LOGIC for DOGS I Owe It Was a Dangerous Project, and You Have
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Chrysippus's Dog As a Case Study in Non-Linguistic Cognition
Chrysippus’s Dog as a Case Study in Non-Linguistic Cognition Michael Rescorla Abstract: I critique an ancient argument for the possibility of non-linguistic deductive inference. The argument, attributed to Chrysippus, describes a dog whose behavior supposedly reflects disjunctive syllogistic reasoning. Drawing on contemporary robotics, I urge that we can equally well explain the dog’s behavior by citing probabilistic reasoning over cognitive maps. I then critique various experimentally-based arguments from scientific psychology that echo Chrysippus’s anecdotal presentation. §1. Language and thought Do non-linguistic creatures think? Debate over this question tends to calcify into two extreme doctrines. The first, espoused by Descartes, regards language as necessary for cognition. Modern proponents include Brandom (1994, pp. 145-157), Davidson (1984, pp. 155-170), McDowell (1996), and Sellars (1963, pp. 177-189). Cartesians may grant that ascribing cognitive activity to non-linguistic creatures is instrumentally useful, but they regard such ascriptions as strictly speaking false. The second extreme doctrine, espoused by Gassendi, Hume, and Locke, maintains that linguistic and non-linguistic cognition are fundamentally the same. Modern proponents include Fodor (2003), Peacocke (1997), Stalnaker (1984), and many others. Proponents may grant that non- linguistic creatures entertain a narrower range of thoughts than us, but they deny any principled difference in kind.1 2 An intermediate position holds that non-linguistic creatures display cognitive activity of a fundamentally different kind than human thought. Hobbes and Leibniz favored this intermediate position. Modern advocates include Bermudez (2003), Carruthers (2002, 2004), Dummett (1993, pp. 147-149), Malcolm (1972), and Putnam (1992, pp. 28-30). -
Skepticism and Pluralism Ways of Living a Life Of
SKEPTICISM AND PLURALISM WAYS OF LIVING A LIFE OF AWARENESS AS RECOMMENDED BY THE ZHUANGZI #±r A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI'I IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHILOSOPHY AUGUST 2004 By John Trowbridge Dissertation Committee: Roger T. Ames, Chairperson Tamara Albertini Chung-ying Cheng James E. Tiles David R. McCraw © Copyright 2004 by John Trowbridge iii Dedicated to my wife, Jill iv ACKNOWLEDGEMENTS In completing this research, I would like to express my appreciation first and foremost to my wife, Jill, and our three children, James, Holly, and Henry for their support during this process. I would also like to express my gratitude to my entire dissertation committee for their insight and understanding ofthe topics at hand. Studying under Roger Ames has been a transformative experience. In particular, his commitment to taking the Chinese tradition on its own terms and avoiding the tendency among Western interpreters to overwrite traditional Chinese thought with the preoccupations ofWestern philosophy has enabled me to broaden my conception ofphilosophy itself. Roger's seminars on Confucianism and Daoism, and especially a seminar on writing a philosophical translation ofthe Zhongyong r:pJm (Achieving Equilibrium in the Everyday), have greatly influenced my own initial attempts to translate and interpret the seminal philosophical texts ofancient China. Tamara Albertini's expertise in ancient Greek philosophy was indispensable to this project, and a seminar I audited with her, comparing early Greek and ancient Chinese philosophy, was part ofthe inspiration for my choice ofresearch topic. I particularly valued the opportunity to study Daoism and the Yijing ~*~ with Chung-ying Cheng g\Gr:p~ and benefited greatly from his theory ofonto-cosmology as a means of understanding classical Chinese philosophy. -
