Another If the Activities *Carried on Within It Are More Autotelic

Total Page:16

File Type:pdf, Size:1020Kb

Another If the Activities *Carried on Within It Are More Autotelic nOCIF04RNT 1111:811MR ED 030 174 24 CG 004 233 By-Moore, Omar K.:.Anderson, Alan Ross Some Principles for the Design Of Clarifying EducationalEnvironments. PrepriGt. 32. Pittsburgh Univ., Pa. Learning Research and Development Center. Spons Agency -Carnegie ,Corp. of New York, N.Y.;Office of Nayal Research, 14shington, D.C. Bureau No -BR -5 -0253 . Pub Date (681 Note-65p.; Preprint .of a Chapt,er to appear in David CoSlin (Ed.).HandbOok of Socialization Theory and Research. Chicago: Rand McNally, 19.68 EDRS Price MF-$050 HC..-S3.35 Descriptors -Audiovisual Instruction, *Computational Linguistics,*Instructional Aids, *Instructional Materials. *Learning, *LearningTheOries,.*Per:ceptual Motor LeaFning,Social Sciences The author'S purp4e !in .this paper is to explain andillustrate four principles for designing learning environments within which even youngchildren can acquire complex symbolic skills with*.relatiye:ease. After discussingthe principles themselves and the theoretical systeM out of which they emerged, the authorconsiders an illustrative application of these :principles to the problemof designing an actual' learning environment.Four. ptinciplesfordesigningclarifyingenvironmentsare.(1) Perspectives Principlero*environment is more conducive to.learning than another if it both permits .and facilitat.e.taking of more perspectives tOwardwhatever is to be learned: (2) Autotelit Principite,-one environment is moreconducive to learning than another if the activities *carried on withinit are more autotelic;(3) Productive Principle- one environmeh.t is. more conducive to learningthaa another if what is to be learned within it is more* productive: (4)Personalization Principle- one enVironment is more conducive to learning'than another if it is more resp9nsive to learneractivities and permits and facilitates the, learner's taking a morereflexive view of himself as a learner. As an illuStrative ekample of a clarifyingenvironment, the .author discusses the talking typewriter. (Author/C,I) UNIVERSITY OFP1TSURGH -LEARNING R &DCENTER PREPRINT 32 SOME PRINCIPLESOMAR K. MOOREFOREDUCATIONAL ANDTHE DESIGNALAN ROSS ENVIRONMENTSOF CLARIFYING ANDERSON EDO30174' SOME PRINCIPLES FOR THE DESIGN OF CLARIFYING EDUCATIONAL ENVIRONMENTS Omar K. Moore Learning Research and Development Center and Alan Ross Anderson Department of Philosophy University of Pittsburgh Preprint of a chapter to appear in David Goslin (Ed.), Handbook of Socialization Theory and Research.Chicago: Rand McNally,T7-- (in press) U.S. DEPARTMENT OF HEALTH, EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE PERSON CR ORGANIZATION ORIGINATING IT.POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR POLICY. Contents 3 Theoretical Background 3 Folk Models Personality 9 Information Processing * 12 Information Processing forHuman Beings 14 Order of Mastering Perspective 15 Complications ConcerningKind-Heartedness 15 17 Interlude 20 Principles for DesigningClarifying Environments Perspectives Principle 21 Autotelic Principle 24 Productive Principle 26 Personalization Principle 28 An Application of the FourPrinciples 31 Perspectives Principle--Application 32 Autotelic Principle--Applications Ito Productive Principle--Application 45 Personalization Principle--Application 47 56 Conclusion References 58 SOME PRINCIPLES FOR THEDESIGN OF CLARIFYING EDUCATIONALENVIRONMENTS* by Omar Khayyam Moore Alan Ross Anderson When the ordinary typewriter was anexciting novelty, MarkTwain, who was an early typewriterbuff, called it a"curiosity-breeding little joker"--and so it was, then. The tallinELtypewriter,invented by Moore and Kobler (Moore, Kobler(1963), Kobler, Moore(1966)], is a contemporary novelty which also elicits agood deal of curiosity. There have been with numerous populararticles about it, and mostof those who have played generated by this it find it fascinating. Unfortunately, the interest machine does not carry over,necessarily, to the theoreticalideas which The machine itself lie behind it. We say "unfortunately" forgood reason. The is less important than theprinciples which guided itsconstruction. talking typewriter is merely oneof a large number of possibleinventions which can be made, we think,using this same theoreticalcontext as a guide. Our main purpose in this paperis to explain and