LOGICAL FORM Kirk Ludwig
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A Companion to Analytic Philosophy
A Companion to Analytic Philosophy Blackwell Companions to Philosophy This outstanding student reference series offers a comprehensive and authoritative survey of philosophy as a whole. Written by today’s leading philosophers, each volume provides lucid and engaging coverage of the key figures, terms, topics, and problems of the field. Taken together, the volumes provide the ideal basis for course use, represent- ing an unparalleled work of reference for students and specialists alike. Already published in the series 15. A Companion to Bioethics Edited by Helga Kuhse and Peter Singer 1. The Blackwell Companion to Philosophy Edited by Nicholas Bunnin and Eric 16. A Companion to the Philosophers Tsui-James Edited by Robert L. Arrington 2. A Companion to Ethics Edited by Peter Singer 17. A Companion to Business Ethics Edited by Robert E. Frederick 3. A Companion to Aesthetics Edited by David Cooper 18. A Companion to the Philosophy of 4. A Companion to Epistemology Science Edited by Jonathan Dancy and Ernest Sosa Edited by W. H. Newton-Smith 5. A Companion to Contemporary Political 19. A Companion to Environmental Philosophy Philosophy Edited by Robert E. Goodin and Philip Pettit Edited by Dale Jamieson 6. A Companion to Philosophy of Mind 20. A Companion to Analytic Philosophy Edited by Samuel Guttenplan Edited by A. P. Martinich and David Sosa 7. A Companion to Metaphysics Edited by Jaegwon Kim and Ernest Sosa Forthcoming 8. A Companion to Philosophy of Law and A Companion to Genethics Legal Theory Edited by John Harris and Justine Burley Edited by Dennis Patterson 9. A Companion to Philosophy of Religion A Companion to African-American Edited by Philip L. -
Reference and Definite Descriptions1
Philosophical Review !"#"$"%&"'(%)'*"#+%+,"'*"-&$+.,+/%- 01,2/$3-45'6"+,2'78'*/%%"99(% 7/1$&"5':2"';2+9/-/.2+&(9'!"<+"=>'?/98'@A>'B/8'C'3D198>'EFGG4>'..8'HIEJCKL ;1M9+-2")'MN5'*1O"'P%+<"$-+,N';$"--'/%'M"2(9#'/#';2+9/-/.2+&(9'!"<+"= 7,(M9"'P!Q5'http://www.jstor.org/stable/2183143 0&&"--")5'KARKIRHKEK'EA5HC 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=duke. 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 service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Duke University Press and Philosophical Review are collaborating with JSTOR to digitize, preserve and extend access to The Philosophical Review. http://www.jstor.org REFERENCE AND DEFINITE DESCRIPTIONS1 I DEFINITE descriptions, I shall argue, have two possible func- tions. -
Sentence Types and Functions
San José State University Writing Center www.sjsu.edu/writingcenter Written by Sarah Andersen Sentence Types and Functions Choosing what types of sentences to use in an essay can be challenging for several reasons. The writer must consider the following questions: Are my ideas simple or complex? Do my ideas require shorter statements or longer explanations? How do I express my ideas clearly? This handout discusses the basic components of a sentence, the different types of sentences, and various functions of each type of sentence. What Is a Sentence? A sentence is a complete set of words that conveys meaning. A sentence can communicate o a statement (I am studying.) o a command (Go away.) o an exclamation (I’m so excited!) o a question (What time is it?) A sentence is composed of one or more clauses. A clause contains a subject and verb. Independent and Dependent Clauses There are two types of clauses: independent clauses and dependent clauses. A sentence contains at least one independent clause and may contain one or more dependent clauses. An independent clause (or main clause) o is a complete thought. o can stand by itself. A dependent clause (or subordinate clause) o is an incomplete thought. o cannot stand by itself. You can spot a dependent clause by identifying the subordinating conjunction. A subordinating conjunction creates a dependent clause that relies on the rest of the sentence for meaning. The following list provides some examples of subordinating conjunctions. after although as because before even though if since though when while until unless whereas Independent and Dependent Clauses Independent clause: When I go to the movies, I usually buy popcorn. -
" CONTENTS of VOLUME XXXVIII—1964 >•