Mit Einer Logischen Kritik Der Mathematischen Logik Und Bibliographie Der Logik
GRUNDRISS DER PYRAMIDALEN LOGIK mit einer logischen Kritik der mathematischen Logik und Bibliographie der Logik Lehrmaterialien aus dem Philosophischen Institut der HHU Düsseldorf Forschungsabteilung für Wissenschaftstheorie Prof. Dr. L. Geldsetzer A AB AC ABD Copyright 2000 vorbehalten Kopieren zum Studiengebrauch erlaubt 2 INHALTSVERZEICHNIS Vorbemerkung Zum Konzept der pyramidalen Logik 4 I. Einführung 4 II. Die logischen Elemente 20 1. Intensionen 20 2. Extensionen 21 3. Der Begriff 24 a. Die reguläreBegriffsstrukturDielogische a. 24 b. Negative Begriffe 25 c. Der widersprüchliche Begriff (contradictio in adiecto bzw. contradictio in terminis) 26 d. Der Dispositionsbegriff 30 e. Der Wahrscheinlichkeitsbegriff 32 f. Der Zahlbegriff 33 g. Sogenannte Relationsbegriffe, Ähnlichkeitsbegriffe und "Familienähnlichkeit" 44 h. Der Begriff des Begriffs in der stoischen Logik 47 i. Methoden der Begriffsbildung: Induktion, Deduktion, Analyse und Synthese 50 4. Die Junktoren 55 a. Die urteilsbildendenDie a.Junktoren 57 1. Die unbeschränkteDie (allgemeine)1.Implikation 57 2. Das unbeschränkte (allgemeine) "Zukommen" 58 3. Die korrelierende Implikation 58 4. Die Kopula bzw. die materiale Implikationmateriale 58Kopula die Diebzw. 4. 5. Das spezielle "Zukommen" bzw. die formale Implikation oder Inklusion 58 6. Die Negation 59 7. Der Existenz- bzw. Produktjunktorbzw.Existenz- Der 7. 59 b. Die ausdrucksbildendenDie b. Junktoren 61 1. Die QuantifikationDie 1. 62 2. Die ÄquivalenzDie 2. 63 3. Die unvollständigeDie Disjunktion3. 63 4. Die vollständige Disjunktion oder Alternative 63 5. Die AdjunktionDie 5. 64 c. Die mathematischenJunktorenDie c. 65 1. Die Summenbildung Die 1. (Additionsjunktor) 68 2. Die SubtraktionDie (Differenzenjunktor)2. 68 3. Die ProduktbildungDie 3. (Multiplikationsjunktor) 68 4. Die Division (Quotienten- oder Proportionsjunktor) 69 5. Die PotenzbildungDie (Potenzjunktor)5. -
7.1 Rules of Implication I
Natural Deduction is a method for deriving the conclusion of valid arguments expressed in the symbolism of propositional logic. The method consists of using sets of Rules of Inference (valid argument forms) to derive either a conclusion or a series of intermediate conclusions that link the premises of an argument with the stated conclusion. The First Four Rules of Inference: ◦ Modus Ponens (MP): p q p q ◦ Modus Tollens (MT): p q ~q ~p ◦ Pure Hypothetical Syllogism (HS): p q q r p r ◦ Disjunctive Syllogism (DS): p v q ~p q Common strategies for constructing a proof involving the first four rules: ◦ Always begin by attempting to find the conclusion in the premises. If the conclusion is not present in its entirely in the premises, look at the main operator of the conclusion. This will provide a clue as to how the conclusion should be derived. ◦ If the conclusion contains a letter that appears in the consequent of a conditional statement in the premises, consider obtaining that letter via modus ponens. ◦ If the conclusion contains a negated letter and that letter appears in the antecedent of a conditional statement in the premises, consider obtaining the negated letter via modus tollens. ◦ If the conclusion is a conditional statement, consider obtaining it via pure hypothetical syllogism. ◦ If the conclusion contains a letter that appears in a disjunctive statement in the premises, consider obtaining that letter via disjunctive syllogism. Four Additional Rules of Inference: ◦ Constructive Dilemma (CD): (p q) • (r s) p v r q v s ◦ Simplification (Simp): p • q p ◦ Conjunction (Conj): p q p • q ◦ Addition (Add): p p v q Common Misapplications Common strategies involving the additional rules of inference: ◦ If the conclusion contains a letter that appears in a conjunctive statement in the premises, consider obtaining that letter via simplification. -
