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The Theory of Extension and Intension Extensions for Words and Phrases

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The Theory of Extension and Intension Extensions for Words and Phrases Frege’s Principle A Farewell Semantics: to Psychol- ogism The Theory of Extension and Intension Extensions for Words and Phrases Set theory in 2 minutes Thomas Ede Zimmermann, Goethe-Universität Frankfurt (and without tears) Extensions Guest Lecture in Greg Scontras’s Psychology of Language for Words UCI, February 2018 and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 1 / 44 tions Logical Space From Proposi- tions to Intensions Frege’s Principle A Farewell to Psychol- ogism Plan: Extensions for Words and Phrases Frege’s Principle Set theory A Farewell to Psychologism in 2 minutes (and Extensions and Truth Values without tears) Propositions and Intensions Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 2 / 44 tions Logical Space From Proposi- tions to Intensions Frege’s Principle . based on material from A Farewell to Psychol- ogism TEXTBOOK IN Sternefeld Thomas Ede Zimmermann, Wolfgang T Thomas Ede Zimmermann, RODUC This textbook introduces undergraduate students of language and linguis- Extensions tics to the basic ideas, insights, and techniques of contemporary semantic Wolfgang Sternefeld theory. The book starts with everyday observations about word meaning and use and then gradually zooms in on the question of how speakers for Words manage to meaningfully communicate with phrases, sentences, and texts TI they have never come across before. Extensive English examples provide ON INTRODUCTION ample illustration. T and O SEMAN f Highly accessible introduction to elementary subfield of linguistics TO SEMANTICS Phrases f Must-have for all first year students of linguistics world-wide THE EssENTIAL STUDENT’S GUIDE TO COMPOSITI- f Requires no previous knowledge of formal logic ON OF MEANING f Contains exercises plus answer key perfect for self-study and classroom TI use C f Rich selection of English examples and phenomena S Set theory f Exceptional in its extensive treatment of compositional semantics in 2 minutes (and without tears) Extensions www.degruyter.com for Words ISBN 978-3-11-030800-6 and Phrases Truth Values as T. E. Zimmermann, W. Sternefeld: Introduction to Semantics. Berlin/New York 2013 Extensions of Sentences Intensions Cases and Proposi- 3 / 44 tions Logical Space From Proposi- tions to Intensions Frege’s Principle Frege’s Principle A Farewell to Psychol- Two arrangements of unambiguous words can lead to different meanings: ogism Extensions (1) a. John’s son introduced Mary’s daughter to Bill and Jane for Words and b. Jane introduced John’s daughter and Mary’s son to Bill Phrases Set theory in 2 minutes . even if the word order is the same (and without tears) (2) John’s son introduced Mary’s daughter to Bill and Jane or Harry Extensions for Words and Phrases ) Syntactic structure has an effect on interpretation Truth Values as Extensions of Sentences Intensions Cases and Proposi- 4 / 44 tions Logical Space From Proposi- tions to Intensions Frege’s Principle Frege’s Principle A Farewell to Psychol- . but how does syntactic structure affect interpretation? ogism Extensions (3) Frege’s Principle of Compositionality for Words and The meaning of a composite expression is a function of the meanings Phrases of its immediate constituents and the way these constituents are put Set theory in 2 minutes together. (and without tears) Extensions for Words ... Yes, but what (kind of objects) are all these meanings? and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 5 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism Frege’s Principle A Farewell to Psychol- ogism Extensions When learning a new word, we learn how to combine a certain for Words pronunciation, its phonetics and phonology, with its meaning. Thereby, a and Phrases previously meaningless sequence of sounds becomes vivid, we associate Set theory with it an idea. In this case, one might be tempted to say that the meaning of in 2 minutes (and an expression is the idea or conception a speaker associates with its without tears) utterance. Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 6 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism Fregean and Wittgensteinian objections . Frege’s Principle A Farewell to Psychol- ogism Extensions for Words and Phrases Set theory in 2 minutes (and without tears) Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 7 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism ... against such a “psychologistic” notion of meaning: Frege’s Principle Subjectivity: Different speakers may associate different things with a A Farewell to Psychol- single word at different occasions: such “meanings,” however, cannot ogism be objective, but will rather be influenced by personal experience, and Extensions for Words one might wonder how these “subjective meanings” serve and communication between different subjects. Phrases Set theory Limited Coverage: We can have mental images of nouns like horse or in 2 minutes (and table, but what on earth could be associated with words like and, most, without tears) only, then, of, if,...? Extensions Irrelevance: Due to different personal experiences, speakers can have for Words and all sorts of associations without this having any influence on the Phrases meaning of an expression. Truth Values as Privacy: The associations of an individual person are in principle Extensions of inaccessible to other speakers. So, again, how can they be used for Sentences interpersonal communication? Intensions Cases and Proposi- 8 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism Frege’s Principle On the other hand ... A Farewell to Psychol- ogism MEANING SERVES COMMUNICATION ... and so: Extensions for Words and Phrases Set theory in 2 minutes (and MEANINGS ought to be identified with without tears) Extensions for Words COMMUNICATIVE FUNCTIONS of expressions and Phrases Truth Values as ... as in the tradition of ... Extensions of Sentences Intensions Cases and Proposi- 9 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism LOGICAL SEMANTICS Frege’s Principle A Farewell to Psychol- ogism Extensions for Words and Phrases Set theory in 2 minutes (and without tears) Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 10 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism Frege’s Principle ... or (more recently) A Farewell to Psychol- FORMAL SEMANTICS ogism Extensions for Words and Phrases Set theory in 2 minutes (and without tears) Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 11 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism Frege’s Principle A Farewell to Psychol- ogism LOGICAL [or FORMAL] SEMANTICS Extensions for Words and Phrases Meanings ≈ (certain) communicative functions of expressions, viz.: Set theory in 2 minutes (and without Content: Which information is expressed ... tears) Reference: ... and what this information is about Extensions for Words and Phrases Truth Values as Extensions of Sentences Intensions Cases and Proposi- 12 / 44 tions Logical Space From Proposi- tions to Intensions A Farewell to Psychologism LOGICAL [or FORMAL] SEMANTICS Frege’s Principle The meaning of any expressions has (at least) two components, viz. its: A Farewell to Psychol- ogism intension ≈ its contribution to the content of expressions in which it Extensions for Words occurs and Phrases extension: ≈ its contribution to the reference of expressions in which it Set theory occurs in 2 minutes (and without . and maybe more (but not in this course) tears) Extensions for Words In the simplest cases: and Phrases Truth Intension is content. Values as Extensions Extension is reference. of Sentences Intensions Cases and We will start with the latter ... Proposi- 13 / 44 tions Logical Space From Proposi- tions to Intensions Extensions for Words and Phrases Frege’s Principle Some examples: A Farewell to Psychol- ogism (4)— Irvine, Noam Chomsky (proper names) Extensions for Words — the president of the US, the capital of Germany (definite and Phrases descriptions) Set theory — table, horse, book (nouns) in 2 minutes (and — bald, red, stupid, alleged (adjectives) without tears) — nobody, nothing, no dog (negative quantifiers) Extensions for Words and Phrases What do these expressions refer to? Truth Values as What is their contribution to reference? Extensions of Sentences Intensions Cases and Proposi- 14 / 44 tions Logical Space From Proposi- tions to Intensions Extensions for Words and Phrases [What do these expressions refer to?] Frege’s Principle Referential expressions like A Farewell to Psychol- ogism proper names (like Vienna, Roman Polanski, ...) Extensions for Words definite descriptions (like the capital of Austria, the director of and Phrases ROSEMARY’S BABY...) Set theory in 2 minutes (some uses of) personal pronouns (like she) (and without ... tears) Extensions for Words (are used to) refer to persons, places, or other individuals. and Phrases Truth Values as Extensions of Sentences The referent of a referential expression also forms its extension. Intensions Cases and Proposi- 15 / 44 tions Logical Space From Proposi- tions to Intensions Extensions for Words and Phrases [What do these
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