In interpretations of the "Transcendental Aesthetic" section of the first Critique, there is a widespread tendency to present Kant as establishing that the representation of space is a condition for individuating or distinguishing objects, and to claim that it is on this basis that Kant establishes the apriority of this representation. The aim of this paper is to criticize this way of interpreting the "Aesthetic," and to defend an alternative interpretation. On this alternative, questions about the formation of the representation (...) of space figure more centrally, and the anti-Leibnizian character of Kant 's argument can be properly appreciated. (shrink)

This intellectual biography of Immanuel Kant's early years--from 1747 when his first book was published, to 1770 when his Critique of Pure Reason was about to be printed--makes an outstanding contribution to Kant scholarship. Schonfeld meticulously examines almost all of Kant's early works, summarizes their content, and exhibits their shortcomings and strengths. He places the early theories in their historical context and describes the scientific discoveries and philosophical innovations that distinguish Kant's pre-critical works. Schonfeld argues that these works were all (...) aspects of a single project carried out by Kant to reconcile metaphysical and scientific perspectives and combine them into a coherent model of nature. (shrink)

This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress.

T HE heart of Kant's views on the nature of mathematics is his thesis that the judgments of pure mathematics are synthetic a priori. Kant usually offers this as one thesis, but it is fruitful to regard it as consisting of two separate claims, a meta- physical subthesis and an epistemological ..

Kant's views on logic and logical theory play an important role in his critical writings, especially the Critique of Pure Reason. However, since he published only one short essay on the subject, we must turn to the texts derived from his logic lectures to understand his views. The present volume includes three previously untranslated transcripts of Kant's logic lectures: the Blumberg Logic from the 1770s; the Vienna Logic (supplemented by the recently discovered Hechsel Logic) from the early 1780s; and the (...) Dohna-Wundlacken Logic from the early 1790s. Also included is a new translation of the Jasche Logic, compiled at Kant's request and published in 1800 but which also appears to stem in part from a transcript of his lectures. Together these texts provide a rich source of evidence for Kant's evolving views on logic, on the relations between logic and other disciplines, and on a variety of topics (e.g. analysis and synthesis) central to Kant's mature philosophy. They also provide a portrait of Kant as lecturer, a role in which he was both popular and influential. This volume contains substantial editorial apparatus: a general introduction, linguistic and factual notes, glossaries of key terms (both German/English and English/German) and concordances relating Kant's lectures to Georg Frederich Meier's Excerpts from the Doctrine of Reason, the book on which Kant lectured throughout his life and in which he left extensive notes. (shrink)

According to Kant, “mathematical knowledge is the knowledge gained by reason from the construction of concepts.” In this paper, I shall make a few suggestions as to how this characterization of the mathematical method is to be understood.

In this paper I argue that Kant's distinction in the Inaugural Dissertation between the sensible and the intelligible arises in part out of certain open questions left open by his comparison between mathematics and metaphysics in the Prize Essay. This distinction provides a philosophical justification for his distinction between the respective methods of mathematics and metaphysics and his claim that mathematics admits of a greater degree of certainty. More generally, this illustrates the importance of Kant's reflections on mathematics for the (...) development of his Critical philosophy. (shrink)

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)

The purpose of the Cambridge edition is to offer translations of the best modern German edition of Kant's work in a uniform format suitable for Kant scholars. This volume is the first to assemble in historical sequence the writings that Kant published between 1783 and 1796 to popularize, summarize, amplify and defend the doctrines of his masterpiece, the Critique of Pure Reason of 1781. The best known of them, the Prolegomena, is often recommended to beginning students, but the other texts (...) are also vintage Kant and are important sources for a fully-rounded picture of Kant's intellectual development. As with other volumes in the series there are copious linguistic notes and a glossary of key terms. The editorial introductions and explanatory notes shed light on the critical reception accorded Kant by the metaphysicians of his day and on Kant's own efforts to derail his opponents. (shrink)

Wayne Waxman here presents an ambitious and comprehensive attempt to link the philosophers of what are known as the British Empiricists--Locke, Berkeley, and Hume--to the philosophy of German philosopher Immanuel Kant. Much has been written about all these thinkers, who are among the most influential figures in the Western tradition. Waxman argues that, contrary to conventional wisdom, Kant is actually the culmination of the British empiricist program and that he shares their methodological assumptions and basic convictions about human thought and (...) knowledge. (shrink)

The first major section of the Critique of Pure Reason, the Transcendental Aesthetic, is concerned with the nature of space and time, and with the nature of our representation of them. In interpretations of this part of the Critique, there is a very widespread tendency to present Kant’s discussion of space as attempting to establish that the representation of space is a condition for individuating or distinguishing objects, and that it is on this basis that Kant establishes the apriority of (...) this representation. I believe that this way of interpreting the Aesthetic is wholly misguided. The interpretive tendency I have in mind takes a number of different forms. On one approach, the role of space is to allow us to distinguish objects even if they are qualitatively identical. This represents Kant as making a certain kind of anti-Leibnizian point, one that concerns Leibniz’s principle of the identity of indiscernibles. On another approach, space—or something closely analogous to space—is regarded as essential on account of its role in allowing us to re-identify objects over time. Interpretations of Kant that follow the second approach are largely inspired by Strawson’s discussions of these matters in chapter 2 of Individuals. (shrink)

Where the possibility of metaphysics as a science is concerned, Kant assigns the exact sciences the function of an exemplar; for these disciplines have long been well established on "the secure path of a science." Accordingly, in the Prolegomena Kant explicitly addresses the question "How is metaphysics possible as a science?" by way of the questions "How is pure mathematics possible?" and "How is pure natural science possible?" Moreover, all these questions arise directly out of the main transcendental question: "How (...) are synthetic judgments a priori possible?" The deplorable situation of the metaphysics of the day would have been entirely attributable to misappraisal of this central transcendental question. (shrink)

Kant's distinction between intuitive and discursive knowledge precludes his giving intuitions linguistic representation. Singular terms represent concepts given what kant calls a 'singular use' and are analyzable as definite descriptions. That the object described exists and that there is only one such object can be given linguistic representation only through an explicit assertion of existence and uniqueness. As an intuitionist in mathematics kant holds that mathematics proclaims the constructibility and not the existence of its objects.

Where the possibility of metaphysics as a science is concerned, Kant assigns the exact sciences the function of an exemplar; for these disciplines have long been well established on "the secure path of a science." Accordingly, in the Prolegomena Kant explicitly addresses the question "How is metaphysics possible as a science?" by way of the questions "How is pure mathematics possible?" and "How is pure natural science possible?" Moreover, all these questions arise directly out of the main transcendental question: "How (...) are synthetic judgments a priori possible?" The deplorable situation of the metaphysics of the day would have been entirely attributable to misappraisal of this central transcendental question. (shrink)

Kant maintains that his Critique of Pure Reason follows a “synthetic method” which he distinguishes from the analytic method of the Prolegomena by saying that the Critique “rests on no other science” and “takes nothing as given except reason itself”. The paper presents an account of the synthetic method of the Critique, showing how it is related to Kant’s conception of the Critique as the “science of an a priori judging reason”. Moreover, the author suggests, understanding its synthetic method sheds (...) light on the structure of the Transcendental Deduction, and its function in the work as a whole. (shrink)