DOCSLIB.ORG

1 Bpy-002 Logic

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

BPY-002 LOGIC: CLASSICAL AND SYMBOLIC LOGIC (4 credits) COURSE INTRODUCTION Cordial welcome to the BA Philosophy Programme of IGNOU. The curriculum prepared for this degree is relevant and significant. We have included latest scholarship on the course prepared by renowned scholars from across the country. The second course that you study is “Logic: Classical and Symbolic Logic.” The concept of logical form is central to logic; it is being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic, which is the study of natural language arguments, includes the study of fallacies too. Formal logic is the study of inference with purely formal content. Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two: propositional logic and predicate logic. Mathematical logic is an extension of symbolic logic into other areas, such as the study of model theory, proof theory, set theory, and recursion theory. This course presents 4 blocks comprising 16 units. Block 1 is an introduction to logic. In this block we have tried to explain the nature and scope of logic, concept and term, definition and division, and proposition. Block 2 deals with meaning and kinds of reasoning, deductive reasoning, syllogisms, and dilemma and fallacies. Block 3 studies induction, the history and utility of symbolic logic, compound statements and their truth values, and truth-functional forms. Block 4 probes into formal proof of validity with rules of inference and rules of replacement. This final unit also explains conditional proof and indirect proof, and quantification. All these four Blocks will enable you to know the core of logic explained in simple terms with profound insights taking into account the latest trends in the discipline. You will have to enhance your knowledge of the subject with the help of the suggested readings and by browsing through the various websites on the topic, especially through the Wikipedia on which many contributors depend for their reference. 1 BLOCK -1 INTRODUCTION Logic is the study of the principles of valid inference and demonstration. The word derives from Greek logike, meaning “possessed of reason, intellectual, dialectical, argumentative;” As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from the study of validity, fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. The present block, consisting of 4 units, introduces logic taking into account its basic nature. Unit 1 on “Nature and Scope of Logic” introduces and familiarizes the nature and scope of the subject to the students. Anyone who ventures to study logic must necessarily know its status among academic disciplines: is it a science or an art? Again, is it a positive science or a normative science? Debates on these cover the problem from various angles. Yet another concern of a student of logic would be the extension and scope of logic. This has been achieved by introspection into the relation between logic and various other sciences. Unit 2 highlights “Concept and Term.” Thought in logic means process or product of thinking concepts. This unit aims at examining major entities in the language of logic like concepts, words and terms. Concept is a word that carries a lot of philosophical significance. Words and terms connote different senses in the language of logic. It is essential that a student of logic gets familiarized with the usage of such technical terms. Unit 3 explains how Logic deals with thought, and thoughts are always expressed in language. Words we use must convey proper idea. If they have no fixed meaning it would be difficult to understand what one means in his use of a word. In such a situation error and confusion are not uncommon. We define a term according to the interest we have in it. But logic deals with correct thinking. Our thoughts can never be coherent unless we determine the meaning of each term. Now the tools which logic devises for the attainment of this purpose are definition and division. Unit 4 discusses “Proposition.” As we know inferential process is the main subject matter of logic. The term refers to the process by which a proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point of the process. To determine whether an inference is correct the logician examines the propositions that are the initial and end points of that process and the relationships between them. This clearly denotes the significance of propositions in the study of logic. Four units mentioned above teach us that knowledge is based directly on perception and indirectly on what we have been told. Much of the knowledge we have is justified by means of reasoning or logical argument, based on other knowledge we have. If we are not willing to use reasoning, our beliefs or values might well be inconsistent, and then we would have no knowledge or proper judgement at all. 1 UNIT 2 CONCEPT AND TERM Contents 2.0 Objectives 2.1 Introduction 2.2 Concept, Word and Terms. 2.3 Terms as a Name of Class 2.4 Extension and Intension 2.5 Inverse Variation 2.6 Classification of Terms 2.7 Let Us Sum Up 2.8 Key Words 2.9 Further Readings and References 2.10 Answers to Check Your Progress 2.0 OBJECTIVES Logic is said to be the study of argument as expressed in language. Language in general is highly ambiguous. In any language words are often used in various senses. For example, sometimes ‘thought’ and knowledge’ are used as synonymous terms. Therefore this unit aims at: • examining major entities in the language of logic like concepts, words and terms and thereby show that they carry lot of philosophical significance and at the same time carry different senses. • familiarizing the students with varieties of technical terms. Terms can be classified under different criteria. There are simple and composite terms, singular and general terms, collective and non-collective terms, absolute and relative terms, concrete and abstract terms, positive, negative and private terms and connotative and non-connotative terms. This unit undertakes a study of these various types of terms to procure a good undertaking of the language of logic with which the student is expected to be sufficiently acquainted. 2.1 INTRODUCTION Language is the external expression of intention, thought etc. It is the means of communicating our ideas to other people. In logic, by language we mean only the verbal expression of our ideas, either spoken or written. The Greeks seem to have used the word ‘logos’ to denote ideas as well as speech. This clearly shows the close relation between language and thought. As Grumbley has rightly pointed out, thought and language are closely connected just like how principles of life and activities of a living organism are connected. Clear thinking and accurate language help each other. Further, it is language that gives thought a name and an abiding reality as a permanent possession. It is popularly said: ‘Thought lives in language’. The multitudes of objects that we 1 see around cannot be remembered unless certain names are endowed to the ideas of those objects. The nature of thought is such that it gets dissolved unless we put them in words. Language not only structures thought by codifying them, but also does the service of preserving them for future generations. It enables us to split complex ideas into atomic ones to analyse and thereby understand them. Hence the philosophers often comment that logic and language are the two sides of the same coin. In order to understand complex ideas we split them into simple words. Words like chastity, nationality, religious are just a few examples to convince ourselves that words can stand representing condensed expression of complex thoughts pregnant with many ideas. In this unit an attempt is made to understand how words, concepts and terms play a decisive role in our study of logic. 2.2 CONCEPT, WORD AND TERM It is necessary to distinguish between word, concept and term. Concept means a general idea. There is difference between the two ideas represented by the terms ‘student’ and ‘a student’. The term ‘a student’ refers to a particular student in an indefinite manner and it is essentially singular in usage. The term ‘student’ is applied in general to all those who undertake studies. The common and essential attributes which are found in every particular individual of the class are thought of separately, and thus we get a concept. In brief, the concept stands for general ideas. When expressed in language concept becomes a term. Judgment is the process of relating two concepts. For instance, the two concepts ‘water’ and ‘cold’ may be related and the result is the judgement, ‘water is cold’. A judgment when expressed in language is called a proposition. Sometimes it is said that concepts are mental entities. They are not visible. Conception or simple apprehension is the function of human mind by which an idea of a concept is formed in the mind. It is a process of forming mental image of an object, e.g., you see an elephant and form an idea of the elephant in the mind. The formation of concepts involves the fallowing processes. (1) Comparison: Different entities are compared with one another so that the attributes they share in common and those on which they differ can be specified.
Recommended publications
  • Tables of Implications and Tautologies from Symbolic Logic