Chapter 9: Answers and Comments Step 1 Exercises 1. Simplification. 2. Absorption. 3. See Textbook. 4. Modus Tollens. 5. Modus P
Chapter 9: Answers and Comments Step 1 Exercises 1. Simplification. 2. Absorption. 3. See textbook. 4. Modus Tollens. 5. Modus Ponens. 6. Simplification. 7. X -- A very common student mistake; can't use Simplification unless the major con- nective of the premise is a conjunction. 8. Disjunctive Syllogism. 9. X -- Fallacy of Denying the Antecedent. 10. X 11. Constructive Dilemma. 12. See textbook. 13. Hypothetical Syllogism. 14. Hypothetical Syllogism. 15. Conjunction. 16. See textbook. 17. Addition. 18. Modus Ponens. 19. X -- Fallacy of Affirming the Consequent. 20. Disjunctive Syllogism. 21. X -- not HS, the (D v G) does not match (D v C). This is deliberate to make sure you don't just focus on generalities, and make sure the entire form fits. 22. Constructive Dilemma. 23. See textbook. 24. Simplification. 25. Modus Ponens. 26. Modus Tollens. 27. See textbook. 28. Disjunctive Syllogism. 29. Modus Ponens. 30. Disjunctive Syllogism. Step 2 Exercises #1 1 Z A 2. (Z v B) C / Z C 3. Z (1)Simp. 4. Z v B (3) Add. 5. C (2)(4)MP 6. Z C (3)(5) Conj. For line 4 it is easy to get locked into line 2 and strategy 1. But they do not work. #2 1. K (B v I) 2. K 3. ~B 4. I (~T N) 5. N T / ~N 6. B v I (1)(2) MP 7. I (6)(3) DS 8. ~T N (4)(7) MP 9. ~T (8) Simp. 10. ~N (5)(9) MT #3 See textbook. #4 1. H I 2. I J 3. -
Education Or Indoctrination? Montaigne and Emerson on Preserving Freedom in the Teacher-Student Relationship Rebecca Sullivan Teachers College, Columbia University
666 Montaigne and Emerson on Preserving Freedom in the Teacher-Student Relationship Education or Indoctrination? Montaigne and Emerson on Preserving Freedom in the Teacher-Student Relationship Rebecca Sullivan Teachers College, Columbia University INTRODUCTION In his Essays, Michel de Montaigne paints a self-portrait that champions individual judgment. In contemporary educational parlance, he is an advocate of critical thinking: a student’s ability to reflectively evaluate information, test assumptions, ask clarifying questions, and form judgments for herself.1 Individ- ual judgment is a hallmark of a learner’s freedom because it indicates that she is not merely repeating inherited wisdom, but personally holds a conviction. Enabling such freedom in students requires careful consideration of the rela- tionship between teacher and student in learning. In this article, I consider how teacher-student positionality impacts individual judgment using the example of Michel de Montaigne and Ralph Waldo Emerson. Montaigne’s Essays raise the still-relevant question of the relationship between inherited wisdom and personal experience in forming individual judg- ments. However, Montaigne fails to offer a conclusive answer. While Montaigne draws heavily on past thinkers, he gives precedence to his own experience over inherited wisdom in forming judgments. This can be seen, for example, in his essay “Of Friendship,” in which he references past thinkers, but rejects their formulations of friendship when they fail to accord with his own experience. However, while Montaigne articulates the prominence of personal experience over inherited wisdom in forming individual judgments, the form of his writ- ing—the essay—suggests the opposite. The colloquial, conversational style Montaigne employs in essays such as “Of Friendship” invites the reader to trust in Montaigne’s wisdom without having recourse to her own experience. -
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”. -
Proposi'onal Logic Proofs Proof Method #1: Truth Table Example
