I have, in fact, almost restricted myself to showing that all classification is fundamentally carried out upon the principles of Formal Logic and the Logical Abecedarium described at the outset. In certain concluding remarks I have expressed the conviction which the study of Logic has by degrees forced upon my mind, that serious misconceptions are entertained by some scientific men as to the logical value of our knowledge of nature. We have heard much of what has been aptly called the Reign of Law, and the necessity and uniformity of natural forces has been not uncommonly interpreted as involving the non-existence of an intelligent and benevolent Power, capable of interfering with the course of natural events. Fears have been expressed that the progress of Scientific Method must therefore result in dissipating the fondest beliefs of the human heart. Even the 'Utility of Religion' is seriously proposed as a subject of discussion. It seemed to be not out of place in a work on Scientific Method to allude to the ultimate results and limits of that method. I fear that I have very imperfectly succeeded in expressing my strong conviction that before a rigorous logical scrutiny the Reign of Law will prove to be an unverified hypothesis, the Uniformity of Nature an ambiguous expression, the certainty of our scientific inferences to a great extent a delusion. The value of science is of course very high, while the conclusions are kept well within the limits of the data on which they are founded, but it is pointed out that our experience is of the most limited character compared with what there is to learn, while our mental powers seem to fall infinitely short of the task of comprehending and explaining fully the nature of any one object. I draw the conclusion that we must interpret the results of Scientific Method in an affirmative sense only. Ours must be a truly positive philosophy, not that false negative philo sophy which, building on a few material facts, presumes to assert that it has compassed the bounds of existence, while it nevertheless ignores the most unquestionable phenomena of the human mind and feelings. I have to thank my colleague, Professor Barker, for carefully revising several of the sheets most abounding in mathematical considerations. It is approximately certain that in freely employing illustrations drawn from many different sciences, I have frequently fallen into errors of detail. In this respect I must throw myself upon the indulgence of the reader, who will bear in mind, as I hope, that the scientific facts are generally mentioned purely for the purpose of illustration, so that inaccuracies of detail will not in the majority of cases affect the truth of the general principles illustrated. December 15th, 1873. CONTENTS. 2. The Powers of Mind concerned in the Creation of Science 3. Laws of Identity and Difference 4. The Nature and Authority of the Laws of Identity and Dif- 3. Inference with Two Simple Identities 4. Inference with a Simple and a Partial Identity 5. Inference of a Partial from Two Partial Identities 6. On the Ellipsis of Terms in Partial Identities 7. Inference of a Simple from Two Partial Identities 8. Inference of a Limited from Two Partial Identities 2. Expression of the Alternative Relation 3. Nature of the Alternative Relation 4. Laws of the Disjunctive Relation 5. Symbolic Expression of the Law of Duality 3. Employment of the Contrapositive Proposition 4. Contrapositive of a Simple Identity 5. Miscellaneous Examples of the Method 2. Induction an Inverse Operation 3. Induction of Simple Identities 4. Induction of Partial Identities 5. Complete Solution of the Inverse or Inductive Logical Pro- 6. The Inverse Logical Problem involving Three Terms 4. Concrete and Abstract Numbers 5. Analogy of Logical and Numerical Terins |