    Tables of Implications and Tautologies from Symbolic Logic

    Tables of Implications and Tautologies from Symbolic Logic Dr. Robert B. Heckendorn Computer Science Department, University of Idaho March 17, 2021 Here are some tables of logical equivalents and implications that I have found useful over the years. Where there are classical names for things I have included them. \Isolation by Parts" is my own invention. By tautology I mean equivalent left and right hand side and by implication I mean the left hand expression implies the right hand. I use the tilde and overbar interchangeably to represent negation e.g. ∼x is the same as x. Enjoy! Table 1: Properties of All Two-bit Operators. The Comm. is short for commutative and Assoc. is short for associative. Iff is short for \if and only if". Truth Name Comm./ Binary And/Or/Not Nands Only Table Assoc. Op 0000 False CA 0 0 (a " (a " a)) " (a " (a " a)) 0001 And CA a ^ b a ^ b (a " b) " (a " b) 0010 Minus b − a a ^ b (b " (a " a)) " (a " (a " a)) 0011 B A b b b 0100 Minus a − b a ^ b (a " (a " a)) " (a " (a " b)) 0101 A A a a a 0110 Xor/NotEqual CA a ⊕ b (a ^ b) _ (a ^ b)(b " (a " a)) " (a " (a " b)) (a _ b) ^ (a _ b) 0111 Or CA a _ b a _ b (a " a) " (b " b) 1000 Nor C a # b a ^ b ((a " a) " (b " b)) " ((a " a) " a) 1001 Iff/Equal CA a $ b (a _ b) ^ (a _ b) ((a " a) " (b " b)) " (a " b) (a ^ b) _ (a ^ b) 1010 Not A a a a " a 1011 Imply a ! b a _ b (a " (a " b)) 1100 Not B b b b " b 1101 Imply b ! a a _ b (b " (a " a)) 1110 Nand C a " b a _ b a " b 1111 True CA 1 1 (a " a) " a 1 Table 2: Tautologies (Logical Identities) Commutative Property: p ^ q $ q
  • Argument Forms and Fallacies

