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Kripke's Theory of Truth
Kripke’s Theory of Truth (for the strong Kleene scheme) Presented by Christopher Gauker Version: July 26, 2006 Contemporary discussions of truth often make reference to Kripke’s theory of truth (presented by Kripke only his 1975 Journal of Philosophy paper). What Kripke did was show how to interpret a language in such a way that it contains its own truth predicate. The fact that the language he describes contains its own truth predicate is proved by means of something called a fixed-point theorem. I have written this document and posted it on the web because it is hard to find a presentation of Kripke’s theory that will be understandable even to readers who have had only a first course in logic. It is my intention that this presentation will be understandable to all readers who have been exposed to at least the following: The languages of ordinary predicate logic. Recursive definitions of truth in a structure for such languages. (Structures are also called models or interpretations.) The basic concepts and notation of set theory, such as curly brackets, membership (“∈”), inclusion (“⊆”), ordered n-tuples, relations and functions. Kripke’s theory of truth builds on a three-valued interpretation of a language. (So sentences may be neither true nor false (N) as well as (T) or false (F).) Various three- valued valuation schemes may be used. Here we will consider only the strong Kleene scheme, which is the only one most people care about. I can take no credit for this presentation. It is nothing more than a distillation from the more general presentation in Anil Gupta and Nuel Belnap’s book, The Revision Theory of Truth (MIT Press, 1993) (who in turn acknowledge debts to Fitting and Visser). -
PLATO's SYMPOSIUM J
50 ccn~ PLATO'S SYMPOSIUM j - - -- ________j e Library of Liberal Arts PLATO'S SYMPOSIUM Tran lated by BENJAMIN JOWETT With an Introduction by FULTON H. ANDERSON Professor of Philosophy, University of Toronto THE LIBERAL ARTS PRESS NEW YORK CONTENTS SELECTED BIBLIOGRAPHY .. .... ................................... ......... ... ........... 6 EDITOR'S INTRODUCTION ................... ............................................. 7 SYMPOSIUM APOLLODORUS 13 THE SPEECH OF PHAEDRUS ...... .......................... .......................... .. 19 THE SPEECH OF PAU ANIAS ................. ... ................................. ... .. 21 THE SPEECH OF ERYXIMACHUS 27 THE SPEECH OF ARISTOPHAN E .. ............................... .................. 30 THE SPEECH OF AGATHON ............ .............................................. .. 35 THE SPEECH OF SocRATES ................................ .. ................... ..... .. 39 THE SPEECH OF ALCIBIADES ................. ............... ... ........... ...... .... .. 55 8 PLATO INTROD CTION 9 crescendo, and culminates in the report by Socrates on wi dom and epistemology, upon all of which the Symposium ha bearing, learned from the "wi e" woman Diotima. are intertwined, we m ay set down briefly a few of the more general The dialogue i a "reported" one. Plato himself could not have principles which are to be found in it author's many-sided thought. been present at the original party. (What went on there was told The human soul, a cording to Plato, is es entially in motion. time and time again about Athens.) He was a mere boy when it It is li fe and the integration of living functions. A dead soul is a con took place. Nor could the narrator Apollodorus have been a guest; _lladiction in terms. Man throughout his whole nature is erotically he was too young at the time. The latter got his report from motivated. His "love" or desire i manifest in three mutually in Aristodemus, a guest at the banquet. -
Online Library of Liberty: the Dialogues of Plato, Vol. 1
