MATH 9: ALGEBRA: FALLACIES, INDUCTION 1. Quantifier Recap First, a Review of Quantifiers Introduced Last Week. Recall That
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CHAPTER XXX. of Fallacies. Section 827. After Examining the Conditions on Which Correct Thoughts Depend, It Is Expedient to Clas
CHAPTER XXX. Of Fallacies. Section 827. After examining the conditions on which correct thoughts depend, it is expedient to classify some of the most familiar forms of error. It is by the treatment of the Fallacies that logic chiefly vindicates its claim to be considered a practical rather than a speculative science. To explain and give a name to fallacies is like setting up so many sign-posts on the various turns which it is possible to take off the road of truth. Section 828. By a fallacy is meant a piece of reasoning which appears to establish a conclusion without really doing so. The term applies both to the legitimate deduction of a conclusion from false premisses and to the illegitimate deduction of a conclusion from any premisses. There are errors incidental to conception and judgement, which might well be brought under the name; but the fallacies with which we shall concern ourselves are confined to errors connected with inference. Section 829. When any inference leads to a false conclusion, the error may have arisen either in the thought itself or in the signs by which the thought is conveyed. The main sources of fallacy then are confined to two-- (1) thought, (2) language. Section 830. This is the basis of Aristotle's division of fallacies, which has not yet been superseded. Fallacies, according to him, are either in the language or outside of it. Outside of language there is no source of error but thought. For things themselves do not deceive us, but error arises owing to a misinterpretation of things by the mind. -
Proving Propositional Tautologies in a Natural Dialogue
Fundamenta Informaticae xxx (2013) 1–16 1 DOI 10.3233/FI-2013-xx IOS Press Proving Propositional Tautologies in a Natural Dialogue Olena Yaskorska Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Katarzyna Budzynska Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Magdalena Kacprzak Department of Computer Science, Bialystok University of Technology, Bialystok, Poland Abstract. The paper proposes a dialogue system LND which brings together and unifies two tradi- tions in studying dialogue as a game: the dialogical logic introduced by Lorenzen; and persuasion dialogue games as specified by Prakken. The first approach allows the representation of formal di- alogues in which the validity of argument is the topic discussed. The second tradition has focused on natural dialogues examining, e.g., informal fallacies typical in real-life communication. Our goal is to unite these two approaches in order to allow communicating agents to benefit from the advan- tages of both, i.e., to equip them with the ability not only to persuade each other about facts, but also to prove that a formula used in an argument is a classical propositional tautology. To this end, we propose a new description of the dialogical logic which meets the requirements of Prakken’s generic specification for natural dialogues, and we introduce rules allowing to embed a formal dialogue in a natural one. We also show the correspondence result between the original and the new version of the dialogical logic, i.e., we show that a winning strategy for a proponent in the original version of the dialogical logic means a winning strategy for a proponent in the new version, and conversely. -
Aristotle's Illicit Quantifier Shift: Is He Guilty Or Innocent
Aristos Volume 1 Issue 2 Article 2 9-2015 Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent Jack Green The University of Notre Dame Australia Follow this and additional works at: https://researchonline.nd.edu.au/aristos Part of the Philosophy Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Recommended Citation Green, J. (2015). "Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent," Aristos 1(2),, 1-18. https://doi.org/10.32613/aristos/ 2015.1.2.2 Retrieved from https://researchonline.nd.edu.au/aristos/vol1/iss2/2 This Article is brought to you by ResearchOnline@ND. It has been accepted for inclusion in Aristos by an authorized administrator of ResearchOnline@ND. For more information, please contact [email protected]. Green: Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent ARISTOTLE’S ILLICIT QUANTIFIER SHIFT: IS HE GUILTY OR INNOCENT? Jack Green 1. Introduction Aristotle’s Nicomachean Ethics (from hereon NE) falters at its very beginning. That is the claim of logicians and philosophers who believe that in the first book of the NE Aristotle mistakenly moves from ‘every action and pursuit aims at some good’ to ‘there is some one good at which all actions and pursuits aim.’1 Yet not everyone is convinced of Aristotle’s seeming blunder.2 In lieu of that, this paper has two purposes. Firstly, it is an attempt to bring some clarity to that debate in the face of divergent opinions of the location of the fallacy; some proposing it lies at I.i.1094a1-3, others at I.ii.1094a18-22, making it difficult to wade through the literature. -