    Argument Forms and Fallacies

    6.6 Common Argument Forms and Fallacies 1. Common Valid Argument Forms: In the previous section (6.4), we learned how to determine whether or not an argument is valid using truth tables. There are certain forms of valid and invalid argument that are extremely common. If we memorize some of these common argument forms, it will save us time because we will be able to immediately recognize whether or not certain arguments are valid or invalid without having to draw out a truth table. Let’s begin: 1. Disjunctive Syllogism: The following argument is valid: “The coin is either in my right hand or my left hand. It’s not in my right hand. So, it must be in my left hand.” Let “R”=”The coin is in my right hand” and let “L”=”The coin is in my left hand”. The argument in symbolic form is this: R ˅ L ~R __________________________________________________ L Any argument with the form just stated is valid. This form of argument is called a disjunctive syllogism. Basically, the argument gives you two options and says that, since one option is FALSE, the other option must be TRUE. 2. Pure Hypothetical Syllogism: The following argument is valid: “If you hit the ball in on this turn, you’ll get a hole in one; and if you get a hole in one you’ll win the game. So, if you hit the ball in on this turn, you’ll win the game.” Let “B”=”You hit the ball in on this turn”, “H”=”You get a hole in one”, and “W”=”you win the game”.
  • Isabelle's Logics: FOL and ZF

    Isabelle's Logics: FOL and ZF

    ZF ∀ = Isabelle α λ β → Isabelle's Logics: FOL and ZF Lawrence C. Paulson Computer Laboratory University of Cambridge [email protected] With Contributions by Tobias Nipkow and Markus Wenzel1 31 October 1999 1Markus Wenzel made numerous improvements. Philippe de Groote con- tributed to ZF. Philippe No¨eland Martin Coen made many contributions to ZF. The research has been funded by the EPSRC (grants GR/G53279, GR/H40570, GR/K57381, GR/K77051) and by ESPRIT project 6453: Types. Abstract This manual describes Isabelle's formalizations of many-sorted first-order logic (FOL) and Zermelo-Fraenkel set theory (ZF). See the Reference Manual for general Isabelle commands, and Introduction to Isabelle for an overall tutorial. Contents 1 Syntax definitions 1 2 First-Order Logic 3 2.1 Syntax and rules of inference ................... 3 2.2 Generic packages ......................... 4 2.3 Intuitionistic proof procedures .................. 4 2.4 Classical proof procedures .................... 9 2.5 An intuitionistic example ..................... 10 2.6 An example of intuitionistic negation .............. 12 2.7 A classical example ........................ 13 2.8 Derived rules and the classical tactics .............. 15 2.8.1 Deriving the introduction rule .............. 16 2.8.2 Deriving the elimination rule ............... 17 2.8.3 Using the derived rules .................. 18 2.8.4 Derived rules versus definitions ............. 20 3 Zermelo-Fraenkel Set Theory 23 3.1 Which version of axiomatic set theory? ............. 23 3.2 The syntax of set theory ..................... 24 3.3 Binding operators ......................... 26 3.4 The Zermelo-Fraenkel axioms .................. 29 3.5 From basic lemmas to function spaces .............. 32 3.5.1 Fundamental lemmas ..................
  • Abstract Consequence and Logics