toillustrate a set of principles, fourin number, for designinglearning environments within which even very youngchildren can acquire complexsymbolic skills along, that these prin- with relative ease. We intend to show, as we go ciples for designing clarifyingeducational environments(where by a "clarifying educational environment" we mean aneducational environment aimed to make the student(subject? victimfl clear about what heis related doing, and more generally, whatis going on) are systematically interpretation of to both a theoretical analysisof human culture and an human infant, the socialization process,i.e., that process whereby a Most of the theoretical workreported here was supported by the Office of Naval Research,Group Psychology Branch,Contract #SAR/Nonr-609 the major source of supporthas been (16). With respect to applications, "talking the Carnegie Corporationof New York. The cost of developing the typewriter" (Edison ResponsiveEnvironment) was borne exclusively by the McGraw-Edison Company of Elgin,Illinois. 2 beginning life as a biological individual, becomes a person--and whose infantile behavior is gradually transformed into adult conduct. In order to understand the "design principles" alluded to above, we must first explain the theoretical system out of which they emerged. We will then go on to a statement of the principles themselves, and final- ly we will consider, in some detail, an illustrative application of these principles to the problem of designing an actual learning environment.At this point, we will have come full circle--the talking typewriter will appear in a meaningful context as one part of a learning environment. It will also be obvious that the talking typewriter is itself fundamentally a "social science invention." Because it is a social science invention, it is difficult to use it or similar devices intelligently with- out an appreciation of the social scientific ideas on which it is based. Finally, before turning to our first task, that of sketching out the theoretical system upon which the zet of principles is founded, we wish to acknowledge the contributions to our thinking of George Herbert Mead (1932, 1934, 1936,1938)51the father of the Symbolic interactionist position in social psychology, and Georg Simmel [English translation (1959)], the originator of the school of Formal Sociology. We regard these men as central figures in the creation of the kind of sociology which can yield applications both at the level of mechanical inventions and social inventions. It may seem strange to some that we believe that Mead and Simmel have ideas which lend themselves to applications.Mead and his followers often have been criticized.for spawning ideas which lacked testable consequences--to say nothing of applications; and to the best of our knowledge we are the only ones who have seriously entertained the thought that Simmel was within a light year of a practical applica- tion. We hope to show here that leading ideas taken from these two men can be reshaped into working principles for designing educational environments. 1 From time to time we will try to acknowledge our indebtedness to various authors, but a complete list of those authors to whom we feel indebted would be impossible for either of us to make out. 3 Theoretical Backgroune Folk Models We think that it is amistake to regard the ordinaryhuman being as an atheoretical or anontheoretical or even anantitheoretical creature. ordinary Some contemporary behavioralscientists seem to assume that the man, a citizen ingood standing in whatevercommunity he lives, is woefully He lacking in intellectual resourcesto guide him in managing hisaffairs. is credited only with somefolk sayings and proverbs, somepractical know- ledge, some skill atrule-of-thumb reasoning, sometradition-based explan- ations--and that is about it. In a contrary vein, wesuggest a different view of"man."We think that early in human history,probably at about the time mendeveloped natural languages, they alsocreated models of the most importantfeatures 3 of their relations with theenvironment. These were relatively abstract models which collectivelycovered relations holding between(1) man and nature--insofar as nature is not randam,(2) man and the random or chancy elements in experience,(3) man in his interactional relations withothers Cul- like himself, and(4) man and the normative aspects of groupliving. tural structures falling withinthese four classes of