Scope Ambiguity in Syntax and Semantics
Scope Ambiguity in Syntax and Semantics Ling324 Reading: Meaning and Grammar, pg. 142-157 Is Scope Ambiguity Semantically Real? (1) Everyone loves someone. a. Wide scope reading of universal quantifier: ∀x[person(x) →∃y[person(y) ∧ love(x,y)]] b. Wide scope reading of existential quantifier: ∃y[person(y) ∧∀x[person(x) → love(x,y)]] 1 Could one semantic representation handle both the readings? • ∃y∀x reading entails ∀x∃y reading. ∀x∃y describes a more general situation where everyone has someone who s/he loves, and ∃y∀x describes a more specific situation where everyone loves the same person. • Then, couldn’t we say that Everyone loves someone is associated with the semantic representation that describes the more general reading, and the more specific reading obtains under an appropriate context? That is, couldn’t we say that Everyone loves someone is not semantically ambiguous, and its only semantic representation is the following? ∀x[person(x) →∃y[person(y) ∧ love(x,y)]] • After all, this semantic representation reflects the syntax: In syntax, everyone c-commands someone. In semantics, everyone scopes over someone. 2 Arguments for Real Scope Ambiguity • The semantic representation with the scope of quantifiers reflecting the order in which quantifiers occur in a sentence does not always represent the most general reading. (2) a. There was a name tag near every plate. b. A guard is standing in front of every gate. c. A student guide took every visitor to two museums. • Could we stipulate that when interpreting a sentence, no matter which order the quantifiers occur, always assign wide scope to every and narrow scope to some, two, etc.? 3 Arguments for Real Scope Ambiguity (cont.) • But in a negative sentence, ¬∀x∃y reading entails ¬∃y∀x reading. -
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. -
Reasoning in School
Reasoning in School For this I’m indebted to my Dad, who has over the years wisely entertained my impassioned ideas about education, to my Mom, whose empathy I’ve internalized, and to many liberal teachers. Preface A fifth grader taught me the word ‘metacognition’, which, following her, we can take to mean “thinking about thinking”. This is an analogical exercise in metacognition. It is secondarily an introduction to the process of reasoning and primarily an examination of basic notions about that process, especially those that are supposed commonsense and those that are missing from our self-concepts. As it turns out, subjecting popular metacognitive attitudes to even minor scrutiny calls some of them seriously into question. It is my goal to do so, and to form in the mind of the reader better founded beliefs about reasoning and thereby a more accurate, and consequently empowering, self-understanding. I would love to set in motion the mind that frees itself. I am in the end interested in reasoning in school as it relates to the practice of Philosophy for Children (p4c). It is amazing that reasoning is not a part of the K-12 curriculum. That it is not I find plainly unjustifiable and seriously unjust. In what follows I defend this position and consider p4c in light of it. Because I am focused on beliefs about thinking, as opposed to the cognitive psychology of thought, I am afforded some writing leeway. I am not a psychologist, but I have a fair metacognitive confidence thanks to my background in philosophy. -
Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic
Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic Richard Mayr University of Edinburgh, UK Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 1 / 23 Outline 1 Predicates 2 Quantifiers 3 Equivalences 4 Nested Quantifiers Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 2 / 23 Propositional Logic is not enough Suppose we have: “All men are mortal.” “Socrates is a man”. Does it follow that “Socrates is mortal” ? This cannot be expressed in propositional logic. We need a language to talk about objects, their properties and their relations. Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 3 / 23 Predicate Logic Extend propositional logic by the following new features. Variables: x; y; z;::: Predicates (i.e., propositional functions): P(x); Q(x); R(y); M(x; y);::: . Quantifiers: 8; 9. Propositional functions are a generalization of propositions. Can contain variables and predicates, e.g., P(x). Variables stand for (and can be replaced by) elements from their domain. Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 4 / 23 Propositional Functions Propositional functions become propositions (and thus have truth values) when all their variables are either I replaced by a value from their domain, or I bound by a quantifier P(x) denotes the value of propositional function P at x. The domain is often denoted by U (the universe). Example: Let P(x) denote “x > 5” and U be the integers. Then I P(8) is true. I P(5) is false. -
Infographic I.10
The Digital Health Revolution: Leaving No One Behind The global AI in healthcare market is growing fast, with an expected increase from $4.9 billion in 2020 to $45.2 billion by 2026. There are new solutions introduced every day that address all areas: from clinical care and diagnosis, to remote patient monitoring to EHR support, and beyond. But, AI is still relatively new to the industry, and it can be difficult to determine which solutions can actually make a difference in care delivery and business operations. 59 Jan 2021 % of Americans believe returning Jan-June 2019 to pre-coronavirus life poses a risk to health and well being. 11 41 % % ...expect it will take at least 6 The pandemic has greatly increased the 65 months before things get number of US adults reporting depression % back to normal (updated April and/or anxiety.5 2021).4 Up to of consumers now interested in telehealth going forward. $250B 76 57% of providers view telehealth more of current US healthcare spend % favorably than they did before COVID-19.7 could potentially be virtualized.6 The dramatic increase in of Medicare primary care visits the conducted through 90% $3.5T telehealth has shown longevity, with rates in annual U.S. health expenditures are for people with chronic and mental health conditions. since April 2020 0.1 43.5 leveling off % % Most of these can be prevented by simple around 30%.8 lifestyle changes and regular health screenings9 Feb. 2020 Apr. 2020 OCCAM’S RAZOR • CONJUNCTION FALLACY • DELMORE EFFECT • LAW OF TRIVIALITY • COGNITIVE FLUENCY • BELIEF BIAS • INFORMATION BIAS Digital health ecosystems are transforming• AMBIGUITY BIAS • STATUS medicineQUO BIAS • SOCIAL COMPARISONfrom BIASa rea• DECOYctive EFFECT • REACTANCEdiscipline, • REVERSE PSYCHOLOGY • SYSTEM JUSTIFICATION • BACKFIRE EFFECT • ENDOWMENT EFFECT • PROCESSING DIFFICULTY EFFECT • PSEUDOCERTAINTY EFFECT • DISPOSITION becoming precise, preventive,EFFECT • ZERO-RISK personalized, BIAS • UNIT BIAS • IKEA EFFECT and • LOSS AVERSION participatory. -
334 CHAPTER 7 INFORMAL FALLACIES a Deductive Fallacy Is
CHAPTER 7 INFORMAL FALLACIES A deductive fallacy is committed whenever it is suggested that the truth of the conclusion of an argument necessarily follows from the truth of the premises given, when in fact that conclusion does not necessarily follow from those premises. An inductive fallacy is committed whenever it is suggested that the truth of the conclusion of an argument is made more probable by its relationship with the premises of the argument, when in fact it is not. We will cover two kinds of fallacies: formal fallacies and informal fallacies. An argument commits a formal fallacy if it has an invalid argument form. An argument commits an informal fallacy when it has a valid argument form but derives from unacceptable premises. A. Fallacies with Invalid Argument Forms Consider the following arguments: (1) All Europeans are racist because most Europeans believe that Africans are inferior to Europeans and all people who believe that Africans are inferior to Europeans are racist. (2) Since no dogs are cats and no cats are rats, it follows that no dogs are rats. (3) If today is Thursday, then I'm a monkey's uncle. But, today is not Thursday. Therefore, I'm not a monkey's uncle. (4) Some rich people are not elitist because some elitists are not rich. 334 These arguments have the following argument forms: (1) Some X are Y All Y are Z All X are Z. (2) No X are Y No Y are Z No X are Z (3) If P then Q not-P not-Q (4) Some E are not R Some R are not E Each of these argument forms is deductively invalid, and any actual argument with such a form would be fallacious. -
The 13Th Annual ISNA-CISNA Education Forum Welcomes You!