9/9/14 Proposi'onal Logic Proofs • An argument is a sequence of proposi'ons: Inference Rules ² Premises (Axioms) are the first n proposi'ons (Rosen, Section 1.5) ² Conclusion is the final proposi'on. p p ... p q TOPICS • An argument is valid if is a ( 1 ∧ 2 ∧ ∧ n ) → tautology, given that pi are the premises • Logic Proofs (axioms) and q is the conclusion. ² via Truth Tables € ² via Inference Rules 2 Proof Method #1: Truth Table Example Proof By Truth Table s = ((p v q) ∧ (¬p v r)) → (q v r) n If the conclusion is true in the truth table whenever the premises are true, it is p q r ¬p p v q ¬p v r q v r (p v q)∧ (¬p v r) s proved 0 0 0 1 0 1 0 0 1 n Warning: when the premises are false, the 0 0 1 1 0 1 1 0 1 conclusion my be true or false 0 1 0 1 1 1 1 1 1 n Problem: given n propositions, the truth 0 1 1 1 1 1 1 1 1 n table has 2 rows 1 0 0 0 1 0 0 0 1 n Proof by truth table quickly becomes 1 0 1 0 1 1 1 1 1 infeasible 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 3 4 1 9/9/14 Proof Method #2: Rules of Inference Inference proper'es n A rule of inference is a pre-proved relaon: n Inference rules are truth preserving any 'me the leJ hand side (LHS) is true, the n If the LHS is true, so is the RHS right hand side (RHS) is also true. -
Does Pyrrhonism Have Practical Or Epistemic Value? 49
DiegoE.Machuca Does Pyrrhonism HavePractical or Epistemic Value? 1Introduction My purpose in this paper is to examine whether Pyrrhonian scepticism, as this stance is described in Sextus Empiricus’sextant works,has practical or epistemic value. More precisely, Iwould like to consider whether the Pyrrhonist’ssuspension of judg- ment (epochē)and undisturbedness (ataraxia)can be deemed to be of practical or epistemic value. By “practical” value Imean both moral value and prudential value. Moral value refers to moral rightness and wrongness; prudential value to per- sonal or social well-being.Hence, when Iask whether the Pyrrhonist’ssuspension and undisturbedness have practical value, Imean whether they make us behave in amannerthat is morallyright or wrong,and whether they allow us to attain those goals thatwould make it possible to live well. As for “epistemic” value, it ba- sicallyrefers to the values of attaining truth and avoiding error. Hence, when Iask whether the Pyrrhonist’ssuspension has epistemic value, Imean whether it allows us to attain truth and avoid error.Mymain focus will be the practical value of both suspension and undisturbedness, because this is the value thatscholars of an- cient philosophycritical of Pyrrhonism have emphasised. The reason for examining the epistemic value of suspension is thatdoing so will enable afuller assessment of the significance of Pyrrhonism as akind of philosophy, which is my primary concern. Iwill begin by brieflydescribing the states of suspension and undisturbedness and their connection, and by succinctlyconsideringsome objections to the effect that,despite claiming to suspend judgmentacross the board, Pyrrhonists actually hold anumber of beliefs. Thiswill provide the necessary framework for the subse- quent discussions. -
Sceptical Paths Studies and Texts in Scepticism
Sceptical Paths Studies and Texts in Scepticism Edited on behalf of the Maimonides Centre for Advanced Studies by Giuseppe Veltri Managing Editor: Yoav Meyrav Editorial Board Heidrun Eichner, Talya Fishman, Racheli Haliva, Henrik Lagerlund, Reimund Leicht, Stephan Schmid, Carsten Wilke, Irene Zwiep Volume 6 Sceptical Paths Enquiry and Doubt from Antiquity to the Present Edited by Giuseppe Veltri, Racheli Haliva, Stephan Schmid, and Emidio Spinelli The series Studies and Texts in Scepticism is published on behalf of the Maimonides Centre for Advanced Studies ISBN 978-3-11-058960-3 e-ISBN (PDF) 978-3-11-059104-0 e-ISBN (EPUB) 978-3-11-059111-8 ISSN 2568-9614 This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 Licence. For details go to http://creativecommons.org/licenses/by-nc-nd/4.0/. Library of Congress Cataloging in Publication Control Number: 2019947115 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2019 Giuseppe Veltri, Racheli Haliva, Stephan Schmid, Emidio Spinelli, published by Walter de Gruyter GmbH, Berlin/Boston Cover image: Staats- und Universitätsbibliothek Hamburg, Ms Cod. Levy 115, fol. 158r: Maimonides, More Nevukhim, Beginn von Teil III. Printing & binding: CPI books GmbH, Leck www.degruyter.com Contents Introduction 1 Carlos Lévy Philo of Alexandria vs. Descartes: An Ignored Jewish -