models werecreated (perhaps it would in early history by many unsungEdisons and Einsteins be more appropriate to saythat they were createdby the unsung Meads exist a society and Simmels ofprehistory). Consequently, there does not /NMI 2Sincethis section is mainly a summaryof our own ideas, some free to paraphrase our worked out jointly, someseparately, we have felt However, anyone who wishesto go own paperswithout specific references. (1959, 1962, more deeply intothese ideas should read(A.R. Anderson, Moore A.R. Anderson 1966), Moore (1957, 1958,1961, 1964, 19659 1968), Moore, (1960a, 1960b, 1960c,1962a, 1962b, 1968)]. acquire a certain 3In common with manycontemporary philosophers, we When one sick
Recommended publications
  • Paraconsistent Extensional Propositional Logics.* 1
    PARACONSISTENT EXTENSIONAL PROPOSITIONAL LOGICS.* Diderik BATENS 1. Introduction In this paper I develop some logics that are as close as possible to the classical propositional calculus (PC) but do not presuppose that the world is consistent. It will turn out that there is one obvious basic logic of this sort, which may be extended in several ways into richer systems. 1 shall study the main formal properties of these systems and offer some philosophical remarks about them. The logics studied in this paper are material (and quasi-material) paraconsistent logics. 1 refer the reader to section 2 for a definition of «material logic» and oquasi-material logic». By a paraconsistent logic I mean, following Ayda I . Arruda (1980), a logic that «can be employed a s underlying lo g ic f o r inconsistent b u t non-trivial theories...» Incidently, the name 'paraconsistent logic' was coined recently by F. Mirô Quesada, but the definition of this kind of logics was offered years ago by Newton C.A. da Costa. Quite some results on paraconsistent logics have been published recently, and it is one of the aims of the present paper to order the domain of those paracon- sistent logics that are extensions o f the full positive propositional calculus. A first embrionic version of this paper was written in 1973. I got interested in the subject because I believed, and still believe, it to be relevant to several problems dealt with by Alan Ross Anderson and Nue! D. Be!nap in connection with their systems E and R. to the problem o f meaning relations (see my (1975a)), to the deduction problem (see my (1975b)), etc.
    [Show full text]
  • The Oberlin Colloquium in Philosophy: Program History
    The Oberlin Colloquium in Philosophy: Program History 1960 FIRST COLLOQUIUM Wilfrid Sellars, "On Looking at Something and Seeing it" Ronald Hepburn, "God and Ambiguity" Comments: Dennis O'Brien Kurt Baier, "Itching and Scratching" Comments: David Falk/Bruce Aune Annette Baier, "Motives" Comments: Jerome Schneewind 1961 SECOND COLLOQUIUM W.D. Falk, "Hegel, Hare and the Existential Malady" Richard Cartwright, "Propositions" Comments: Ruth Barcan Marcus D.A.T. Casking, "Avowals" Comments: Martin Lean Zeno Vendler, "Consequences, Effects and Results" Comments: William Dray/Sylvan Bromberger PUBLISHED: Analytical Philosophy, First Series, R.J. Butler (ed.), Oxford, Blackwell's, 1962. 1962 THIRD COLLOQUIUM C.J. Warnock, "Truth" Arthur Prior, "Some Exercises in Epistemic Logic" Newton Garver, "Criteria" Comments: Carl Ginet/Paul Ziff Hector-Neri Castenada, "The Private Language Argument" Comments: Vere Chappell/James Thomson John Searle, "Meaning and Speech Acts" Comments: Paul Benacerraf/Zeno Vendler PUBLISHED: Knowledge and Experience, C.D. Rollins (ed.), University of Pittsburgh Press, 1964. 1963 FOURTH COLLOQUIUM Michael Scriven, "Insanity" Frederick Will, "The Preferability of Probable Beliefs" Norman Malcolm, "Criteria" Comments: Peter Geach/George Pitcher Terrence Penelhum, "Pleasure and Falsity" Comments: William Kennick/Arnold Isenberg 1964 FIFTH COLLOQUIUM Stephen Korner, "Some Remarks on Deductivism" J.J.C. Smart, "Nonsense" Joel Feinberg, "Causing Voluntary Actions" Comments: Keith Donnellan/Keith Lehrer Nicholas Rescher, "Evaluative Metaphysics" Comments: Lewis W. Beck/Thomas E. Patton Herbert Hochberg, "Qualities" Comments: Richard Severens/J.M. Shorter PUBLISHED: Metaphysics and Explanation, W.H. Capitan and D.D. Merrill (eds.), University of Pittsburgh Press, 1966. 1965 SIXTH COLLOQUIUM Patrick Nowell-Smith, "Acts and Locutions" George Nakhnikian, "St. Anselm's Four Ontological Arguments" Hilary Putnam, "Psychological Predicates" Comments: Bruce Aune/U.T.