The Online Library of Liberty A Project Of Liberty Fund, Inc. Plato, The Dialogues of Plato, vol. 1 [387 AD] The Online Library Of Liberty This E-Book (PDF format) is published by Liberty Fund, Inc., a private, non-profit, educational foundation established in 1960 to encourage study of the ideal of a society of free and responsible individuals. 2010 was the 50th anniversary year of the founding of Liberty Fund. It is part of the Online Library of Liberty web site http://oll.libertyfund.org, which was established in 2004 in order to further the educational goals of Liberty Fund, Inc. To find out more about the author or title, to use the site's powerful search engine, to see other titles in other formats (HTML, facsimile PDF), or to make use of the hundreds of essays, educational aids, and study guides, please visit the OLL web site. This title is also part of the Portable Library of Liberty DVD which contains over 1,000 books and quotes about liberty and power, and is available free of charge upon request. The cuneiform inscription that appears in the logo and serves as a design element in all Liberty Fund books and web sites is the earliest-known written appearance of the word “freedom” (amagi), or “liberty.” It is taken from a clay document written about 2300 B.C. in the Sumerian city-state of Lagash, in present day Iraq. To find out more about Liberty Fund, Inc., or the Online Library of Liberty Project, please contact the Director at [email protected]. -
A Cardinal Sin: the Infinite in Spinoza's Philosophy
Macalester College DigitalCommons@Macalester College Philosophy Honors Projects Philosophy Department Spring 2014 A Cardinal Sin: The nfinitI e in Spinoza's Philosophy Samuel H. Eklund Macalester College, [email protected] Follow this and additional works at: http://digitalcommons.macalester.edu/phil_honors Part of the Philosophy Commons Recommended Citation Eklund, Samuel H., "A Cardinal Sin: The nfinitI e in Spinoza's Philosophy" (2014). Philosophy Honors Projects. Paper 7. http://digitalcommons.macalester.edu/phil_honors/7 This Honors Project is brought to you for free and open access by the Philosophy Department at DigitalCommons@Macalester College. It has been accepted for inclusion in Philosophy Honors Projects by an authorized administrator of DigitalCommons@Macalester College. For more information, please contact [email protected]. A Cardinal Sin: The Infinite in Spinoza’s Philosophy By: Samuel Eklund Macalester College Philosophy Department Honors Advisor: Geoffrey Gorham Acknowledgements This thesis would not have been possible without my advisor, Professor Geoffrey Gorham. Through a collaborative summer research grant, I was able to work with him in improving a vague idea about writing on Spinoza’s views on existence and time into a concrete analysis of Spinoza and infinity. Without his help during the summer and feedback during the past academic year, my views on Spinoza wouldn’t have been as developed as they currently are. Additionally, I would like to acknowledge the hard work done by the other two members of my honors committee: Professor Janet Folina and Professor Andrew Beveridge. Their questions during the oral defense and written feedback were incredibly helpful in producing the final draft of this project. -
Anselm's Cur Deus Homo
Anselm’s Cur Deus Homo: A Meditation from the Point of View of the Sinner Gene Fendt Elements in Anselm's Cur Deus Homo point quite differently from the usual view of it as the locus classicus for a theory of Incarnation and Atonement which exhibits Christ as providing the substitutive revenging satisfaction for the infinite dishonor God suffers at the sin of Adam. This meditation will attempt to bring out how the rhetorical ergon of the work upon faith and conscience drives the sinner to see the necessity of the marriage of human with divine natures offered in Christ and how that marriage raises both man and creation out of sin and