This entirely new translation of Critique of Pure Reason by Paul Guyer and Allan Wood is the most accurate and informative English translation ever produced of this epochal philosophical text. Though its simple, direct style will make it suitable for all new readers of Kant, the translation displays a philosophical and textual sophistication that will enlighten Kant scholars as well. This translation recreates as far as possible a text with the same interpretative nuances and richness as the original.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

One of the cornerstone books of Western philosophy, Critique of Pure Reason is Kant's seminal treatise, where he seeks to define the nature of reason itself and builds his own unique system of philosophical thought with an approach known as transcendental idealism. He argues that human knowledge is limited by the capacity for perception and attempts a logical designation of two varieties of knowledge: a posteriori, the knowledge acquired through experience; and a priori, knowledge not derived through experience. This accurate (...) translation by J. M. D. Meiklejohn offers a simple and direct rendering of Kant's work that is suitable for readers at all levels. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with the (...) modern structural approach in mathematics. (shrink)

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph (...) begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst. By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science. (shrink)

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work.

This paper discusses the connection between the actual history of mathematics and Lakatos's philosophy of mathematics, in three parts. The first points to studies by Lakatos and others which support his conception of mathematics and its history. In the second I suggest that the apparent poverty of Lakatosian examples may be due to the way in which the history of mathematics is usually written. The third part argues that Lakatos is right to hold philosophy accountable to history, even if Lakatos's (...) own view of mathematics fails that test. (shrink)

At their extremes, the modernization of ancient mathematical texts (absolute presentism) leaves nothing of the source and the refusal to modernize (absolute antiquarism) changes nothing. The extremes exist only as tendencies. This paper attempts to justify the admissibility of broad modernization of mathematical sources (presentism) in the context of a socio-cultural (non-fundamentalist) philosophy of mathematics.

The dissertation is a detailed analysis of Berkeley's writings on mathematics, concentrating on the link between his attack on the theory of abstract ideas and his philosophy of mathematics. Although the focus is on Berkeley's works, I also trace the important connections between Berkeley's views and those of Isaac Barrow, John Wallis, John Keill, and Isaac Newton . The basic thesis I defend is that Berkeley's philosophy of mathematics is a natural extension of his views on abstraction. The first chapter (...) is devoted to a consideration of Berkeley's treatment of abstraction, including his arguments against the doctrine of abstract ideas and his own account of how the explanatory ideas traditionally assigned to abstract ideas can be filled by a non-abstractionist account of human knowledge. In chapter two I investigate the details of Berkeley's proposed new foundations for geometry, showing how his rejection of abstract ideas led him to a critique of the traditional conception of geometry . Of particular importance in this context is Berkeley's denial of infinite divisibility and his attempts to show that a satisfactory account of geometry does not require that geometric magnitudes be infinitely divisible. Chapter three is concerned with Berkeley's treatment of arithmetic and algebra. Here I argue that Berkeley's denial of the claim that arithmetic is the science of abstract ideas of number ultimately results in his advocacy of a strongly nominalistic conception of arithmetic which has strong similarities to modern fomalism. In chapter four I discuss Berkeley's famous critique of the calculus in The Analyst and other works, concluding that his criticism of the calculus is essentially correct, although his attempted explanation of the success of infinitesimal methods is unconvincing. (shrink)

At their extremes, the modernization of ancient mathematical texts leaves nothing of the source and the refusal to modernize changes nothing. The extremes exist only as tendencies. This paper attempts to justify the admissibility of broad modernization of mathematical sources in the context of a socio-cultural philosophy of mathematics.

When rare documents are collected and reprinted as Opere, Oeuvres, and Gesammelte Schriften, new diagrams are introduced. For the most part the new are faithful reproductions of the old. Sometimes, however, editors correct or simplify diagrams. Thus, before one writes, “so-and-so represents the area to be squared by seven parallelograms,” the more meticulous among us make a before-and-after comparison to insure that the “So-and-so” dividing the space is in fact the mathematician under scrutiny, and not some subsequent draftsman. This underlines (...) the importance of the facsimile edition. (shrink)

Mathematics, and mechanics conceived as a formal science, have their own proper subject matters, their own proper unities, which ground the characteristic way of constituting problems and solutions in each domain, the discoveries that expand and integrate domains with each other, and so in particular allow them, in the end, to be connected in a partial way with empirical fact. Criticizing both empiricist and structuralist accounts of mathematics, I argue that only an account of the formal sciences which attributes to (...) them objects as well as structure, proper semantics as well as syntax, can do justice to their intelligibility, heuristic force and explanatory power. (shrink)