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the testimony of Lambert, Joh. Chr. Lange, in his Nucleus Logice Weisiannæ, 1712, uses circles, and that Christ. Weise, Rector of the Gymnasium at Zittau (d. 1708), was probably the inventor?.” Hamilton uses circles in his Lectures to illustrate his demonstration of valid moods by canons and rules. Ueberweg fully adopts the method of circles in his “System of Logic and History of Logical Doctrines," and proves by this method alone the various forms of immediate and mediate inference.

In this work an account has been given of the Aristotelian and the Scholastic methods of determining valid moods, so that the reader will find in it all that is usually given on this subject in manuals of Deductive Logic.

As regards the nature of deductive inference, it is held that all deductive inference is hypothetically necessary,that is, that the conclusion must be true if the premisses are true.

The chapter on Probable Reasoning and Probability treats of probable propositions and inferences. A probable proposition is shown to have its origin in a proportional proposition. General propositions are either universal, such as “All A is B,” or proportional, such as " Nine in ten A's are B.” Universal propositions are treated of in ordinary Logic; proportional propositions in Probability. Where we fail to establish universal propositions, we cannot draw inferences by the canons and rules of ordinary Logic; but if we can establish proportional propositions, we may still draw inferences in accordance with the laws and rules of Probability.

The Appendix is partly supplementary to the text, and partly supplies additional matter to the reader.

i Ueberweg's Logic, English Translation, p. 302,

A special feature of this work is the large number of examples given at the end of almost every chapter, or important division of a chapter. Repeated practice in applying the laws and rules of Logic to concrete examples is the most important part of the study of Logic regarded as a mental training; and it is with a view to this practice that so large an amount of space has been devoted to the exercises. Most of the examples of propositions, and many of the examples of syllogisms, have been selected from well-known authors, and given exactly in the form in which they occur in their writings. Some have been taken from other works on Logic, and some from University and College Examination Papers. The rest have been especially prepared for this work.

My best thanks are due to Mr A. W. Garrett, Principal, Dacca College, for the very valuable help I have received from him in the preparation of this work. On many important points connected both with the language and the matter of the work, I have had the advantage of his help. My thanks are also due to Mr Jagad Bandhu Laha, Head Master, Dacca Normal School, and Mr Rajoni Kant Ghose, Assistant Master, Dacca Collegiate School, who have kindly revised the proofs, and assisted me with their suggestions.

Dacca COLLEGE,

September, 1883.

PREFACE TO THE SECOND EDITION.

This edition has been carefully revised; and alterations and additions have been made wherever they appeared desirable. The chapter on “The Theory of Predication and the Import of Propositions” has been, in part, rewritten. The chapter on “The Various kinds of Terms” has been subjected to a careful revision. Appendix E, "The Nature and Province of Objective Logic,” as well as some foot-notes and references have been added. I ought to add that some of these alterations and additions are due to the criticism of my reviewers, to some of whom I have referred in the body of the Work,

Dacca COLLEGE,

November 29, 1885.

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