    [Show full text]
  • What Does It Mean to Say That Logic Is Formal?
    WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? by John Gordon MacFarlane A.B., Philosophy, Harvard College, 1991 M.A., Philosophy, University of Pittsburgh, 1994 M.A., Classics, University of Pittsburgh, 1997 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2000 i Robert Brandom, Distinguished Service Professor of Philosophy (Director) Nuel Belnap, Alan Ross Anderson Distinguished Professor of Philosophy (Second Reader) Joseph Camp, Professor of Philosophy Danielle Macbeth, Associate Professor of Philosophy, Haverford College (Outside Reader) Kenneth Manders, Associate Professor of Philosophy Gerald Massey, Distinguished Service Professor of Philosophy ii WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? John Gordon MacFarlane, PhD University of Pittsburgh, 2000 Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a pri- ori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought.
    [Show full text]
  • Introduction: at the Intersection of Truth and Falsity
    Introduction: At the Intersection of Truth and Falsity JC Beall ‘Now we will take another line of reasoning. When you follow two separate chains of thought, Watson, you will find some point of intersection which should approximate to the truth.’—Sherlock Holmes, in ‘The Disappearance of Lady Frances Carfax’. 1. TOWARDS THE INTERSECTION Suppose that we have (at least) two categories X and Y for any meaningful, declarative sentence A of our language.É Pending further information about X and Y, there seem to be four options for an arbitrary sentence A: » A is only in X » A is only in Y » A is in both X and Y » A is in neither X nor Y Whether each such ‘option’ is logically possible depends not only on our logic (about which more below) but on the details of X and Y. Suppose that X comprises all (and only) sentences composed of exactly six words, and Y those with exactly nineteen words. In that case, only the third option is ruled out: X and Y are exclusive—their intersection X ∩ Y is empty—since no A can be composed of exactly six words and also be composed of exactly nineteen words.Ê Despite being exclusive, X and Y are not exhaustive—their union X ∪ Y does not exhaust all sentences—since some A may fall into neither X nor Y. (Just consider ‘Max sat on Agnes’.) Consider another example. Let X comprise all sentences of your favourite novel and Y your all-time favourite sentences. In that case, exclusion is not ruled out; the intersection of X and Y may well be non-empty.
    [Show full text]
  • Two Entries from the Dictionary of Modern American Philosophers Edited by John R
    Two entries from the Dictionary Of Modern American Philosophers edited by John R. Shook, Thoemmes Continuum, 2005 belnap, nuel dinsmore jr. (1930– ) Nuel Belnap was born on 1 May 1930 in Evanston, Illinois. He received an Illinois BA in 1952, and moving to Yale for postgraduate study in logic under the supervision of Alan Anderson, he received an MA in 1957 and a PhD in 1960. After graduation, Belnap continued to work at Yale as an Assistant Professor until 1963, whereupon he moved to the Department of Philosophy at the University of Pittsburgh to take up a position as an Associate Professor. He remains there to this day, where he is now the Alan Ross Anderson Distinguished Professor of Philosophy, in addition to holding positions in Sociology, History and Philosophy of Science, and in the Intelligent Systems Program. Belnap’s research covers logic and related fields such as the philosophy of language and metaphysics and philosophy of science. His name is most often associated with his teacher and colleague Alan Anderson and their research program in relevance logic. Belnap’s research, with Anderson, and their colleagues and students, first at Yale, and then at Pittsburgh, provided a rigorous formal theory of logical consequence and implication that takes account of relevance. The two volumes Entailment (1975, 1992) provide a survey of work in this field, which has continued since the 1950’s. Belnap’s contributions to relevance logic are too numerous to list here, but many have gone on to shape a thriving, if not quite orthodox, research community. A good example of Belnap’s contributions here is his paper “Display Logic” (1982), which develops a new way of seeing the structure of proof, encompassing classical, intuitionistic, modal and relevance logic.
