Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)

§30. Significance of Desargues's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 CHAPTER VI. PASCAL'S THEOREM. §31. ...

In this new book, Michael Friedman argues that Kant's continuing efforts to find a metaphysics that could provide a foundation for the sciences is of the utmost ...

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 ..

We cannot imagine two straight lines intersecting at two points even though they may do so. In this case our abilities to imagine depend upon our abilities to visualise.

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

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)

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.