Table of Contents

I. The Traditional Syllogism.- 1. Whately and the Revival of Formal Logic.- 2. Euclid and the Syllogism.- 3. Reid, Hamilton and Mansel on Relational Inferences.- II. First Thoughts on the Copula.- 1. The Two Copulas.- 2. First Notions of Logic.- 3. Relations and Identity.- III. Generalizing the Copula.- 1. The Abstract Copula.- 2. The Bicopular Syllogism and the Composition of Relations.- 3. Oblique Inferences and De Morgan’s Dictum.- IV. The Problem of Form and Matter.- 1. “Sundry Perversions of the Syllogistic Form”.- 2. The Material Copula.- 3. De Morgan’s Response.- 4. The Issues.- 5. Heads and Tails.- V. The Logic of Relations.- 1. Philosophical Preliminaries.- 2. General Logic of Relations.- 3. Properties of Relations.- 4. Singular Relational Syllogisms (Unit Syllogisms).- 5. Quantified Relational Syllogisms.- 6. The Limited Unit Syllogism.- 7. The Ordinary Syllogism and the Relational Syllogism.- VI. The Logic of Relations and the Theory of the Syllogism.- 1. The Two Views.- 2. Objective View—The Basic Account.- 3. Objective View—The Relational Form.- 4. The Subjective View.- VII. Logic and Mathematics.- 1. “A Mathematical Logic”.- 2. Algebraic Techniques and Analogies in Logic.- 3. Logic and Geometrical Proof.- 4. Logic and Algebraic Reasoning.- 5. Form in Algebra and Logic.- 6. Conclusions.- VIII. A Rigorous Formulation.- 1. Basic Issues.- 2. The System D.- 3. Properties of Inclusion and Identity.- 4. De Morgan’s Basic Identities.- 5. Theorem K.- 6. Properties of Relations.- 7. Additional Inclusion Laws.- 8. The Full System of Three-Relation Terms.- 9. De Morgan’s Logic with Identity.- 10. More Properties of Relations.- 11. A Surrogate for Quantification Theory.- 12. Postscript-1864.- 13. De Morgan’s Conjectures.- Notes.