its defects. This explanation should exhibit both to believers, who seek to understand, and to unbelievers (primarily Jews and Muslims), from a common root, a solution "intelligible to all, and appealing because of its utility and the beauty of its reasoning" (1.1). Anselm’s Cur Deus Homo is the locus classicus for a theory of Incarnation and Atonement which exhibits Christ as providing the substitutive revenging satisfaction for the infinite dishonor God suffers at the sin of Adam (and company).1 There are elements in it, however, which seem to point quite differently from such a view. This meditation will attempt to bring further into the open how the rhetorical ergon of the work upon “faith and conscience”2 shows something new in this Paschal event, which cannot be well accommodated to the view which makes Christ a scapegoat killed for our sin.3 This ergon upon the conscience I take—in what I trust is a most suitably monastic fashion—to be more important than the theoretical theological shell which Anselm’s discussion with Boso more famously leaves behind. -
BY PLATO• ARISTOTLE • .AND AQUINAS I
i / REF1,l!;CTit.>NS ON ECONOMIC PROBLEMS / BY PLATO• ARISTOTLE • .AND AQUINAS ii ~FLECTIONS ON ECONO:MIC PROBLEMS 1 BY PLA'I'O, ARISTOTLE, JJJD AQUINAS, By EUGENE LAIDIBEL ,,SWEARINGEN Bachelor of Science Oklahoma Agricultural and Mechanical Collage Stillwater, Oklahoma 1941 Submitted to the Depertmeut of Economics Oklahoma Agricultural and Mechanical College In Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE 1948 iii f.. 'I. I ···· i·: ,\ H.: :. :· ··: ! • • ~ ' , ~ • • !·:.· : i_ ·, 1r 1i1. cr~~rJ3t L l: i{ ,\ I~ Y , '•T •)() 1 0 ,1 8 API-'HOV~D BY: .J ,.· 1.., J l.;"t .. ---- -··- - ·- ______.,.. I 7 -.. JI J ~ L / \ l v·~~ u ' ~) (;_,LA { 7 {- ' r ~ (\.7 __\ _. ...A'_ ..;f_ ../-_" ...._!)_.... ..." ___ ......._ ·;...;;; ··-----/ 1--.,i-----' ~-.._.._ :_..(__,,---- ....... Member of the Report Committee 1..j lj:,;7 (\ - . "'·- -· _ .,. ·--'--C. r, .~-}, .~- Q_ · -~ Q.- 1Head of the Department . · ~ Dean of the Graduate School 502 04 0 .~ -,. iv . r l Preface The purpose and plan of this report are set out in the Introduction. Here, I only wish to express my gratitude to Professor Russell H. Baugh who has helped me greatly in the preparation of this report by discussing the various subjects as they were in the process of being prepared. I am very much indebted to Dr. Harold D. Hantz for his commentaries on the report and for the inspiration which his classes in Philosophy have furnished me as I attempted to correlate some of the material found in these two fields, Ecor!.Omics and Philosophy. I should like also to acknowledge that I owe my first introduction into the relationships of Economics and Philosophy to Dean Raymond Thomas, and his com~ents on this report have been of great value. -
EPISTEMIC CIRCULARITY: MALIGNANT and BENIGN Michael Bergmann
EPISTEMIC CIRCULARITY: MALIGNANT AND BENIGN Michael Bergmann Consider the following dialogue: Juror #1: You know that witness named Hank? I have doubts about his trustworthiness. Juror #2: Well perhaps this will help you. Yesterday I overheard Hank claiming to be a trustworthy witness. Juror #1: So Hank claimed to be trustworthy did he? Well, that settles it then. I’m now convinced that Hank is trustworthy. Is the belief of Juror #1 that Hank is a trustworthy witness justified? Most of us would be inclined to say it isn’t. Juror #1 begins by having some doubts about Hank’s trustworthiness, and then he comes to believe that Hank is trustworthy. The problem is that he arrives at this belief on the basis of Hank’s own testimony. That isn’t reasonable. You can’t sensibly come to trust a doubted witness on the basis of that very witness’s testimony on his own behalf.1 Now consider the following soliloquy: Doubter: I have some doubts about the trustworthiness of my senses. After all, for all I know, they are deceiving me. Let’s see ... Hey, wait a minute. They are trustworthy! I recall many occasions in the past when I was inclined to hold certain perceptual beliefs. On each of those occasions, the beliefs I formed were true. I know that because the people I was with confirmed to me that they were true. By inductive reasoning, I can safely conclude from those past cases that my senses are trustworthy. There we go. It feels good to have those doubts about my senses behind me. -