" CONTENTS OF VOLUME XXXVIII—1964 >• it ARTICLES: pAGE Anderson, James F., Was St. Thomas a Philosopher? 435 Boh, Ivan, An Examination of Some Proofs in Burleigh's Propo- sitional Logic 44 Brady, Jules M., St. Augustine's Theory of Seminal Reasons.. 141 Burns, J. Patout, Action in Suarez 453 Burrell, David B., Kant and Philosophical Knowledge 189 Chroust, Anton-Hermann, Some Reflections on the Origin of the Term " Philosopher " 423 Collins, James, The Work of Rudolf Allers 28 Fairbanks, Matthew J., C. S. Peirce and Logical Atomism 178 Grisez, Germain G., Sketch of a Future Metaphysics 310 O'Brien, Andrew J., Duns Scotus' Teaching on the Distinction between Essence and Existence 61 McWilliams, James A., The Concept as Villain 445 Pax, Clyde V., Philosophical Reflection: Gabriel Marcel 159 Smith, John E., The Relation of Thought and Being: Some Lessons from Hegel's Encyclopedia 22 Stokes, Walter E., Whitehead's Challenge to Theistic Realism. ... 1 Tallon, Andrew, Personal Immortality in Averroes' Tahafut Al- Tahafut 341 REVIEW ARTICLE : O'Neil, Charles J., Another Notable Study of Aristotle's Meta physics 509 ill iv Contents of Volume XXXVIII DEPARTMENTS : PAGE Book Brevities 551 Books Received 133, 274, 415, 557 Chronicles: The Husserl Archives and the Edition of Husserl's Works 473 International Congresses of Philosophy in Mexico City.. 278 Progress Report: Philosophy in the NCE 214 The Secretary's Chronicle 80, 218, 358, 483 BOOK REVIEWS: Anderson, James P., Natural Theology: The Metaphysics of God 265 Austin, J. L., Philosophical Papers 125 Capek, Milec, The Philosophical Impact of Contemporary Physics 248 Caturelli, Alberto, La fdosofiu en Argentina actual 403 Crocker, Lester G., Nature and Cidture: Ethical Thought in the French Englightement 539 Dufrenne, Mikel, Language and Philosophy, transl. -
The Meaning of Language
01:615:201 Introduction to Linguistic Theory Adam Szczegielniak The Meaning of Language Copyright in part: Cengage learning The Meaning of Language • When you know a language you know: • When a word is meaningful or meaningless, when a word has two meanings, when two words have the same meaning, and what words refer to (in the real world or imagination) • When a sentence is meaningful or meaningless, when a sentence has two meanings, when two sentences have the same meaning, and whether a sentence is true or false (the truth conditions of the sentence) • Semantics is the study of the meaning of morphemes, words, phrases, and sentences – Lexical semantics: the meaning of words and the relationships among words – Phrasal or sentential semantics: the meaning of syntactic units larger than one word Truth • Compositional semantics: formulating semantic rules that build the meaning of a sentence based on the meaning of the words and how they combine – Also known as truth-conditional semantics because the speaker’ s knowledge of truth conditions is central Truth • If you know the meaning of a sentence, you can determine under what conditions it is true or false – You don’ t need to know whether or not a sentence is true or false to understand it, so knowing the meaning of a sentence means knowing under what circumstances it would be true or false • Most sentences are true or false depending on the situation – But some sentences are always true (tautologies) – And some are always false (contradictions) Entailment and Related Notions • Entailment: one sentence entails another if whenever the first sentence is true the second one must be true also Jack swims beautifully. -
Gottlob Frege Patricia A
Gottlob Frege Patricia A. Blanchette This is the penultimate version of the essay whose final version appears in the Oxford Handbook of Nineteenth-Century German Philosophy, M. Forster and K. Gjesdal (eds), Oxford University Press 2015, pp 207-227 Abstract Gottlob Frege (1848-1925) made significant contributions to both pure mathematics and philosophy. His most important technical contribution, of both mathematical and philosophical significance, is the introduction of a formal system of quantified logic. His work of a more purely- philosophical kind includes the articulation and persuasive defense of anti-psychologism in mathematics and logic, the rigorous pursuit of the thesis that arithmetic is reducible to logic, and the introduction of the distinction between sense and reference in the philosophy of language. Frege’s work has gone on to influence contemporary work across a broad spectrum, including the philosophy of mathematics and logic, the philosophy of language, and the philosophy of mind. This essay describes the historical development of Frege’s central views, and the connections between those views. Introduction Friedrich Ludwig Gottlob Frege was born on November 8, 1848 in the Hanseatic town of Wismar. He was educated in mathematics at the University of Jena and at the University of Göttingen, from which latter he received his doctorate in 1873. He defended his Habilitation the next year in Jena, and took up a position immediately at the University of Jena. Here he spent his entire academic career, lecturing in mathematics and logic, retiring in 1918. His death came on July 26, 1925 in the nearby town of Bad Kleinen.1 Frege is best known for three significant contributions to philosophy. -
Against Logical Form
