This volume contains the published contributions of one of the founders of modern logic and America's greatest logical genius. It is not only of historical but of contemporary interest because of its many acute discussions of fundamental logical problems. To assist the general reader, the editors have prefixed to the text a selected list of important topics and have provided many footnotes and an exhaustive index.
The present, the longest volume of the series of Peirce's Collected Papers, reveals most clearly his stature as a logician and a student of the foundations of mathematics. It includes not only some striking anticipations of recent work in logic and the foundations of mathematics but also a number of vital contributions to these subjects as now understood. In addition there is an entirely original treatment of logical diagrams which makes possible a detailed analysis of the process of reasoning and provides the link between modern logic and Peirce's conception of pragmatism. It is the most advanced and important of the volumes on exact logic.
Charles Hartshorne is Ashbel Smith Professor of Philosophy at the University of Texas. Paul Weiss is Heffer Professor of Philosophy at The Catholic University of America, Washington, D.C.
Introduction Editorial Note Chapter I: On an Improvement in Boole's Calculus of Logic (1867) Chapter II: Upon the Logic of Mathematics (1867) 1. The Boolian Calculus 2. On Arithmetic Chapter III: Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic (1870) 1. De Morgan's Notation 2. General Definitions of the Algebraic Signs 3. Application of the Algebraic Signs to Logic 4. General Formula 5. General Method of Working with this Notation 6. Properties of Particular Relative Terms Chapter IV: On the Application of Logical Analysis to Multiple Algebra (1875) Chapter V: Note on Grassmann's Calculus of Extension (1877) Chapter VI: On the Algebra of Logic (1880) Part I: Syllogistic 1. Derivation of Logic 2. Syllogism and Dialogism 3. Forms of Propositions 4. The Algebra of the Copula Part II: The Logic of Non-Relative Terms 1. The Internal Multiplication and the Addition of Logic 2. The Resolution of Problems in Non-Relative Logic Part III: The Logic of Relatives 1. Individual and Simple Terms 2. Relatives 3. Relatives connected by Transposition of Relate and Correlate 4. Classification of Relatives 5. The Composition of Relatives 6. Methods in the Algebra of Relatives 7. The General Formula for Relatives Chapter VII: On the Logic of Number (1881) 1. Definition of Quantity 2. Simple Quantity 3. Discrete Quantity 4. Semi-infinite Quantity 5. Discrete Simple Quantity Infinitein both Directions 6. Limited Discrete Simple Quantity Chapter VIII: Associative Algebras (1881) 1. On the Relative Forms of the Algebras 2. On the Algebras in which Division is Unambiguous Chapter IX: Brief Description of the Algebra of Relatives (1882) Chapter X: On the Relative Forms of Quaternions (1882) Chapter XI: On a Class of Multiple Algebras (1882) Chapter XII: The Logic of Relatives (1883) Chapter XIII: On the Algebra of Logic: A Contribution to the Philosophy of Notation (1885) 1. Three Kinds of Signs 2. Non-Relative Logic 3. First-Intentional Logic of Relatives 4. Second-Intentional Logic 5. Note Chapter XIV: The Critic of Arguments (1892) 1. Exact Thinking 2. The Reader is Introduced to Relatives Chapter XV: The Regenerated Logic (1896) Chapter XVI: The Logic of Relations (1897) 1. Three Grades of Clearness 2. Of the Term Relation in its First Grade of Clearness 3. Of Relation in the Second Grade of Clearness 4. Of Relation in the Third Grade of Clearness 5. Triads, the Primitive Relatives 6. Relatives of Second Intention 7. The Algebra of Dyadic Relatives 8. General Algebra of Logic 9. Method of Calculating with the General Algebra 10. Schroder's Conception of Logical Problems 11. Professor Schroder's Pentagrammatical Notation 12. Professor Schroder's Iconic Solution of 13. Introduction to the Logic of Quantity Chapter XVII: The Logic of Mathematics in Relation to Education (1808) 1. Of Mathematics in General 2. Of Pure Number Chapter XVIII: Infinitesimals (1900) Chapter XIX: Nomenclacture and Divisions of Dyadic Relations (1903) 1. Nomenclature 2. First System of Divisions 3. Second System of Divisions 4. Third System of Divisions 5. Fourth System of Divisions 6. Note on the Nomenclature and Divisions of Modal Dyadic Relations Chapter XX: Notes on Symbolic Logic and Mathematics (1901 and 1911) 1. Imaging 2. Individual 3. Involution 4. Logic (exact) 5. Multitude (in mathematics) 6. Postulate 7. Presupposition 8. Relatives 9. Transposition Appendix: On Nonions Index of Proper Names Index of Subjects