Essentials of Formal Logic-III Sem Core Course
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6.5 Rules for Evaluating Syllogisms
6.5 Rules for Evaluating Syllogisms Comment: Venn Diagrams provide a clear semantics for categorical statements that yields a method for determining validity. Prior to their discovery, categorical syllogisms were evaluated by a set of rules, some of which are more or less semantic in character, others of which are entirely syntactic. We will study those rules in this section. Rule 1: A valid standard form categorical syllogism must contain exactly three terms, and each term must be used with the same meaning throughout the argument. Comment: A fallacy of equivocation occurs if a term is used with more than one meaning in a categorical syllogism, e.g., Some good speakers are woofers. All politicians are good speakers. So, some politicians are woofers. In the first premise, “speakers” refers to an electronic device. In the second, it refers to a subclass of human beings. Definition (sorta): A term is distributed in a statement if the statement “says something” about every member of the class that the term denotes. A term is undistributed in a statement if it is not distributed in it. Comment: To say that a statement “says something” about every member of a class is to say that, if you know the statement is true, you can legitimately infer something nontrivial about any arbitrary member of the class. 1 The subject term (but not the predicate term) is distributed in an A statement. Example 1 All dogs are mammals says of each dog that it is a mammal. It does not say anything about all mammals. Comment: Thus, if I know that “All dogs are mammals” is true, then if I am told that Fido is a dog, I can legitimately infer that Fido is a mammal. -
Western Logic Formal & Informal Fallacy Types of 6 Fallacies
9/17/2021 Western Logic Formal & Informal Fallacy Types of 6 Fallacies- Examrace Examrace Western Logic Formal & Informal Fallacy Types of 6 Fallacies Get unlimited access to the best preparation resource for competitive exams : get questions, notes, tests, video lectures and more- for all subjects of your exam. Western Logic - Formal & Informal Fallacy: Types of 6 Fallacies (Philosophy) Fallacy When an argument fails to support its conclusion, that argument is termed as fallacious in nature. A fallacious argument is hence an erroneous argument. In other words, any error or mistake in an argument leads to a fallacy. So, the definition of fallacy is any argument which although seems correct but has an error committed in its reasoning. Hence, a fallacy is an error; a fallacious argument is an argument which has erroneous reasoning. In the words of Frege, the analytical philosopher, “it is a logician՚s task to identify the pitfalls in language.” Hence, logicians are concerned with the task of identifying fallacious arguments in logic which are also called as incorrect or invalid arguments. There are numerous fallacies but they are classified under two main heads; Formal Fallacies Informal Fallacies Formal Fallacies Formal fallacies are those mistakes or errors which occur in the form of the argument. In other words, formal fallacies concern themselves with the form or the structure of the argument. Formal fallacies are present when there is a structural error in a deductive argument. It is important to note that formal fallacies always occur in a deductive argument. There are of six types; Fallacy of four terms: A valid syllogism must contain three terms, each of which should be used in the same sense throughout; else it is a fallacy of four terms. -
Philosophy of Physical Activity Education (Including Educational Sport)
eBook Philosophy of Physical Activity Education (Including Educational Sport) by EARLEPh.D., F. LL.D., ZEIGLER D.Sc. PHILOSOPHY OF PHYSICAL ACTIVITY EDUCATION (INCLUDING EDUCATIONAL SPORT) Earle F. Zeigler Ph.D., LL.D., D.Sc., FAAKPE Faculty of Kinesiology The University of Western Ontario London, Canada (This version is as an e-book) 1 PLEASE LEAVE THIS PAGE EMPTY FOR PUBLICATION DATA 2 DEDICATION This book is dedicated to the following men and women with whom I worked very closely in this aspect of our work at one time or another from 1956 on while employed at The University of Michigan, Ann Arbor; the University of Illinois, U-C; and The University of Western Ontario, London, Canada: Susan Cooke, (Western Ontario, CA); John A. Daly (Illinois, U-C); Francis W. Keenan, (Illinois, U-C); Robert G. Osterhoudt (Illinois, U-C); George Patrick (Illinois, U-C); Kathleen Pearson (Illinois, U-C); Sean Seaman (Western Ontario, CA; Danny Rosenberg (Western Ontario, CA); Debra Shogan (Western Ontario, CA); Peter Spencer-Kraus (Illinois, UC) ACKNOWLEDGEMENTS In the mid-1960s, Dr. Paul Weiss, Heffer Professor of Philosophy, Catholic University of America, Washington, DC, offered wise words of counsel to me on numerous occasions, as did Prof. Dr. Hans Lenk, a "world scholar" from the University of Karlsruhe, Germany, who has been a friend and colleague for whom I have the greatest of admiration. Dr. Warren Fraleigh, SUNY at Brockport, and Dr. Scott Kretchmar. of The Pennsylvania State University have been colleagues, scholars, and friends who haven't forgotten their roots in the physical education profession. -