Against logical form Zolta´n Gendler Szabo´ Conceptions of logical form are stranded between extremes. On one side are those who think the logical form of a sentence has little to do with logic; on the other, those who think it has little to do with the sentence. Most of us would prefer a conception that strikes a balance: logical form that is an objective feature of a sentence and captures its logical character. I will argue that we cannot get what we want. What are these extreme conceptions? In linguistics, logical form is typically con- ceived of as a level of representation where ambiguities have been resolved. According to one highly developed view—Chomsky’s minimalism—logical form is one of the outputs of the derivation of a sentence. The derivation begins with a set of lexical items and after initial mergers it splits into two: on one branch phonological operations are applied without semantic effect; on the other are semantic operations without phono- logical realization. At the end of the first branch is phonological form, the input to the articulatory–perceptual system; and at the end of the second is logical form, the input to the conceptual–intentional system.1 Thus conceived, logical form encompasses all and only information required for interpretation. But semantic and logical information do not fully overlap. The connectives “and” and “but” are surely not synonyms, but the difference in meaning probably does not concern logic. On the other hand, it is of utmost logical importance whether “finitely many” or “equinumerous” are logical constants even though it is hard to see how this information could be essential for their interpretation. -
Truth-Bearers and Truth Value*
Truth-Bearers and Truth Value* I. Introduction The purpose of this document is to explain the following concepts and the relationships between them: statements, propositions, and truth value. In what follows each of these will be discussed in turn. II. Language and Truth-Bearers A. Statements 1. Introduction For present purposes, we will define the term “statement” as follows. Statement: A meaningful declarative sentence.1 It is useful to make sure that the definition of “statement” is clearly understood. 2. Sentences in General To begin with, a statement is a kind of sentence. Obviously, not every string of words is a sentence. Consider: “John store.” Here we have two nouns with a period after them—there is no verb. Grammatically, this is not a sentence—it is just a collection of words with a dot after them. Consider: “If I went to the store.” This isn’t a sentence either. “I went to the store.” is a sentence. However, using the word “if” transforms this string of words into a mere clause that requires another clause to complete it. For example, the following is a sentence: “If I went to the store, I would buy milk.” This issue is not merely one of conforming to arbitrary rules. Remember, a grammatically correct sentence expresses a complete thought.2 The construction “If I went to the store.” does not do this. One wants to By Dr. Robert Tierney. This document is being used by Dr. Tierney for teaching purposes and is not intended for use or publication in any other manner. 1 More precisely, a statement is a meaningful declarative sentence-type. -
Ludwig.Wittgenstein.-.Philosophical.Investigations.Pdf
PHILOSOPHICAL INVESTIGATIONS By LUDWIG WITTGENSTEIN Translated by G. E. M. ANSCOMBE BASIL BLACKWELL TRANSLATOR'S NOTE Copyright © Basil Blackwell Ltd 1958 MY acknowledgments are due to the following, who either checked First published 1953 Second edition 1958 the translation or allowed me to consult them about German and Reprint of English text alone 1963 Austrian usage or read the translation through and helped me to Third edition of English and German text with index 1967 improve the English: Mr. R. Rhees, Professor G. H. von Wright, Reprint of English text with index 1968, 1972, 1974, 1976, 1978, Mr. P. Geach, Mr. G. Kreisel, Miss L. Labowsky, Mr. D. Paul, Miss I. 1981, 1986 Murdoch. Basil Blackwell Ltd 108 Cowley Road, Oxford, OX4 1JF, UK All rights reserved. Except for the quotation of short passages for the purposes of criticism and review, no part of this publication may be NOTE TO SECOND EDITION reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or THE text has been revised for the new edition. A large number of otherwise, without the prior permission of the publisher. small changes have been made in the English text. The following passages have been significantly altered: Except in the United States of America, this book is sold to the In Part I: §§ 108, 109, 116, 189, 193, 251, 284, 352, 360, 393,418, condition that it shall not, by way of trade or otherwise, be lent, re- 426, 442, 456, 493, 520, 556, 582, 591, 644, 690, 692. -
The Theory of Descriptions 1. Bertrand Russell (1872-1970): Mathematician, Logician, and Philosopher
