Philosophy of mathematics : selected writings

The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.

Table of Contents Preface Introduction 1 [The Nature of Mathematics] 2 The Regenerated Logic 3 The Logic of Mathematics in Relation to Education 4 The Simplest Mathematics 5 The Essence of Reasoning 6 New Elements of Geometry 7 On the Logic of Quantity 8 Sketch of Dichotomic Mathematics 9 [Pragmatism and Mathematics] 10 Prolegomena to an Apology for Pragmaticism 11 ['Collection' in The Century Dictionary] 12 [On Collections and Substantive Possibility] 13 [The Ontology of Collections] 14 The Logic of Quantity 15 Recreations in Reasoning 16 Topical Geometry 17 A Geometrico-Logical Discussion 18 ['Continuity' in The Century Dictionary] 19 The Law of Mind 20 [Scientific Fallibilism] 21 On Quantity [The Continuity of Time and Space] 22 Detached Ideas Continued and the Dispute between Nominalists and Realists 23 The Logic of Continuity 24 [On Multitudes] 25 Infinitesimals 26 The Bed-Rock beneath Pragmaticism 27 [Note and Addendum on Continuity] 28 Addition [on Continuity] 29 Supplement [on Continuity] Notes Bibliography Index