    Abstract Consequence and Logics

    Abstract Consequence and Logics Essays in honor of Edelcio G. de Souza edited by Alexandre Costa-Leite Contents Introduction Alexandre Costa-Leite On Edelcio G. de Souza PART 1 Abstraction, unity and logic 3 Jean-Yves Beziau Logical structures from a model-theoretical viewpoint 17 Gerhard Schurz Universal translatability: optimality-based justification of (not necessarily) classical logic 37 Roderick Batchelor Abstract logic with vocables 67 Juliano Maranh~ao An abstract definition of normative system 79 Newton C. A. da Costa and Decio Krause Suppes predicate for classes of structures and the notion of transportability 99 Patr´ıciaDel Nero Velasco On a reconstruction of the valuation concept PART 2 Categories, logics and arithmetic 115 Vladimir L. Vasyukov Internal logic of the H − B topos 135 Marcelo E. Coniglio On categorial combination of logics 173 Walter Carnielli and David Fuenmayor Godel's¨ incompleteness theorems from a paraconsistent perspective 199 Edgar L. B. Almeida and Rodrigo A. Freire On existence in arithmetic PART 3 Non-classical inferences 221 Arnon Avron A note on semi-implication with negation 227 Diana Costa and Manuel A. Martins A roadmap of paraconsistent hybrid logics 243 H´erculesde Araujo Feitosa, Angela Pereira Rodrigues Moreira and Marcelo Reicher Soares A relational model for the logic of deduction 251 Andrew Schumann From pragmatic truths to emotional truths 263 Hilan Bensusan and Gregory Carneiro Paraconsistentization through antimonotonicity: towards a logic of supplement PART 4 Philosophy and history of logic 277 Diogo H. B. Dias Hans Hahn and the foundations of mathematics 289 Cassiano Terra Rodrigues A first survey of Charles S.
  • Early Russell on Types and Plurals of Analytical Philosophy Kevin C

    Early Russell on Types and Plurals of Analytical Philosophy Kevin C

    Journal FOR THE History Early Russell ON TYPES AND PlurALS OF Analytical Philosophy KeVIN C. Klement VOLUME 2, Number 6 In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be Editor IN Chief considered many things, and not one, and used this thesis to SandrA Lapointe, McMaster University explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction Editorial BoarD between singular and plural. The view, however, was short- Juliet Floyd, Boston University lived—rejected before PoM even appeared in print. However, GrEG Frost-Arnold, Hobart AND William Smith Colleges aside from mentions of a few misgivings, there is little evidence Henry Jackman, YORK University about why he abandoned this view. In this paper, I attempt to Chris Pincock, Ohio State University clarify Russell’s early views about plurality, arguing that they Mark TExtor, King’S College London did not involve countenancing special kinds of plural things RicharD Zach, University OF Calgary distinct from individuals. I also clarify what his misgivings about these views were, making it clear that while the plural understanding of classes helped solve certain forms of Russell’s PrODUCTION Editor paradox, certain other Cantorian paradoxes remained. Finally, Ryan Hickerson, University OF WESTERN OrEGON I aim to show that Russell’s abandonment of something like plural logic is understandable given his own conception of Editorial Assistant logic and philosophical aims when compared to the views and Daniel Harris, CUNY GrADUATE Center approaches taken by contemporary advocates of plural logic.
  • An Introduction to Critical Thinking and Symbolic Logic: Volume 1 Formal Logic

    An Introduction to Critical Thinking and Symbolic Logic: Volume 1 Formal Logic

    An Introduction to Critical Thinking and Symbolic Logic: Volume 1 Formal Logic Rebeka Ferreira and Anthony Ferrucci 1 1An Introduction to Critical Thinking and Symbolic Logic: Volume 1 Formal Logic is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. 1 Preface This textbook has developed over the last few years of teaching introductory symbolic logic and critical thinking courses. It has been truly a pleasure to have beneted from such great students and colleagues over the years. As we have become increasingly frustrated with the costs of traditional logic textbooks (though many of them deserve high praise for their accuracy and depth), the move to open source has become more and more attractive. We're happy to provide it free of charge for educational use. With that being said, there are always improvements to be made here and we would be most grateful for constructive feedback and criticism. We have chosen to write this text in LaTex and have adopted certain conventions with symbols. Certainly many important aspects of critical thinking and logic have been omitted here, including historical developments and key logicians, and for that we apologize. Our goal was to create a textbook that could be provided to students free of charge and still contain some of the more important elements of critical thinking and introductory logic. To that end, an additional benet of providing this textbook as a Open Education Resource (OER) is that we will be able to provide newer updated versions of this text more frequently, and without any concern about increased charges each time.
  • Students' Language in Computer-Assisted Tutoring of Mathematical Proofs