Louis deRosset { Spring 2019 Russell: The Theory of Descriptions 1. Bertrand Russell (1872-1970): mathematician, logician, and philosopher. He's one of the founders of analytic philosophy. \On Denoting" is a founding document of analytic philosophy. It is a paradigm of philosophical analysis. An analysis of a concept/phenomenon c: a recipe for eliminating c-vocabulary from our theories which still captures all of the facts the c-vocabulary targets. FOR EXAMPLE: \The Name View Analysis of Identity." 2. Russell's target: Denoting Phrases By a \denoting phrase" I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the centre of mass of the Solar System at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. (479) Includes: • universals: \all F 's" (\each"/\every") • existentials: \some F " (\at least one") • indefinite descriptions: \an F " • definite descriptions: \the F " Later additions: • negative existentials: \no F 's" (480) • Genitives: \my F " (\your"/\their"/\Joe's"/etc.) (484) • Empty Proper Names: \Apollo", \Hamlet", etc. (491) Russell proposes to analyze denoting phrases. 3. Why Analyze Denoting Phrases? Russell's Project: The distinction between acquaintance and knowledge about is the distinction between the things we have presentation of, and the things we only reach by means of denoting phrases. [. ] In perception we have acquaintance with the objects of perception, and in thought we have acquaintance with objects of a more abstract logical character; but we do not necessarily have acquaintance with the objects denoted by phrases composed of words with whose meanings we are ac- quainted. -
PHI 565-Russell
Philosophy 565: Philosophy of Language Prof. Clare Batty Russell, “On Denoting” 1. More Philosophical Jargon definite description: a singular noun phrase which applies to exactly one person, often beginning with the definite article: e.g., ‘the funniest woman in Canada’, the present King of France’. According to Russell, a phrase is denoting solely “in virtue of its form”. This is to say, the phrase needn’t actually denote in order to be a denoting phrase. Law of the Excluded Middle: By the law of the excluded middle, either ‘A is B’ or ‘A is not B’ must be true. 2. Frege and Russell We now know that Frege is committed to: (F3) Ordinary proper names and definite descriptions are singular terms. (F4) Ordinary proper names and definite descriptions all have sense (and perhaps reference). (ST1) The business of a singular term is to refer to an object. (ST2) A sentence containing a singular term has no truth-value if there is no object corresponding to that singular term. Russell’s focus is on definite descriptions. Not under discussion at this point: proper names (e.g. ‘Clare’, ‘Kentucky’, etc.) Russell denies (F3) and, as a result (he claims), (F4). Like Frege, Russell thinks that his alternative view can deal with certain problems. “The evidence for [my] theory is derived from difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur." We have seen some of these before: (P1) Frege’s Puzzle About Identity (P2) Substitutivity (P3) Apparent Reference to Non-Existents And some more: (P4) Law of the Excluded Middle (LEM) By the LEM, either (S1) ‘The King of France is bald’ or (S2) ‘The King of France is not bald’ had better be true. -
Notes on Mathematical Logic David W. Kueker
Notes on Mathematical Logic David W. Kueker University of Maryland, College Park E-mail address: [email protected] URL: http://www-users.math.umd.edu/~dwk/ Contents Chapter 0. Introduction: What Is Logic? 1 Part 1. Elementary Logic 5 Chapter 1. Sentential Logic 7 0. Introduction 7 1. Sentences of Sentential Logic 8 2. Truth Assignments 11 3. Logical Consequence 13 4. Compactness 17 5. Formal Deductions 19 6. Exercises 20 20 Chapter 2. First-Order Logic 23 0. Introduction 23 1. Formulas of First Order Logic 24 2. Structures for First Order Logic 28 3. Logical Consequence and Validity 33 4. Formal Deductions 37 5. Theories and Their Models 42 6. Exercises 46 46 Chapter 3. The Completeness Theorem 49 0. Introduction 49 1. Henkin Sets and Their Models 49 2. Constructing Henkin Sets 52 3. Consequences of the Completeness Theorem 54 4. Completeness Categoricity, Quantifier Elimination 57 5. Exercises 58 58 Part 2. Model Theory 59 Chapter 4. Some Methods in Model Theory 61 0. Introduction 61 1. Realizing and Omitting Types 61 2. Elementary Extensions and Chains 66 3. The Back-and-Forth Method 69 i ii CONTENTS 4. Exercises 71 71 Chapter 5. Countable Models of Complete Theories 73 0. Introduction 73 1. Prime Models 73 2. Universal and Saturated Models 75 3. Theories with Just Finitely Many Countable Models 77 4. Exercises 79 79 Chapter 6. Further Topics in Model Theory 81 0. Introduction 81 1. Interpolation and Definability 81 2. Saturated Models 84 3. Skolem Functions and Indescernables 87 4. Some Applications 91 5.