The Influence of Pyrrho of Elis and the Pyrrhonian Praxis of Aporetic
The Influence of Pyrrho of Elis and the Pyrrhonian Praxis of Aporetic Language by © Christopher Craig Dupuis A Thesis submitted to the School of Graduate Studies in partial fulfillment of the requirements for the degree of Master of Arts in Philosophy, Faculty of Arts, Department of Philosophy Memorial University of Newfoundland May, 2014 St. John’s Newfoundland and Labrador 2 Table of Contents Abstract 4 Introduction and Overview 5 Chapter One 1 Pyrrho’s Aporetic Linguistic Praxis 12 1.1 Ataraxia in Epictetus and Epicurus 21 1.2 The Role of Epoche and Ataraxia in Pyrrho 23 1.3 Plato’s Socrates as Pyrrho’s Sage 43 1.4 Pyrrho and Plato’s Phaedo 45 1.5 Pyrrho, the Meno, and The Soul of The Hellenes 48 1.6 Appearances, Customs, and The Soul of the Sceptic 51 1.7 Pyrrho and Plato’s Theaetetus 55 1.8 Chapter One Conclusion 62 Chapter Two 2.1 Introduction: Academic Scepticism 64 2.2 Scepticism up to this Point 65 2.3 Arcesilaus And the Early Academic Sceptics 68 2.4 Carneades And the ‘New’ Academic Sceptics 81 2.5 Connecting with Pyrrho 91 Chapter Three 3.1 Introduction: Later Pyrrhonian Scepticism 95 3.2 Aenesidemus and the Revival of Pyrrhonism 97 3.3 Aenesidemus, Relativity, and Language Practice 107 3.4 Later Pyrrhonism: Sextus Empiricus 112 3.5 Outline of Sextus 118 3.6 Phantasiai 119 3.7 Apprehension 122 3.8 What the Sceptics Do 125 3.9 Ataraxia and Epoche 128 3.10 The Five Ways to Epoche 133 3 3.10.1 The First Trope: Diaphonia 136 3.10.2 The Second Trope: Infinite Regression 138 3.10.3 The Third Trope: Relativity 139 3.10.4 The Fourth -
Introduction to Logic and Critical Thinking
Introduction to Logic and Critical Thinking Version 1.4 Matthew J. Van Cleave Lansing Community College Introduction to Logic and Critical Thinking by Matthew J. Van Cleave is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Table of contents Preface Chapter 1: Reconstructing and analyzing arguments 1.1 What is an argument? 1.2 Identifying arguments 1.3 Arguments vs. explanations 1.4 More complex argument structures 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form 1.6 Validity 1.7 Soundness 1.8 Deductive vs. inductive arguments 1.9 Arguments with missing premises 1.10 Assuring, guarding, and discounting 1.11 Evaluative language 1.12 Evaluating a real-life argument Chapter 2: Formal methods of evaluating arguments 2.1 What is a formal method of evaluation and why do we need them? 2.2 Propositional logic and the four basic truth functional connectives 2.3 Negation and disjunction 2.4 Using parentheses to translate complex sentences 2.5 “Not both” and “neither nor” 2.6 The truth table test of validity 2.7 Conditionals 2.8 “Unless” 2.9 Material equivalence 2.10 Tautologies, contradictions, and contingent statements 2.11 Proofs and the 8 valid forms of inference 2.12 How to construct proofs 2.13 Short review of propositional logic 2.14 Categorical logic 2.15 The Venn test of validity for immediate categorical inferences 2.16 Universal statements and existential commitment 2.17 Venn validity for categorical syllogisms Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies 3.1 Inductive arguments and statistical generalizations 3.2 Inference to the best explanation and the seven explanatory virtues 3.3 Analogical arguments 3.4 Causal arguments 3.5 Probability 3.6 The conjunction fallacy 3.7 The base rate fallacy 3.8 The small numbers fallacy 3.9 Regression to the mean fallacy 3.10 Gambler’s fallacy Chapter 4: Informal fallacies 4.1 Formal vs.