Stephen M. Rice, Leveraging Logical Form in Legal Argument
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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. -
UNIT-I Mathematical Logic Statements and Notations
UNIT-I Mathematical Logic Statements and notations: A proposition or statement is a declarative sentence that is either true or false (but not both). For instance, the following are propositions: “Paris is in France” (true), “London is in Denmark” (false), “2 < 4” (true), “4 = 7 (false)”. However the following are not propositions: “what is your name?” (this is a question), “do your homework” (this is a command), “this sentence is false” (neither true nor false), “x is an even number” (it depends on what x represents), “Socrates” (it is not even a sentence). The truth or falsehood of a proposition is called its truth value. Connectives: Connectives are used for making compound propositions. The main ones are the following (p and q represent given propositions): Name Represented Meaning Negation ¬p “not p” Conjunction p q “p and q” Disjunction p q “p or q (or both)” Exclusive Or p q “either p or q, but not both” Implication p ⊕ q “if p then q” Biconditional p q “p if and only if q” Truth Tables: Logical identity Logical identity is an operation on one logical value, typically the value of a proposition that produces a value of true if its operand is true and a value of false if its operand is false. The truth table for the logical identity operator is as follows: Logical Identity p p T T F F Logical negation Logical negation is an operation on one logical value, typically the value of a proposition that produces a value of true if its operand is false and a value of false if its operand is true. -
Introduction to Logic
IntroductionI Introduction to Logic Propositional calculus (or logic) is the study of the logical Christopher M. Bourke relationship between objects called propositions and forms the basis of all mathematical reasoning. Definition A proposition is a statement that is either true or false, but not both (we usually denote a proposition by letters; p, q, r, s, . .). Computer Science & Engineering 235 Introduction to Discrete Mathematics [email protected] IntroductionII ExamplesI Example (Propositions) Definition I 2 + 2 = 4 I The derivative of sin x is cos x. The value of a proposition is called its truth value; denoted by T or I 6 has 2 factors 1 if it is true and F or 0 if it is false. Opinions, interrogative and imperative sentences are not Example (Not Propositions) propositions. I C++ is the best language. I When is the pretest? I Do your homework. ExamplesII Logical Connectives Connectives are used to create a compound proposition from two Example (Propositions?) or more other propositions. I Negation (denoted or !) ¬ I 2 + 2 = 5 I And (denoted ) or Logical Conjunction ∧ I Every integer is divisible by 12. I Or (denoted ) or Logical Disjunction ∨ I Microsoft is an excellent company. I Exclusive Or (XOR, denoted ) ⊕ I Implication (denoted ) → I Biconditional; “if and only if” (denoted ) ↔ Negation Logical And A proposition can be negated. This is also a proposition. We usually denote the negation of a proposition p by p. ¬ The logical connective And is true only if both of the propositions are true. It is also referred to as a conjunction. Example (Negated Propositions) Example (Logical Connective: And) I Today is not Monday. -
Chapter 1 Logic and Set Theory
Chapter 1 Logic and Set Theory To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. – Ian Stewart Does God play dice? The mathematics of chaos In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. That is, a proof is a logical argument, not an empir- ical one. One must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics. An unproven proposition for which there is some sort of empirical evidence is known as a conjecture. Mathematical logic is the framework upon which rigorous proofs are built. It is the study of the principles and criteria of valid inference and demonstrations. Logicians have analyzed set theory in great details, formulating a collection of axioms that affords a broad enough and strong enough foundation to mathematical reasoning. The standard form of axiomatic set theory is denoted ZFC and it consists of the Zermelo-Fraenkel (ZF) axioms combined with the axiom of choice (C). Each of the axioms included in this theory expresses a property of sets that is widely accepted by mathematicians. It is unfortunately true that careless use of set theory can lead to contradictions. Avoiding such contradictions was one of the original motivations for the axiomatization of set theory. 1 2 CHAPTER 1. LOGIC AND SET THEORY A rigorous analysis of set theory belongs to the foundations of mathematics and mathematical logic. -
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. -
Folktale Documentation Release 1.0