    Students' Language in Computer-Assisted Tutoring of Mathematical Proofs

    Saarbrücken Dissertations band 40_Layout 1 28.08.2015 13:34 Seite 1 Saarbrücken Dissertations | Volume 40 | in Language Science and Technology s f o o r p Students' language l a c i t in computer-assisted tutoring a m e h Truth and proof are central to mathematics. Proving (or disproving) t of mathematical proofs seemingly simple statements often turns out to be one of the hardest a m mathematical tasks. Yet, doing proofs is rarely taught in the class - f o room. Studies on cognitive difficulties in learning to do proofs have g n shown that pupils and students not only often do not understand or i r cannot apply basic formal reasoning techniques and do not know how o t Magdalena A. Wolska to use formal mathematical language, but, at a far more fundamental u t level, they also do not understand what it means to prove a statement d e or even do not see the purpose of proof at all. Since insight into the t s importance of proof and doing proofs as such cannot be learnt other i s than by practice, learning support through individualised tutoring is s a - in demand. r e This volume presents a part of an interdisciplinary project, set at the t u intersection of pedagogical science, artificial intelligence, and (com - p putational) linguistics, which investigated issues involved in provisio - m o ning computer-based tutoring of mathematical proofs through c n dialogue in natural language. The ultimate goal in this context, ad - i dressing the above-mentioned need for learning support, is to build e g intelligent automated tutoring systems for mathematical proofs.
  • Logic Machines and Diagrams

    Logic Machines and Diagrams

    LOGIC M ACH IN ES AND DIAGRAMS Martin Gardner McGRAW-HILL BOOK COMPANY, INC. New York Toronto London 1958 LOGIC MACHINES AND DIAGRAMS Copyright 1958 by the McGraw-Hill Book Company, Inc. Printed in the United States of America. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. Library of Congress Catalog Card Number: 58-6683 for C. G. Who thinks in a multivalued system all her own. Preface A logic machine is a device, electrical or mechanical, designed specifically for solving problems in formal logic. A logic diagram is a geometrical method for doing the same thing. The two fields are closely intertwined, and this book is the first attempt in any language to trace their curious, fascinating histories. Let no reader imagine that logic machines are merely the play- of who to have a recreational interest in things engineers happen , symbolic logic. As we move with terrifying speed into an age of automation, the engineers and mathematicians who design our automata constantly encounter problems that are less mathemati- cal in form than logical. It has been discovered, for example, that symbolic logic can be applied fruitfully to the design and simplification of switching circuits. It has been found that electronic calculators often require elaborate logic units to tell them what steps to follow in tackling certain problems. And in the new field of operations research, annoying situations are constantly arising for which techniques of symbolic logic are surprisingly appropriate. The last chaptej: of this book suggests some of the ways in which logic machines may play essential roles in coping with the stagger- ing complexities of an automated technology.
  • Form and Content: an Introduction to Formal Logic

    Form and Content: an Introduction to Formal Logic

    Connecticut College Digital Commons @ Connecticut College Open Educational Resources 2020 Form and Content: An Introduction to Formal Logic Derek D. Turner Connecticut College, [email protected] Follow this and additional works at: https://digitalcommons.conncoll.edu/oer Recommended Citation Turner, Derek D., "Form and Content: An Introduction to Formal Logic" (2020). Open Educational Resources. 1. https://digitalcommons.conncoll.edu/oer/1 This Book is brought to you for free and open access by Digital Commons @ Connecticut College. It has been accepted for inclusion in Open Educational Resources by an authorized administrator of Digital Commons @ Connecticut College. For more information, please contact [email protected]. The views expressed in this paper are solely those of the author. Form & Content Form and Content An Introduction to Formal Logic Derek Turner Connecticut College 2020 Susanne K. Langer. This bust is in Shain Library at Connecticut College, New London, CT. Photo by the author. 1 Form & Content ©2020 Derek D. Turner This work is published in 2020 under a Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, you must give appropriate credit. If you remix, transform, add to, or modify the text in any way, you may not then redistribute the modified text. 2 Form & Content A Note to Students For many years, I had relied on one of the standard popular logic textbooks for my introductory formal logic course at Connecticut College. It is a perfectly good book, used in countless logic classes across the country.
  • Bertrand Russell – Principles of Mathematics