    [Show full text]
  • Alan Ross Anderson and Nuel D.Belnap, Jr. Entailment the Logic
    (", , ENTAILMENT ,l THE LOGIC OF RELEVANCE AND NECESSITY by ALAN ROSS ANDERSON and I i--' NUEL D. BELNAP, JR. wUh contributions by J. MICHAEL DUNN j ROBERT K. MEYER Ii l and further contributions by JOHN R. CHIDGEY STORRS MCCALL J. ALBERTO COPPA ZANE PARKS DOROTHY L. GROYER GARREL POTTINGER BAS YAN FRAASSEN RICHARD ROUTLEY HUGUES LEBLANC ALASDAIR URQUHART ROBERT G. WOLF i J VOLUME I PRINCETON UNIVERSITY PRESS Dedicated to the memory of WILHELM ACKERMANN (1896-1962) whose insights in BegrUndung einer strengen Implikatiol1 (Journal of symbolic logic, 1956) provided the impetus for this enterprise COPYRIGHT © 1975 BY PRINCETON UNIVERSITY PRESS Published by Princeton University Press Princeton and London All Rights Reserved LCC: 72-14016 ISBN: G-691-07192-6 Library of Congress cataloging in Publication Data will be found on the last printed page of this book Printed in the United States of America by Princeton University Press Princeton, New Jersey CONTENTS VOLUME I Analytical Table of Contents IX Preface xxi Acknowledgments xxix I. THE PURE CALCULUS OF ENTAILMENT 3 II. ENTAILMENT AND NEGATION 107 III. ENTAILMENT BETWEEN TRUTH FUNCTIONS 150 IV. THE CALCULUS E OF ENTAILMENT 231 V. NEIGHBORS OF E 339 Appendix: Grammatical propaedeutic 473 Bibliography for Volume I 493 Indices to Volume I 517 VOLUME II (tentative) VI. THE THEORY OF ENTAILMENT VII. INDIVIDUAL QUANTIFICATION VIII. ACKERMANN'S Strengen Implikation IX. SEMANTIC ANALYSIS OF RELEVANCE LOGICS X. ASSORTED TOPICS Comprehensive Bibliography (by Robert G. Wolf) Combined Indices vii ANALYTICAL TABLE OF CONTENTS VOLUME I I. THE PURE CALCULUS OF ENTAILMENT §1. The heart of logic 3 § 1.1.
    [Show full text]
  • QUANTIFYING OVER PROPOSITIONS in RELEVANCE LOGIC: NONAXIOMATISABILITY of PRIMARY INTERPRETATIONS of Vp and 3P*
    THE JOURNAL OF SYMBOLIC LOGIC Volume 58, Number 1, March 1993 QUANTIFYING OVER PROPOSITIONS IN RELEVANCE LOGIC: NONAXIOMATISABILITY OF PRIMARY INTERPRETATIONS OF Vp AND 3p* PHILIP KREMER A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take a model to be one of these structures, a, together with some function or relation which associates with every formula A a subset of a. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of a with which a for­ mula can be associated: for example, in the semantics of Routley and Meyer [1973], a formula can only be associated with subsets which are closed upwards. It is nat­ ural to take a proposition of a. to be such a subset of a, and, further, to take the propositional quantifiers to range over these propositions. (Routley and Meyer [1973] explicitly consider this interpretation.) Given such an algebraic semantics, we call (following Routley and Meyer [1973], who follow Henkin [1950]) the above- described interpretation of the quantifiers the primary interpretation associated with the semantics.1 Received April 11, 1991; revised December 18, 1991. *I am much indebted to Nuel Belnap for his constant help and encouragement, and, not least of all, for rather closely inspecting the proofs. I thank Aldo Antonelli for asking me whether the systems studied here fail to be arithmetical (in the recursion theoretic sense of Hinman [1978], Odifreddi [1989] and others) as well as recursively enumerable. Not only are the systems here nonarithmetical, they are recursively isomorphic to full second-order logic.
