STUDIES AND EXERCISES IN FOBMAL LOGIC STUDIES AND EXERCISES IN FORMAL LOGIC NGLUDING GENERALISATION OF LOGICAL PROCESSES IN THEIll APPLICATION TO COMPLEX INFERENCES JOHN NEVILLE KEYNES, M. A., Sc. D. L. IVERSITY LECTURER IN MOIUL SCIENCE AND FORMERLY FELLOW OF COLLEflE IN THE UNIVERSITY OF CAMBRIDGE FOURTH EDITION RE-WRITTEN AND ENLARGED Uonbon MACMILLAN AND CO., LIMITED NEW YORK THE MACMILLAN COMPANY I9OU The Right of Translation and Reproduction itt reserved First Edition Crown Svo. printed 18R1. Second Edition Croirn Sro. 1887. Third Edition Demy Svo. 1894. Fourth Edition Demy Svo. 1900. PREFACE TO THE FOURTH EDITION. IN this edition many of the sections have been re-written and a good deal of new matter has been introduced. The following are some of the more important modifications. In Part I a new definition of connotative name is proposed, in the hope that some misunderstanding may thereby be avoided siiicl the treatment of negative names has been revised. In Part II the problem of the import of judgments and propositions in its various aspects is dealt with in much more detail than before, and greater importance is attached to distinctions of imulality. Wfrty in consequence of this, the treatment of conditional and hypothetical propositions has been modified. 1 have partially re-written the chapter on the existential import of propositions in order to meet some recent criticisms and to explain my position more clearly. Many other minor changes in Part II have been made. Amongst the changes in Part III are a more systematic treatment of the process of the indirect reduction of syllogisms, and the introduction of a chapter on the characteristics of inference. An appendix on thefundamental laws of thought has been added and the treatment of complex propositions which previously constituted Part IV of the book has now been placed in an appendix. The reader of this edition will perceive my indebtedness to Sigwari s Logic. I have received valuable help from Professor J. S. Mackenzie and from my son, Mr J. M. Keynes arid I cannot express too strongly the debt I once more owe to Mr W. E. Johnson, who by his criticisms has enabled me to improve my exposition in many parts of the book, and also to avoid some errors. J. N. KEYNES. 6, HARVEY EOAL, CAMBRIDGE, 4 ShtenSter 190C VI PREFACE. PREFACE TO THE FIRST EDITION 1 . IN . addition to a somewhat detailed exposition of certain portions of what may be called the book-work of formal logic, the following pages contain a number of problen. s worked out in detail and unsolved problems, by means of which the student may test his command over logical processes. In the expository portions of Parts I, II, and III, dealing respectively with terms, propositions, and syllogisms, the traditional lines are in the main followed, though with certain modifications e. g., in the systematisation of immediate inferences, and in several points of detail in connexion with the syllogism. For purposes of illustration Eulers diagrams are employed to a greater extent than is usual in English manuals. In Part IV, which contains a generalisation of logical processes in their application to complex inferences, a some what new departure is taken. So far as I am aware this part constitutes the first systematic attempt that has been made to deal with formal reasonings of the most complicated character without the aid of mathematical or other symbolsof operation, and without abandoning the ordinary non-cquational or predic ative form of proposition. This attempt has on the whole met with greater success than I had anticipated and I believe that the methods formulated will be found to be both as easy and as effective as the symbolical methods of Boole arid his followers. The book concludes with a general and sure method of solution of what Professor Jevons called the in orse problem, and which he himself seemed to regard as soluble only by a series of guesses...

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Formal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website offers supplemental practice software and tutorial videos.

STUDIES AND EXERCISES IN FORMAL LOGICINCLUDING A GENERALISATION OF LOGICAL PROCESSES IN THEIR APPLICATION TO COMPLEX INFERENCESby JOHN NEVILLE KEYNES

Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.