A Note on Extension, Intension, and Truth Author(S): Anil Gupta and Nuel Belnap Source: the Journal of Philosophy, Vol
Journal of Philosophy, Inc. A Note on Extension, Intension, and Truth Author(s): Anil Gupta and Nuel Belnap Source: The Journal of Philosophy, Vol. 84, No. 3 (Mar., 1987), pp. 168-174 Published by: Journal of Philosophy, Inc. Stable URL: http://www.jstor.org/stable/2026597 Accessed: 28/05/2009 11:06 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=jphil. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. Journal of Philosophy, Inc. is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Philosophy. http://www.jstor.org 168 THE JOURNAL OF PHILOSOPHY A NOTE ON EXTENSION, INTENSION, AND TRUTH* I T is common knowledge that two predicates may coincide in extension but differ in intension and that, for any predicate, one can construct an infinity of coextensional predicates that differ in intension. -
The Historicity of Plato's Apology of Socrates
Loyola University Chicago Loyola eCommons Master's Theses Theses and Dissertations 1946 The Historicity of Plato's Apology of Socrates David J. Bowman Loyola University Chicago Follow this and additional works at: https://ecommons.luc.edu/luc_theses Part of the Classical Literature and Philology Commons Recommended Citation Bowman, David J., "The Historicity of Plato's Apology of Socrates" (1946). Master's Theses. 61. https://ecommons.luc.edu/luc_theses/61 This Thesis is brought to you for free and open access by the Theses and Dissertations at Loyola eCommons. It has been accepted for inclusion in Master's Theses by an authorized administrator of Loyola eCommons. For more information, please contact [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License. Copyright © 1946 David J. Bowman !HE HISTORICITY OP PLATO'S APOLOGY OF SOCRATES BY DA.VID J. BOWJWf~ S.J• .l. !BESIS SUBMITTED Ilf PARTIAL FULFILIJIE.NT OF THB: R}gQUIRE'IIENTS POR THE DEGREE OF IIA.STER OF ARTS Ill LOYOLA UlfiVERSITY JULY 1946 -VI'fA. David J. Bowman; S.J•• was born in Oak Park, Ill1no1a, on Ma7 20, 1919. Atter b!a eleaentar7 education at Ascension School# in Oak Park, he attended LoJola AcademJ ot Chicago, graduat1DS .from. there in June, 1937. On September 1, 1937# he entered the Sacred Heart Novitiate ot the SocietJ ot Jesus at Milford~ Ohio. Por the tour Jear• he spent there, he was aoademicallJ connected with Xavier Univeraitr, Cincinnati, Ohio. In August ot 1941 he tranaterred to West Baden College o.f Lorol& Universit7, Obicago, and received the degree ot Bachelor o.f Arts with a major in Greek in Deo.aber, 1941. -
Plato Apology of Socrates and Crito
COLLEGE SERIES OF GREEK AUTHORS EDITED UNDER THE SUPERVISION OF JOHN WILLIAMS WHITE, LEWIS R. PACKARD, a n d THOMAS D. SEYMOUR. PLATO A p o l o g y o f S o c r a t e s AND C r i t o EDITED ON THE BASIS OF CRON’S EDITION BY LOUIS DYER A s s i s t a n t ·Ρι;Οχ'ε&^ο^ ι ν ^University. BOSTON: PUBLISHED BY GINN & COMPANY. 1902. I P ■ C o p · 3 Entered, according to Act of Congress, in the year 1885, by J o h n W il l ia m s W h i t e a n d T h o m a s D. S e y m o u r , In the Office of the Librarian of Congress, at Washington. J . S. C u s h in g & Co., P r i n t e r s , B o s t o n . PREFACE. T his edition of the Apology of Socrates and the Crito is based upon Dr. Christian Cron’s eighth edition, Leipzig, 1882. The Notes and Introduction here given have in the main been con fined within the limits intelligently drawn by Dr. Cron, whose commentaries upon various dialogues of Plato have done and still do so much in Germany to make the study of our author more profitable as well as pleasanter. No scruple has been felt, how ever, in making changes. I trust there are few if any of these which Dr. Cron might not himself make if he were preparing his work for an English-thinking and English-speaking public. -
