The book also includes a chronological table of significant events, select bibliography, succinct explanatory notes, and an index--all of which supply ...

It's well-known that Kant believed that intuition was central to an account of mathematical knowledge. What that role is and how Kant argues for it are, however, still open to debate. There are, broadly speaking, two tendencies in interpreting Kant's account of intuition in mathematics, each emphasizing different aspects of Kant's general doctrine of intuition. On one view, most recently put forward by Michael Friedman, this central role for intuition is a direct result of the limitations of the syllogistic logic (...) available to Kant. On this view, Kant's reasons for introducing intuition are taken to be logical or mathematical, rather than philosophical. The other tendency, which I shall try to develop here, emphasizes an epistemological or phenomenological role for intuition in mathematics arising out of what may loosely be called Kant's ‘antiformalism.’This paper, which focuses specifically on the case of geometry, falls into two parts. First, I consider Kant's discussion of intuition in the Metaphysical Exposition of the concept of space. (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)

What would something unlike us--a chimpanzee, say, or a computer--have to be able to do to qualify as a possible knower, like us? To answer this question at the very heart of our sense of ourselves, philosophers have long focused on intentionality and have looked to language as a key to this condition. Making It Explicit is an investigation into the nature of language--the social practices that distinguish us as rational, logical creatures--that revises the very terms of this inquiry. Where (...) accounts of the relation between language and mind have traditionally rested on the concept of representation, this book sets out an alternate approach based on inference, and on a conception of certain kinds of implicit assessment that become explicit in language. Making It Explicit is the first attempt to work out in detail a theory that renders linguistic meaning in terms of use--in short, to explain how semantic content can be conferred on expressions and attitudes that are suitably caught up in social practices. -/- At the center of this enterprise is a notion of discursive commitment. Being able to talk--and so in the fullest sense being able to think--is a matter of mastering the practices that govern such commitments, being able to keep track of one’s own commitments and those of others. Assessing the pragmatic significance of speech acts is a matter of explaining the explicit in terms of the implicit. As he traces the inferential structure of the social practices within which things can be made conceptually explicit, the author defines the distinctively expressive role of logical vocabulary. This expressive account of language, mind, and logic is, finally, an account of who we are. (shrink)

A collection of Lewis Beck's writings on the philosophy and interpretation of Immanuel Kant.

This comprehensive history of German philosophy from its medieval beginnings to near the end of the eighteenth century explores the spirit of German intellectual life and its distinctiveness from that of other countries. Beck devotes whole chapters to four great philosophers -- Nicholas of Cusa, Leibniz, Lessing, and Kant -- and extensively examines many others, including Albertus Magnus, Meister Eckhart, Paracelsus, Kepler, Mendelssohn, Wolff, and Herder. Questioning explanations of philosophy by the racial or ethnic character of its exponents, Beck's conclusion (...) is that German philosophy developed as a series of diverse responses to the historical experiences of the German people. The peculiarities of German philosophy must be viewed in the light of German political problems and educational structures. In particular he stresses the importance of the connections between philosophy and Germany's intellectual, literary, religious, and political history. (shrink)

This landmark book is now reissued in a new edition that has been vastly rewritten and updated to respond to recent Kantian literature.

Legendary since his own time as a universal genius, Gottfried Wilhelm Leibniz (1646-1716) contributed significantly to almost every branch of learning. One of the creators of modern mathematics, and probably the most sophisticated logician between the Middle Ages and Frege, as well as a pioneer of ecumenical theology, he also wrote extensively on such diverse subjects as history, geology, and physics. But the part of his work that is most studied today is probably his writings in metaphysics, which have been (...) the focus of particularly lively philosophical discussion in the last twenty years or so. The writings contain one of the great classic systems of modern philosophy, but the system must be pieced together from a vast and miscellaneous array of manuscripts, letters, articles, and books, in a way that makes especially strenuous demands on scholarship. This book presents an in-depth interpretation of three important parts of Leibniz's metaphysics, thoroughly grounded in the texts as well as in philosophical analysis and critique. The three areas discussed are the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance (the famous theory of monads). (shrink)

Designed for students with no prior training in logic, INTRODUCTION TO LOGIC AND CRITICAL THINKING offers an accessible treatment of logic that enhances understanding of reasoning in everyday life. The text begins with an introduction to arguments. After some linguistic preliminaries, the text presents a detailed analysis of inductive reasoning and associated fallacies. This order of presentation helps to motivate the use of formal methods in the subsequent sections on deductive logic and fallacies. Lively and straightforward prose assists students in (...) gaining facility with the sometimes challenging concepts of logic. By combining a sensitive treatment of ordinary language arguments with a simple but rigorous exposition of basic principles of logic, the text develops students' understanding of the relationships between logic and language, and strengthens their skills in critical thinking. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

