding legislates laws to nature. (shrink)

kant famously claims that space is merely a feature of the mind—something subjective—rather than a mind-independent feature of reality in itself.1 In accepting the subjectivity thesis, Kant rejects the transcendental realist assumption that he thinks has traditionally, albeit tacitly, been made in debates about the nature of space. According to this assumption, space has to do with things in themselves. For the Newtonians, as Kant understands their position, space is a substance-like thing in itself; for the Leibnizians, space consists in (...) relations among things in themselves.2 Kant breaks sharply with these traditional accounts.However, it would be a mistake to think that Kant's commitment to the... (shrink)

This paper tries to make sense of Kant's scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant's attitude towards mathematics and the way he understood the cognitive resources available to us to do mathematics.

This new translation of the first Critique forms part of a fifteen-volume English-language edition of the works of Immanuel Kant under the general editorship of this volume’s editor-translators, Paul Guyer and Allen Wood. The edition, which is almost complete by now, comprises all of Kant’s published works along with extensive selections from his literary remains, his correspondence, and student transcripts of his lecture courses in metaphysics, ethics, logic, and anthropology. The Cambridge edition aims at a consistent English rendition of Kant’s (...) works, both within a given volume and across volumes. In terms of scope and detail, the Cambridge edition is unrivaled in any language, except for the authoritative Academy edition begun under the directorship of Wilhelm Dilthey in 1900, which, however, is still not completed and several volumes of which are in serious need of re-editing. In one case, that of the Opus postumum, the best edition currently available seems to be the one in the Cambridge edition. (shrink)

In the Transcendental Aesthetic, Kant famously characterizes space as a unity, understood as an essentially singular whole. He further develops his account of the unity of space in the B-Deduction, where he relates the unity of space to the original synthetic unity of apperception, and draws an infamous distinction between form of intuition and formal intuition. Kant ’s cryptic remarks in this part of the Critique have given rise to two widespread and diametrically opposed readings, which I call the Synthesis (...) and Brute Given Readings. I argue for an entirely new reading, which I call the Part-Whole Reading, in part by considering the development of Kant ’s views on the unity of space from his earliest works up through crucial reflections written during the silent decade. (shrink)

Kant claims that we cannot cognize the mutual interaction of substances without their being in space; he also claims that we cannot cognize a ‘spatial community’ among substances without their being in mutual interaction. I situate these theses in their historical context and consider Kant’s reasons for accepting them. I argue that they rest on commitments regarding the metaphysical grounding of, first, the possibility of mutual interaction among substances-as-appearances and, second, the actuality of specific distance-relations among such substances. By illuminating (...) these commitments, I shed light on Kant’s metaphysics of space and its relation to Newton and Leibniz’s views. (shrink)

While interest in Kant's philosophy has increased in recent years, very little of it has focused on his theory of science. This book gives a general account of that theory, of its motives and implications, and of the way it brought forth a new conception of the nature of philosophical thought. To reconstruct Kant's theory of science, the author identifies unifying themes of his philosophy of mathematics and philosophy of physics, both undergirded by his distinctive logical doctrines, and shows how (...) they come together to form a relatively consistent system of ideas. A new analysis of the structure of central arguments in the Critique of Pure Reason and the Prolegomena draws on recent developments in logic and the philosophy of science. Professor Brittan's unified account of the philosophies of mathematics and physics explores the nature of Kant's commitment to Euclidean geometry and Newtonian mechanics as well as providing an integrated reading of the Critique of Pure Reason and the Metaphysical Foundations of Natural Science. Contemporary ideas help both to illuminate Kant's position and to show how that position, in turn, illuminates contemporary problems in the philosophy of science. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)