    [Show full text]
  • There Is No Logical Negation: True, False, Both and Neither
    Australasian Journal of Logic There is no logical negation: true, false, both and neither Jc Beall entailments.net University of Connecticut University of Tasmania 1 Unscientific preamble: Confession of a former logical exhaustivist I have thought hard and long about truth-theoretic paradoxes and I am con- vinced that they are best understood as motivating nonclassical logic. At an early stage { though mostly behind published doors { I strongly believed that the natural position on logical negation was to maintain that paradox- ical phenomena motivate a rejection of both excluded middle and its dual `explosion'. Some of this thinking showed up in early work [5], but for one reason or another (embarrassingly, peer pressure probably being part of it) I found myself sticking to just one side or the other { rejecting excluded mid- dle or its dual explosion but not both. Eventually, when the pressures to publicly pronounce a position grew strong I wound up embracing excluded middle, landing in the vicinity of glut theorists like Florencio Asenjo [3, 4], Routley/Sylvan [44], Priest [37, 38], Dowden [17], Mortensen [33], Weber [51], Hyde [52], Colyvan [11], Berto [14] and others. But even in my prin- cipal work on the topic [6] I explicitly expressed discomfort in embracing excluded middle for logical negation while rejecting its dual. I lived with the discomfort until now. I'm now back to my roots. And the simple reason is at bottom tied to balance, simplicity, naturalness and the like { the very things that had me rejecting both excluded middle and explosion in my youthful thinking.
    [Show full text]
  • Nuel Belnap: Curriculum Vitae
    NUEL BELNAP: CURRICULUM VITAE PRESENT POSITION: Alan Ross Anderson Distinguished Professor of Philosophy, Professor of Sociology, Professor of History and Philosophy of Science, and Professor of the Intelligent Systems Program, University of Pittsburgh. PERSONAL: born Evanston, Illinois, May 1, 1930. EDUCATION: B. A., University of Illinois, 1952; M. A., Yale University, 1957; Ph. D., Yale University, 1960. EMPLOYMENT: Yale University, Department of Philosophy, Instructor, 1958-1960; Assistant Professor, 1960--1963. University of Pittsburgh, Department of Philosophy, Associate Professor, 1963- 1966; Professor, 1966 to date; Professor of Sociology, 1967 to date; Professor of History and Philosophy of Science, 1971 to date; Alan Ross Anderson Lecturer, 1983-84; Alan Ross Anderson Distinguished Professor, 1984 to date; Professor in the Intelligent Systems Program, 1988 to date. University of California at Irvine, Visiting Professor of Philosophy, Winter, 1973. Indiana University, Visiting Oscar R. Ewing Professor of Philosophy, Fall, 1977, Fall, 1978, and Fall, 1979. PROFESSIONAL ASSOCIATIONS: American Philosophical Association; Associa­ tion for Symbolic Logic (Program Committee Chairman, 1961; Executive Com­ mittee, 1970--1973; representative to Section L ofthe AAAS, 1974-84; Commit­ tee on reviews policy, 1974-1976; Oversight Committee 1988-1989; Nomination Committee 1989); American Association for the Advancement of Science; So­ ciety for Exact Philosophy (Vice president, 1971-1974; President, 1974-1976; Program coordinator, 1978; treasurer,
    [Show full text]
  • Arxiv:2006.00642V3 [Math.LO] 26 Jun 2021 Beth Definability in the Logic KR
    Beth Definability in the Logic KR Jacob Garber June 29, 2021 Abstract The Beth Definability Property holds for an algebraizable logic if and only if every epimorphism in the corresponding category of algebras is surjective. Using this tech- nique, Urquhart in 1999 showed that the Beth Definability Property fails for a wide class of relevant logics, including T, E, and R. However, the counterexample for those logics does not extend to the algebraic counterpart of the super relevant logic KR, the so-called Boolean monoids. Following a suggestion of Urquhart, we use modular lattices constructed by Freese to show that epimorphisms need not be surjective in a wide class of relation algebras. This class includes the Boolean monoids, and thus the Beth Definability Property fails for KR. 1 Introduction Relevant logics were first introduced to avoid the paradoxes of material implication, which are counterintuitive inferences that result from a mismatch between the intuitive meaning of implication and its formalization in classical logic. This work lead to the development of a wide swath of relevant logics, spanning from the basic logic B to the logic of relevant implication R, with many other relevant logics (such as ticket entailment T and relevant entailment E) in between. A comprehensive description of these logics and relevant logic in general can be found in any of [1, 2, 7, 16, 5]. In this paper we will focus our attention on the logic KR, which consists of adding the paradoxical axiom (A∧¬A) → B to R. Despite being R KR arXiv:2006.00642v3 [math.LO] 26 Jun 2021 stronger than and thus not a purely relevant logic, avoids various other paradoxes of material implication and does not collapse to classical logic (see Kerr [14]).