Plato's Symposium: the Ethics of Desire
Plato’s Symposium: The Ethics of Desire FRISBEE C. C. SHEFFIELD 1 Contents Introduction 1 1. Ero¯s and the Good Life 8 2. Socrates’ Speech: The Nature of Ero¯s 40 3. Socrates’ Speech: The Aim of Ero¯s 75 4. Socrates’ Speech: The Activity of Ero¯s 112 5. Socrates’ Speech: Concern for Others? 154 6. ‘Nothing to do with Human AVairs?’: Alcibiades’ Response to Socrates 183 7. Shadow Lovers: The Symposiasts and Socrates 207 Conclusion 225 Appendix : Socratic Psychology or Tripartition in the Symposium? 227 References 240 Index 249 Introduction In the Symposium Plato invites us to imagine the following scene: A pair of lovers are locked in an embrace and Hephaestus stands over them with his mending tools asking: ‘What is it that you human beings really want from each other?’ The lovers are puzzled, and he asks them again: ‘Is this your heart’s desire, for the two of you to become parts of the same whole, and never to separate, day or night? If that is your desire, I’d like to weld you together and join you into something whole, so that the two of you are made into one. Look at your love and see if this is what you desire: wouldn’t this be all that you want?’ No one, apparently, would think that mere sex is the reason each lover takes such deep joy in being with the other. The soul of each lover apparently longs for something else, but cannot say what it is. The beloved holds out the promise of something beyond itself, but that something lovers are unable to name.1 Hephaestus’ question is a pressing one. -
On the Arrangement of the Platonic Dialogues
Ryan C. Fowler 25th Hour On the Arrangement of the Platonic Dialogues I. Thrasyllus a. Diogenes Laertius (D.L.), Lives and Opinions of Eminent Philosophers 3.56: “But, just as long ago in tragedy the chorus was the only actor, and afterwards, in order to give the chorus breathing space, Thespis devised a single actor, Aeschylus a second, Sophocles a third, and thus tragedy was completed, so too with philosophy: in early times it discoursed on one subject only, namely physics, then Socrates added the second subject, ethics, and Plato the third, dialectics, and so brought philosophy to perfection. Thrasyllus says that he [Plato] published his dialogues in tetralogies, like those of the tragic poets. Thus they contended with four plays at the Dionysia, the Lenaea, the Panathenaea and the festival of Chytri. Of the four plays the last was a satiric drama; and the four together were called a tetralogy.” b. Characters or types of dialogues (D.L. 3.49): 1. instructive (ὑφηγητικός) A. theoretical (θεωρηµατικόν) a. physical (φυσικόν) b. logical (λογικόν) B. practical (πρακτικόν) a. ethical (ἠθικόν) b. political (πολιτικόν) 2. investigative (ζητητικός) A. training the mind (γυµναστικός) a. obstetrical (µαιευτικός) b. tentative (πειραστικός) B. victory in controversy (ἀγωνιστικός) a. critical (ἐνδεικτικός) b. subversive (ἀνατρεπτικός) c. Thrasyllan categories of the dialogues (D.L. 3.50-1): Physics: Timaeus Logic: Statesman, Cratylus, Parmenides, and Sophist Ethics: Apology, Crito, Phaedo, Phaedrus, Symposium, Menexenus, Clitophon, the Letters, Philebus, Hipparchus, Rivals Politics: Republic, the Laws, Minos, Epinomis, Atlantis Obstetrics: Alcibiades 1 and 2, Theages, Lysis, Laches Tentative: Euthyphro, Meno, Io, Charmides and Theaetetus Critical: Protagoras Subversive: Euthydemus, Gorgias, and Hippias 1 and 2 :1 d.