So far as I may venture to form an independent opinion on the subject, it is to the effect that Professor Clifford is right, and that the known laws of nature do not enable us to assign a “beginning.” Science leads us backwards into infinite past duration. But that Professor Clifford is right on this point, is no reason why we should suppose him to be right in his other opinions, some of which I am sure are wrong. Nor is it a reason why other parts of my last chapter should be wrong. The question only affects the single paragraph on pp. 744–5 of this book, which might, I believe, be struck out without necessitating any alteration in the rest of the text. It is always to be remembered that the failure of an argument in favour of a proposition does not, generally speaking, add much, if any, probability to the contradictory proposition. I cannot conclude without expressing my acknowledgments to Professor Clifford for his kind expressions regarding my work as a whole. 2, The Chestnuts, West Heath, Hampstead, N. W. *August 15, 1877.* CONTENTS. BOOK I. FORMAL LOGIC, DEDUCTIVE AND INDUCTIVE. CHAPTER I. INTRODUCTION. SECTION PAGE 1. Introduction 1 2. The Powers of Mind concerned in the Creation of Science 4 3. Laws of Identity and Difference 5 4. The Nature of the Laws of Identity and Difference 6 5. The Process of Inference 9 6. Deduction and Induction 11 7. Symbolic Expression of Logical Inference 13 8. Expression of Identity and Difference 14 9. General Formula of Logical Inference 17 10. The Propagating Power of Similarity 20 11. Anticipations of the Principle of Substitution 21 12. The Logic of Relatives 22 CHAPTER II. TERMS. 1. Terms 24 2. Twofold meaning of General Names 25 3. Abstract Terms 27 4. Substantial Terms 28 5. Collective Terms 29 6. Synthesis of Terms 30 7. Symbolic Expression of the Law of Contradiction 31 8. Certain Special Conditions of Logical Symbols 32 CHAPTER III. PROPOSITIONS. 1. Propositions 36 2. Simple Identities 37 3. Partial Identities 40 4. Limited Identities 42 5. Negative Propositions 43