By what process of development he came to this opinion, though in itself an important and interesting question, is logically irrelevant to the inquiry how far the opinion itself is correct ; and among his opinions, when these have been ascertained, it becomes desirable to prune away such as seem inconsistent with his main doctrines, before those doctrines themselves are subjected to a critical scrutiny. Philosophic truth and falsehood, in short, rather than historical fact, are what primarily demand our attention (...) in this inquiry. (shrink)

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the develop ment (...) of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve. (shrink)

This influential study of Kant in which Strawson seeks to detach the true analytical and critical achievement of Kant's work from the unacceptable metaphysics with which it is entangled. This title available in eBook format. Click here for more information.Visit our eBookstore at: www.ebookstore.tandf.co.uk.

'Mr Bennett, as was to be expected, has written a first-rate book on Kant's Analytic. It is vivid, entertaining, and extremely instructive. It will be found of absorbing interest both by those who already know the Critique and by those - if there are any such - who have a developed interest in philosophy, yet no direct acquaintance with Kant. These last it will surely drive to the text and, as surely, will drive them to approach it in a truly (...) philosophical spirit. Bennett's Kant is not a giant immersed, or frozen, in time. He is a great contemporary - a little out of touch, admittedly, with recent developments in mathematics and physics - but one with whom we can all argue, against him, at his side, or obliquely to him. And so Bennett does argue, continuously, fiercely, and fruitfully; and summons to join in the argument, at appropriate moments, those older contemporaries, Locke, Leibniz, Berkeley, and Hume, and those younger contemporaries, Wittgenstein, Ryle, Ayler, Quine, Quinton, Warnock, and others. This is splendid, and a necessary corrective to that extraordinary isolation in which Kant tends to be islanded, partly indeed, by his own unique qualities, but partly by oceans of the wrong kind of respect. Bennett, continuously engaging his great antagonist, shows the right kind.'. (shrink)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (shrink)

In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...) interpretations and criticisms of Kant’s conception of mathematics on this small section of the Critique. (shrink)

The historical researches of Louis Couturat saved the logical work of Leibniz from the oblivion of neglect and forgetfulness. They revealed that Leibniz developed in succession several versions of a “logical calculus” (calculus ratiocinatororcalculus universalis). In consequence of Couturat's investigations it has become well known that Leibniz's development of these logical calculi adumbrated the notion of a logistic system; and for these foreshadowings of the logistic treatment of formal logic Leibniz is rightly regarded as the father of symbolic logic.It is (...) clear from what has been said that it is scarcely possible to overestimate the debt which the contemporary student of Leibniz's logic owes to Couturat. This gratitude must, however, be accompanied by the realization that Couturat's own theory of logic is gravely defective. Couturat was persuaded that the extensional point of view in logic is the only one which is correct, an opinion now quite antiquated, and shared by no one. This prejudice of Couturat's marred his exposition of Leibniz's logic. It led him to battle with windmills: he viewed the logic of Leibniz as rife with shortcomings stemming from an intensional approach.The task of this paper is a re-examination of Leibniz's logic. It will consider without prejudgment how Leibniz conceived of the major formal systems he developed aslogicalcalculi – that is, these systems will be studied with a view to the interpretation or interpretations which Leibniz himself intends for them. The aim is to undo some of the damage which Couturat's preconception has done to the just understanding of Leibniz's logic and to the proper evaluation of his contribution. (shrink)

"Kant and the Capacity to Judge" will prove to be an important and influential event in Kant studies and in philosophy.

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 ..

In this innovative study Patricia Kitcher argues that we can only understand the deduction of the categories in Kant's Critique of Pure Reason in terms of his attempt to fathom the psychological prerequisites of thought. Thus a consideration of his conception of psychology is essential to an understanding of his philosophy. Kitcher specifically considers Kant's claims about the unity of the thinking self; the spatial forms of human perceptions; the relations among mental states necessary for them to have content; the (...) relations between perceptions and judgment; and the limits of philosophical insight into psychological processes. (shrink)

This is the first volume of the first ever comprehensive edition of the works of Immanuel Kant in English translation. The eleven essays in this volume constitute Kant's theoretical, pre-critical philosophical writings from 1755 to 1770. Several of these pieces have never been translated into English before; others have long been unavailable in English. We can trace in these works the development of Kant's thought to the eventual emergence in 1770 of the two chief tenets of his mature philosophy: the (...) subjectivity of space and time, and the phenomena-noumena distinction. The volume has been furnished with substantial editorial apparatus, including a general introduction to the main themes of Kant's early thought, introduction to the individual works and re;sume;s of their contents, linguistic and factual notes, bibliographies, a glossary of key terms, and biographical-bibliographical sketches of persons mentioned by Kant. (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.