    [Show full text]
  • Logical Instrumentalism
    Logical Instrumentalism Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Teresa Kouri ∼6 6 Graduate Program in Philosophy The Ohio State University 2016 Dissertation Committee: Professor Stewart Shapiro, Advisor Professor Chris Pincock Professor Craige Roberts Professor Kevin Scharp Professor Neil Tennant c Teresa Kouri, 2016 Abstract Logic and reasoning go hand in hand. So often, we hear that someone has reasoned poorly about something if they have not reasoned logically, or that an argument is bad because it is not logically valid. To date, research has been devoted to exactly just what types of logical systems are appropriate for guiding our reasoning. Traditionally, classical logic has been the logic suggested as the ideal for this purpose. More recently, non-classical logics have been suggested as alternatives. Even more recently, it has been suggested that multiple logics are reasoning guiding, or none are. So far, no one has addressed the impact that natural language has on our ability to reason well. My project fills this gap. I focus on the relationship between the meaning of the connectives (\and", \or", \not", etc.) in natural language and logic. By assessing what these connectives mean in natural language, we can figure out what they must mean in the formal language in order to guide our reasoning. I show that the connectives do not have a single meaning across all contexts in natural language, and thus there can be no single meaning to the connectives in the formal language which guides our reasoning.
    [Show full text]
  • Af7fb205-44E1-4410-99Eb-77Fb56b2d124.Pdf
    ENTAILMENT ENTAILMENT THE LOGIC OF RELEVANCE AND NECESSITY by ALAN ROSS ANDERSON and NUEL D. BELNAP, JR. and J. MICHAEL DUNN with contributions by KIT FINE ALASDAIR URQUHART and further contributions by DANIEL COHEN GLEN HELMAN STEVE GIAMBRONE ERROL P. MARTIN DOROTHY L. GROVER MICHAEL A, MCROBBIE ANIL GUPTA STUART SHAPIRO and including a Bibliography of Entailment by ROBERT G. WOLF VOLUME II PRINCETON UNIVERSITY PRESS COPYRIGHT © 1992 BY PRINCETON UNIVERSITY PRESS Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, Oxford All Rights Reserved Library of Congress Cataloging-in-Publication Data (Revised for vol. 2) Anderson, Alan Ross. Entailment: the logic of relevance and necessity. Vol. 2. written by Alan Ross Anderson, Nuel D. Belnap and J. Michael Dunn with contribution by Kit Fine ... et al. Includes bibliographical references. 1. Entailment (Logic). I. Belnap, Nuel D., 1930- —joint author. II. Dunn, J. Michael, 1941- III. Fine, Kit. IV. Title. BC199.E58A53 1975 160 72-14016 ISBN 0-691-07192-6 (v. 1) ISBN 0-691-07339-2 (v. 2) This book has been composed in Monotype Times Roman by Syntax International Pte Ltd Princeton University Press books are printed on acid-free paper, and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton University Press Princeton, New Jersey 10 987654321 Dedicated to six generous parents SELMA WETTELAND ANDERSON ROSS ELMER ANDERSON ELIZABETH DAFTER BELNAP · NUEL DINSMORE BELNAP PHILOMENA LAUER DUNN · JON HARDIN DUNN CONTENTS VOLUME I Analytical Table of Contents ix Preface xxi Acknowledgments xxix I.
    [Show full text]