REMARKS ON LOGIC AND CRITICAL THINKING 1 Copyright, 2021, Mudasir Ahmad Tantray All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy recording, or any information storage or retrieval system, without permission in writing from the publisher. The opinions/ contents expressed in this book are solely of the author and do not represent the opinions/ standings/ thoughts of Publications Name. No responsibility or liability is assumed by the publisher for any injury damage or financial loss sustained to persons or property form the use of the information, personal or otherwise, either directly or indirectly. 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ISBN: 978-93-90835-21-8 Price: 299.00 Publishing Year 2021 Published and printed by: Rudra Publications Office Address: Kapil Nagar, New Sarkanda, Bilaspur, Chhattisgarh – 495001 Phones: +91 9522285558 +91 9522263336 Email: [email protected] Website: www.rudrapublications.com Print in India 2 REMARKS ON LOGIC AND CRITICAL THINKING Mudasir Ahmad Tantray 3 4 Preface This work is compiled for the students, research scholars, academicians, who are interested in logic, philosophy, mathematics and critical thinking. The main objective of this book is to provide basics or fundamental knowledge for those who have chosen logic as their subject in order to develop analytical and critical ideas. It has been primarily developed to serve as an introductory piece of work which includes explanatory notes on different courses like Inductive logic, Deductive logic, propositional logic, Symbolic logic, Quantification logic, Modal logic and Critical thinking. Besides this, it also includes illustrations in decision making and scientific research methods in logic. This book is mainly devised to clear fundamental problems of logic. It contains eight chapters which are simply described and elaborated. First chapter deals with the description of propositions, arguments, terms, reasoning, and the classes. It is concerned with those statements which could qualify the criteria of reasoning. We have differentiated thinking from thought and different types of terms and class distribution. Second chapter “Proposition” deals with the definition, qualification, types of propositions, and philosopher’s contribution to proposition. In this we are concerned with the difference between proposition and sentence. This chapter further explains the role of proposition in the logical world. Third chapter “Deductive logic” enlightens the world of deductive logic which includes the evaluation of deductive argument, valid and invalid argument as well as the strength and soundness of it. In this, I have explained syllogism, square of opposition, mediate inference, immediate inference, dilemma, figures, moods and Venn diagrams that represent the syllogism. Fourth chapter “Inductive logic” deals with inductive argument, their probability and their weakness and strength. In inductive logic, we regard Mill's method of induction and scientific investigation, methodology and procedure as the basic tools and techniques for the evaluation of inductive arguments. 5 In the fifth chapter Mathematical logic (Symbolic logic), we will deal with mathematical or symbolic logic which includes the symbols and their representation i.e. negation, conjunction, disjunction, material implication and equivalence and their truth tables. Moreover, I have also described statements and statement forms along with argument and argument form. Sixth chapter “Quantification logic” deals with quantification logic or predicate logic and the problems which I have described in this chapter are; quantifier: universal and existential and the square which represents propositions though quantifiers. In this chapter, I have also explained the approach in quantification logic which has modified and rectified Aristotelian logic though existential quantifier operators and universal quantifier operators. Seventh chapter “Modal logic” deals with the modal propositions like, possible, impossible, necessary, contingent, actual, and non-actual propositions. In modal logic, I have described modal argument with symbols and square of opposition of model propositions. I have also defined modal propositions with reference to possible world and actual world. Seventh chapter “Critical Thinking” is concerned with the orders of thinking i.e. first order thinking and second order thinking. Critical thinking is a skill to analyze arguments, decisions, identifying errors and it helps us in every sphere of life or in any field or sector. This chapter is very much important in this book only to enhance skills in students, research scholars, writers, professionals and counselors to reflect in decision making through logical reasoning. One more thing which I have portrayed in this chapter is the relation between Philosophy and critical thinking. Sopore, J&K. M. A. Tantray Nov. 2020 6 S.No. CHAPTERS PAGES 1 Chapter-I 12 – 31 INTRODUCTION What is reasoning Definition of logic Scope of logic Sentence Proposition Characteristics of proposition Types of proposition Term Laws of thought 2 Chapter-II 33 – 41 PROPOSITION Meaning of proposition Propositional function Proposition and sentence Proposition and its significance Judgment and proposition Sentence: A grammatical unit Relation between sentence and proposition Sentential logic in Aristotle and afterwards 3 Chapter-III 43 – 68 DEDUCTIVE LOGIC Truth and validity Syllogism Figures Mood Rules of validity of syllogism Venn diagram technique for testing syllogism Square of opposition of propositions Inference Immediate inference Conversion Obversion Contraposition Dilemma 7 4 Chapter-IV 70– 101 INDUCTIVE LOGIC Hypothesis Steps of hypothesis Kinds of hypothesis Scientific and unscientific explanation Evaluating scientific explanation Mills method The method of agreement Method of difference Joint method of agreement and difference The method of residue The method of concomitant variation Definitions and its types Fallacies 5 Chapter-V 103 – 128 MATHEMATICAL LOGIC (SYMBOLIC LOGIC) Historical contribution to symbolic logic Symbols Truth table technique Negation Conjunction Disjunction Material implication Material equivalence Common argument forms Modus Ponens Modus Tollens Disjunctive syllogism Hypothetic syllogism Rules of inference (valid argument forms) Rules of replacement (logically equivalent forms) Statement forms and statements Tautology Contradiction Contingency 8 6 Chapter- VI 130 – 148 PREDICATE LOGIC (QUANTIFICATION LOGIC) Predicate logic (Quantification logic) Quantification and rules of quantification Universal quantification Existential quantification Symbolic representation Quantification square of opposition of propositions Examples using universal and existential quantifiers Validity and Invalidity of arguments 7 Chapter-VII 150 – 157 MODAL LOGIC Modalities with symbol Modal propositions Modalities with symbol Modal operators and their examples Modal expressions symbolized Modal square Types of modal logic Deontic logic Epistemic logic Alethic logic 8 Chapter-VIII 159– 189 CRITICAL THINKING Critical thinking and philosophy Identification and analysis of the problem Identifying inconsistencies Soundness Seven stages of scientific investigation Identification of errors in research Evaluating argument Validity, invalidity, soundness and strength Fairness and sensitivity Evaluating decision making from multiple approaches 9 BIBLIOGRAPHY 189 – 192 9 10 CHAPTER - I INTRODUCTION 11 Logic is the science of argumentation and reasoning. It is derived from the Greek word “Logos’ which means reason or to think, so logic is the “art of reasoning” or “art of thinking. Human mind is always thinking and judging, to think is to judge. Whatever we think and reason, we express it in language and this language is only the means to logic. Traditionally logic is the branch of philosophy and sub-branch of Axiology which recognizes its three fundamental values; truth, goodness and beauty. Logic is the study of one of its value i.e. principle of “truth”. Truth is the attribute of thought and thought is the crux of argumentation. Every thought is not logical, only those thoughts are logical that are expressed in the form of propositions. Logic is the science of truth and always protects us from committing fallacies. Logic is the epitome of philosophy. Without logic philosophy is incomplete and ambiguous. Logic is in our thoughts which we express in language. Aristotle is credited to be the founder of Logic. His own school was “Lyceum”. He wrote his work “Organon” in Greek which when translated means “tool” or “instrument”. While