Folktale Documentation Release 1.0 Quildreen Motta Nov 05, 2017 Contents 1 Guides 3 2 Indices and tables 5 3 Other resources 7 3.1 Getting started..............................................7 3.2 Folktale by Example........................................... 10 3.3 API Reference.............................................. 12 3.4 How do I................................................... 63 3.5 Glossary................................................. 63 Python Module Index 65 i ii Folktale Documentation, Release 1.0 Folktale is a suite of libraries for generic functional programming in JavaScript that allows you to write elegant modular applications with fewer bugs, and more reuse. Contents 1 Folktale Documentation, Release 1.0 2 Contents CHAPTER 1 Guides • Getting Started A series of quick tutorials to get you up and running quickly with the Folktale libraries. • API reference A quick reference of Folktale’s libraries, including usage examples and cross-references. 3 Folktale Documentation, Release 1.0 4 Chapter 1. Guides CHAPTER 2 Indices and tables • Global Module Index Quick access to all modules. • General Index All functions, classes, terms, sections. • Search page Search this documentation. 5 Folktale Documentation, Release 1.0 6 Chapter 2. Indices and tables CHAPTER 3 Other resources • Licence information 3.1 Getting started This guide will cover everything you need to start using the Folktale project right away, from giving you a brief overview of the project, to installing it, to creating a simple example. Once you get the hang of things, the Folktale By Example guide should help you understanding the concepts behind the library, and mapping them to real use cases. 3.1.1 So, what’s Folktale anyways? Folktale is a suite of libraries for allowing a particular style of functional programming in JavaScript. -
The Critical Thinking Toolkit
Galen A. Foresman, Peter S. Fosl, and Jamie Carlin Watson The CRITICAL THINKING The THE CRITICAL THINKING TOOLKIT GALEN A. FORESMAN, PETER S. FOSL, AND JAMIE C. WATSON THE CRITICAL THINKING TOOLKIT This edition first published 2017 © 2017 John Wiley & Sons, Inc. Registered Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Offices 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK For details of our global editorial offices, for customer services, and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell. The right of Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson to be identified as the authors of this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. -
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. -
Emergent Properties of Terrorist Networks, Percolation and Social Narrative
Emergent Properties of Terrorist Networks, Percolation and Social Narrative Maurice Passman Adaptive Risk Technology, Ltd. London, UK [email protected] Philip V. Fellman American Military University Charles Town, WV [email protected] Abstract In this paper, we have initiated an attempt to develop and understand the driving mechanisms that underlies fourth-generation warfare (4GW). We have undertaken this from a perspective of endeavoring to understand the drivers of these events (i.e. the 'Physics') from a Complexity perspective by using a threshold-type percolation model. We propose to integrate this strategic level model with tactical level Big Data, behavioral, statistical projections via a ‘fractal’ operational level model and to construct a hierarchical framework that allows dynamic prediction. Our initial study concentrates on this strategic level, i.e. a percolation model. Our main conclusion from this initial study is that extremist terrorist events are not solely driven by the size of a supporting population within a socio-geographical location but rather a combination of ideological factors that also depends upon the involvement of the host population. This involvement, through the social, political and psychological fabric of society, not only contributes to the active participation of terrorists within society but also directly contributes to and increases the likelihood of the occurrence of terrorist events. Our calculations demonstrate the links between Islamic extremist terrorist events, the ideologies within the Muslim and non-Muslim population that facilitates these terrorist events (such as Anti-Zionism) and anti- Semitic occurrences of violence against the Jewish population. In a future paper, we hope to extend the work undertaken to construct a predictive model and extend our calculations to other forms of terrorism such as Right Wing fundamentalist terrorist events within the USA. -
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”. -
Logical Reasoning
updated: 11/29/11 Logical Reasoning Bradley H. Dowden Philosophy Department California State University Sacramento Sacramento, CA 95819 USA ii Preface Copyright © 2011 by Bradley H. Dowden This book Logical Reasoning by Bradley H. Dowden is licensed under a Creative Commons Attribution- NonCommercial-NoDerivs 3.0 Unported License. That is, you are free to share, copy, distribute, store, and transmit all or any part of the work under the following conditions: (1) Attribution You must attribute the work in the manner specified by the author, namely by citing his name, the book title, and the relevant page numbers (but not in any way that suggests that the book Logical Reasoning or its author endorse you or your use of the work). (2) Noncommercial You may not use this work for commercial purposes (for example, by inserting passages into a book that is sold to students). (3) No Derivative Works You may not alter, transform, or build upon this work. An earlier version of the book was published by Wadsworth Publishing Company, Belmont, California USA in 1993 with ISBN number 0-534-17688-7. When Wadsworth decided no longer to print the book, they returned their publishing rights to the original author, Bradley Dowden. If you would like to suggest changes to the text, the author would appreciate your writing to him at [email protected]. iii Praise Comments on the 1993 edition, published by Wadsworth Publishing Company: "There is a great deal of coherence. The chapters build on one another. The organization is sound and the author does a superior job of presenting the structure of arguments.