    Bertrand Russell – Principles of Mathematics

    Principles of Mathematics “Unless we are very much mistaken, its lucid application and develop- ment of the great discoveries of Peano and Cantor mark the opening of a new epoch in both philosophical and mathematical thought” – The Spectator Bertrand Russell Principles of Mathematics London and New York First published in 1903 First published in the Routledge Classics in 2010 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2010 The Bertrand Russell Peace Foundation Ltd Introduction © 1992 John G. Slater All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-86476-X Master e-book ISBN ISBN 10: 0-415-48741-2 ISBN 10: 0-203-86476-X (ebk) ISBN 13: 978-0-415-48741-2 ISBN 13: 978-0-203-86476-0 (ebk) CONTENTS introduction to the 1992 edition xxv introduction to the second edition xxxi preface xliii PART I THE INDEFINABLES OF MATHEMATICS 1 1 Definition of Pure Mathematics 3 1.
  • Essentials of Formal Logic-III Sem Core Course

    Essentials of Formal Logic-III Sem Core Course

    School of Distance Education UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION BA PHILOSOPHY (2011 Admission Onwards) III Semester Core Course ESSENTIALS OF FORMAL LOGIC QUESTION BANK 1. Logic is the science of-----------. A)Thought B)Beauty C) mind D)Goodness 2. Aesthetics is the science of ------------. A) Truth B) Matter C) Goodness D) Beauty. 3. Logic is a ------------ science A) Positive B) Normative C) Descriptive D) Natural. 4. A normative science is also called ------------ science. A) Natural B)descriptive C) Positive D) Evaluative. 5. The ideal of logic is A) truth B) Beauty C) Goodness D) God 6. The ideal of ethics is A) Truth B) Beauty C) Goodness D) God 7. The ideal of aesthetics is A) Truth B) Beauty C) Goodness D) God. Essential of Formal Logic Page 1 School of Distance Education 8. The process by which one proposition is arrived at on the basis of other propositions is called-----------. A) Term B) Concept C) Inference D) Connotation. 9. Only--------------- sentences can become propositions. A) Indicative B) Exclamatory C) Interogative D) Imperative. 10. Propositions which supports the conclusion of an argument are called A) Inferences B) Premises C) Terms D) Concepts. 11. That proposition which is affirmed on the basis of premises is called A) Term B) Concept C) Idea D) Conclusion. 12. The etymological meaning of the word logic is A) the science of mind B) the science of thought C) the science of conduct D) the science of beautyody . 13. The systematic body of knowledge about a particular branch of the universe is called------- . A) Science B) Art C) Religion D) Opinion.
  • A History of Natural Deduction and Elementary Logic Textbooks

    A History of Natural Deduction and Elementary Logic Textbooks

    A History of Natural Deduction and Elementary Logic Textbooks Francis Jeffry Pelletier 1 Introduction In 1934 a most singular event occurred. Two papers were published on a topic that had (apparently) never before been written about, the authors had never been in contact with one another, and they had (apparently) no common intellectual background that would otherwise account for their mutual interest in this topic. 1 These two papers formed the basis for a movement in logic which is by now the most common way of teaching elementary logic by far, and indeed is perhaps all that is known in any detail about logic by a number of philosophers (especially in North America). This manner of proceeding in logic is called ‘natural deduction’. And in its own way the instigation of this style of logical proof is as important to the history of logic as the discovery of resolution by Robinson in 1965, or the discovery of the logistical method by Frege in 1879, or even the discovery of the syllogistic by Aristotle in the fourth century BC.2 Yet it is a story whose details are not known by those most affected: those ‘or- dinary’ philosophers who are not logicians but who learned the standard amount of formal logic taught in North American undergraduate and graduate departments of philosophy. Most of these philosophers will have taken some (series of) logic courses that exhibited natural deduction, and may have heard that natural deduc- tion is somehow opposed to various other styles of proof systems in some number of different ways.