13th Annual ISNA Education Forum April 6th -8th, 2011 The 13th Annual ISNA-CISNA Education Forum Welcomes You! The ISNA-CISNA Education Forum, which has fostered professional growth and development and provided support to many Islamic schools, is celebrating its 13-year milestone this April. We have seen accredited schools sprout from grassroots efforts across North America; and we credit Allah, subhanna wa ta‘alla, for empowering the many men and women who have made the dreams for our schools a reality. Today the United States is home to over one thousand weekend Islamic schools and several hundred full-time Islamic schools. Having survived the initial challenge of galvanizing community support to form a school, Islamic schools are now attempting to find the most effective means to build curriculum and programs that will strengthen the Islamic faith and academic excellence of their students. These schools continue to build quality on every level to enable their students to succeed in a competitive and increasingly multicultural and interdependent world. The ISNA Education Forum has striven to be a major platform for this critical endeavor from its inception. The Annual Education Forum has been influential in supporting Islamic schools and Muslim communities to carry out various activities such as developing weekend schools; refining Qur‘anic/Arabic/Islamic Studies instruction; attaining accreditation; improving board structures and policies; and implementing training programs for principals, administrators, and teachers. Thus, the significance of the forum lies in uniting our community in working towards a common goal for our youth. Specific Goals 1. Provide sessions based on attendees‘ needs, determined by surveys. -
Reply to the Prosecutors' Legal and Factual Claims
STATE OF NEW YORK – COURT OF APPEALS -------------------------------------------------------------------x PEOPLE OF THE STATE OF NEW YORK, ) -against- ) APL-2013-00064 RAPHAEL GOLB, ) Appellant. ) --------------------------------------------------------------------x REPLY BRIEF OF DEFENDANT-APPELLANT RONALD L. KUBY LEAH M. BUSBY Law Office of Ronald L. Kuby 119 West 23rd St., Suite 900 New York, New York 10011 (212) 529-0223 (212) 529-0644 (facsimile) For Appellant Raphael Golb Dated: New York, New York January 24, 2014 TABLE OF CONTENTS Table of Cases and Authorities ................................................................................. ii REPLY TO RESPONDENT’S COUNTERSTATEMENT OF FACTS .................... 1 ARGUMENT .......................................................................................................... 12 I. WHEN LITERALLY ANYTHING CAN BE A LEGALLY COGNIZABLE BENEFIT OR HARM, RESPONDENT CAN CRIMINALIZE ANYONE FOR WRITING UNDER THE NAME OF ANOTHER....................................................................... 12 A. RESPONDENT ERRONEOUSLY ASSERTS THAT ANY FORM OF DISCOMFORT IS AN INJURY AND ANY FORM OF GRATIFICATION IS A BENEFIT ............. 12 B. RESPONDENT ARTICULATES NO LIMITING PRINCIPLE EXCEPT ITS OWN DISCRETION. ................... 16 C. RESPONDENT MISREADS ALVAREZ ................................. 21 D. THE TRIAL COURT DIRECTED THE JURY TO NOT CONSIDER GOLB’S FIRST AMENDMENT RIGHTS OR ISSUES OF FREEDOM OF SPEECH. ............................. 23 II. THE COMMUNICATIONS THAT ARE THE SUBJECT