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 -
Indiscernible Logic: Using the Logical Fallacies of the Illicit Major Term and the Illicit Minor Term As Litigation Tools
WLR_47-1_RICE (FINAL FORMAT) 10/28/2010 3:35:39 PM INDISCERNIBLE LOGIC: USING THE LOGICAL FALLACIES OF THE ILLICIT MAJOR TERM AND THE ILLICIT MINOR TERM AS LITIGATION TOOLS ∗ STEPHEN M. RICE I. INTRODUCTION Baseball, like litigation, is at once elegant in its simplicity and infinite in its complexities and variations. As a result of its complexities, baseball, like litigation, is subject to an infinite number of potential outcomes. Both baseball and litigation are complex systems, managed by specialized sets of rules. However, the results of baseball games, like the results of litigation, turn on a series of indiscernible, seemingly invisible, rules. These indiscernible rules are essential to success in baseball, in the same way the rules of philosophic logic are essential to success in litigation. This article will evaluate one of the philosophical rules of logic;1 demonstrate how it is easily violated without notice, resulting in a logical fallacy known as the Fallacy of the Illicit Major or Minor Term,2 chronicle how courts have identified this logical fallacy and used it to evaluate legal arguments;3 and describe how essential this rule and the fallacy that follows its breach is to essential effective advocacy. However, because many lawyers are unfamiliar with philosophical logic, or why it is important, this article begins with a story about a familiar subject that is, in many ways, like the rules of philosophic logic: the game of baseball. ∗ Stephen M. Rice is an Assistant Professor of Law, Liberty University School of Law. I appreciate the efforts of my research assistant, Ms. -
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”. -
Tel Aviv University the Lester & Sally Entin Faculty of Humanities the Shirley & Leslie Porter School of Cultural Studies
Tel Aviv University The Lester & Sally Entin Faculty of Humanities The Shirley & Leslie Porter School of Cultural Studies "Mischief … none knows … but herself": Intrigue and its Relation to the Drive in Late Seventeenth-Century Intrigue Drama Thesis Submitted for the Degree of "Doctor of Philosophy" by Zafra Dan Submitted to the Senate of Tel Aviv University October 2011 This work was carried out under the supervision of Professor Shirley Sharon-Zisser, Tel Aviv University and Professor Karen Alkalay-Gut, Tel Aviv University This thesis, this labor of love, would not have come into the world without the rigorous guidance, the faith and encouragement of my supervisors, Prof. Karen Alkalay-Gut and Prof. Shirley Sharon-Zisser. I am grateful to Prof. Sharon-Zisser for her Virgilian guidance into and through the less known, never to be taken for granted, labyrinths of Freudian and Lacanian thought and theory, as well as for her own ground-breaking contribution to the field of psychoanalysis through psycho-rhetoric. I am grateful to Prof. Alkalay-Gut for her insightful, inspiring yet challenging comments and questions, time and again forcing me to pause and rethink the relationship between the literary aspects of my research and psychoanalysis. I am grateful to both my supervisors for enabling me to explore a unique, newly blazed path to literary form, and rediscover thus late seventeenth-century drama. I wish to express my gratitude to Prof. Ruth Ronen for allowing me the use of the manuscript of her book Aesthetics of Anxiety before it was published. Her instructive work has been a source of enlightenment and inspiration in its own right. -
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. -
Leading Logical Fallacies in Legal Argument – Part 1 Gerald Lebovits
University of Ottawa Faculty of Law (Civil Law Section) From the SelectedWorks of Hon. Gerald Lebovits July, 2016 Say It Ain’t So: Leading Logical Fallacies in Legal Argument – Part 1 Gerald Lebovits Available at: https://works.bepress.com/gerald_lebovits/297/ JULY/AUGUST 2016 VOL. 88 | NO. 6 JournalNEW YORK STATE BAR ASSOCIATION Highlights from Today’s Game: Also in this Issue Exclusive Use and Domestic Trademark Coverage on the Offensive Violence Health Care Proxies By Christopher Psihoules and Jennette Wiser Litigation Strategy and Dispute Resolution What’s in a Name? That Which We Call Surrogate’s Court UBE-Shopping and Portability THE LEGAL WRITER BY GERALD LEBOVITS Say It Ain’t So: Leading Logical Fallacies in Legal Argument – Part 1 o argue effectively, whether oral- fact.3 Then a final conclusion is drawn able doubt. The jury has reasonable ly or in writing, lawyers must applying the asserted fact to the gen- doubt. Therefore, the jury hesitated.”8 Tunderstand logic and how logic eral rule.4 For the syllogism to be valid, The fallacy: Just because the jury had can be manipulated through fallacious the premises must be true, and the a reasonable doubt, the jury must’ve reasoning. A logical fallacy is an inval- conclusion must follow logically. For hesitated. The jury could’ve been id way to reason. Understanding falla- example: “All men are mortal. Bob is a entirely convinced and reached a con- cies will “furnish us with a means by man. Therefore, Bob is mortal.” clusion without hesitation. which the logic of practical argumen- Arguments might not be valid, tation can be tested.”1 Testing your though, even if their premises and con- argument against the general types of clusions are true. -
Formal Fallacies
First Steps in Formal Logic Handout 16 Formal Fallacies A formal fallacy is an invalid argument grounded in logical form. Validity, again: an argument is valid iff the premises could not all be true yet the conclusion false; or, a rule of inference is valid iff it cannot lead from truth to falsehood, i.e. if the infer- ence preserves truth. The semantic turnstile ‘⊧’ indicates validity, so where P is the set of premises and C is the conclusion, P ⊧ C. We can also say that C is a ‘logical consequence’ of, or follows from, P. In a fallacious argument, this may seem to be the case, but P ⊭ C. There are also many informal fallacies (e.g., begging the question: petitio principii) that do not preserve truth either, but these are not grounded in logical form. Fallacies of Propositional Logic (PL) (1) Affirming the Consequent: φ ⊃ ψ, ψ ⊦ φ Examples: (a) ‘If Hume is an atheist, then Spinoza is an atheist too. Spinoza is an atheist. So, Hume is an atheist.’ (b) ‘If it rains, the street is wet. The street is wet. So it rains.’ (2) Denying the Antecedent: φ ⊃ ψ, ~φ ⊦ ~ψ Examples: (a) ‘If Locke is a rationalist, then Spinoza grinds lenses for a living. But Locke is not a rationalist. So, Spinoza does not grind lenses for a living.’ (b) ‘If it rains, the street it wet. It does not rain. So the street is not wet.’ Affirming the consequent and denying the antecedent are quite common fallacies. They ignore that the material implication lacks an intrinsic connection between antecedent and consequent. -
Logic Made Easy: How to Know When Language Deceives
LOGIC MADE EASY ALSO BY DEBORAH J. BENNETT Randomness LOGIC MADE EASY How to Know When Language Deceives You DEBORAH J.BENNETT W • W • NORTON & COMPANY I ^ I NEW YORK LONDON Copyright © 2004 by Deborah J. Bennett All rights reserved Printed in the United States of America First Edition For information about permission to reproduce selections from this book, write to Permissions, WW Norton & Company, Inc., 500 Fifth Avenue, New York, NY 10110 Manufacturing by The Haddon Craftsmen, Inc. Book design by Margaret M.Wagner Production manager: Julia Druskin Library of Congress Cataloging-in-Publication Data Bennett, Deborah J., 1950- Logic made easy : how to know when language deceives you / Deborah J. Bennett.— 1st ed. p. cm. Includes bibliographical references and index. ISBN 0-393-05748-8 1. Reasoning. 2. Language and logic. I.Title. BC177 .B42 2004 160—dc22 2003026910 WW Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110 www. wwnor ton. com WW Norton & Company Ltd., Castle House, 75/76Wells Street, LondonWlT 3QT 1234567890 CONTENTS INTRODUCTION: LOGIC IS RARE I 1 The mistakes we make l 3 Logic should be everywhere 1 8 How history can help 19 1 PROOF 29 Consistency is all I ask 29 Proof by contradiction 33 Disproof 3 6 I ALL 40 All S are P 42 Vice Versa 42 Familiarity—help or hindrance? 41 Clarity or brevity? 50 7 8 CONTENTS 3 A NOT TANGLES EVERYTHING UP 53 The trouble with not 54 Scope of the negative 5 8 A and E propositions s 9 When no means yes—the "negative pregnant" and double negative 61 k SOME Is PART OR ALL OF ALL 64 Some -
Categorical Syllogism
Unit 8 Categorical Syllogism What is a syllogism? Inference or reasoning is the process of passing from one or more propositions to another with some justification. This inference when expressed in language is called an argument. An argument consists of more than one proposition (premise and conclusion). The conclusion of an argument is the proposition that is affirmed on the basis of the other propositions of the argument. These other propositions which provide support or ground for the conclusion are called premises of the argument. Inferences have been broadly divided as deductive and inductive. A deductive argument makes the claim that its conclusion is supported by its premises conclusively. An inductive argument, in contrast, does not make such a claim. It claims to support its conclusion only with some degrees of probability. Deductive inferences are again divided into Immediate and Mediate. Immediate inference is a kind of deductive inference in which the conclusion follows from one premise only. In mediate inference, on the other hand, the conclusion follows from more them one premise. Where there are only two premises, and the conclusion follows from them jointly, it is called syllogism. A syllogism is a deductive argument in which a conclusion is inferred from two premises. The syllogisms with which we are concerned here are called categorical because they are arguments based on the categorical relations of classes or categories. Such relations are of three kinds. 1. The whole of one class may be included in the other class such as All dogs are mammals. 2. Some members of one class may be included in the other such as Some chess players are females.