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
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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 t roduc ti on Thomas Ede Zimmermann, Wolfgang Sternefeld Thomas Ede Zimmermann, 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 they have never come across before. Extensive English examples provide Introduction ample illustration.
and o Seman ti tag">c s ff Highly accessible introduction to elementary subfield of linguistics to Semantics Phrases ff Must-have for all first year students of linguistics world-wide The Essential Student’s Guide to Compositi- ff Requires no previous knowledge of formal logic on of Meaning ff Contains exercises plus answer key perfect for self-study and classroom use
ff Rich selection of English examples and phenomena Set theory ff 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
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Cases and Proposi- 4 / 44 tions
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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
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Cases and Proposi- 5 / 44 tions
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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
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Cases and Proposi- 6 / 44 tions
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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
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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
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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
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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
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Cases and Proposi- 10 / 44 tions
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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
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Cases and Proposi- 11 / 44 tions
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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
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Cases and Proposi- 12 / 44 tions
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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
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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
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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
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From Proposi- tions to Intensions Extensions for Words and Phrases
[What do these expressions refer to?]
Frege’s Principle A Farewell common (count) nouns like table, car, ... to Psychol- ogism
Extensions for Words as well as some (’intersective‘) and Phrases
Set theory adjectives like blond, rectangular, ... in 2 minutes (and without tears) do not refer to single individuals but show multiple reference. Extensions for Words and Phrases
Truth Values as Extensions of The set of all its referents forms the extension of such a multiply Sentences extensional expression. Intensions
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From Proposi- tions to Intensions Set theory in 2 minutes (and without tears)
A set is an abstract collection of (possibly, but not necessarily concrete) Frege’s objects, their elements. Principle
A Farewell Elementhood is a relational concept: an object x is or is not an element to Psychol- of a given set y. ogism Notation: x ∈ y vs. x ∈/ y Extensions for Words and A set A is a subset of a (not necessarily distinct) set B iff [= if and only Phrases if] Set theory every element of A is an element of B and vice versa. in 2 minutes (and Notation: A ⊆ B without tears) The identity criterion for sets A and B is sharing the same elements Extensions for Words (‘extensionality’): and A = B iff A ⊆ B and B ⊆ A Phrases
Truth Sets are defined by set abstraction: Values as Extensions {x : ... x ... } is that set whose elements are of Sentences precisely those objects x such that the condition ... x ... holds.
Intensions Notation: ∅ is {x: x 6= x}
Cases and Proposi- 17 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases
[What do these expressions refer to?]
Frege’s Principle A Farewell common (count) nouns like table, car, ... to Psychol- ogism
Extensions for Words as well as some (’intersective‘) and Phrases
Set theory adjectives like blond, rectangular, ... in 2 minutes (and without tears) do not refer to single individuals but show multiple reference. Extensions for Words and Phrases
Truth Values as Extensions of The set of all its referents forms the extension of such a multiply Sentences extensional expression. Intensions
Cases and Proposi- 18 / 44 tions
Logical Space
From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle A Farewell NB1: The extension of to Psychol- ogism
Extensions for Words the current German chancellor and Phrases
Set theory is Angela Merkel in 2 minutes (and without but this will change . . . tears)
Extensions for Words In four years from now the extension of the current German chancellor is and going to be another person and it used to be 20 years ago . . . Phrases
Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell to Psychol- ogism
Extensions for Words SO: and Phrases
Set theory The extension of the current German chancellor is changing over time in 2 minutes (and . . . and so are extensions in general. without tears)
Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell to Psychol- ogism
Extensions NB2: The extension of for Words and Phrases current German chancellor Set theory in 2 minutes (and without is the set of all current German chancellors – i.e., a set with one member. tears)
Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell to Psychol- ogism
Extensions However, the extension of for Words and Phrases the current German chancellor Set theory in 2 minutes (and without is the current German chancellor, i.e., a person. tears)
Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 22 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle A Farewell SO: to Psychol- ogism Extensions current German chancellor (whose extension is {A.M.}), for Words and Phrases
Set theory and: in 2 minutes (and without tears) the current German chancellor
Extensions for Words 1 and do not have the same extension! Phrases
Truth Values as Extensions of Sentences
Intensions 1 Cases and on standard set-theoretic assumptions Proposi- 23 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell to Psychol- ogism
Extensions NB3: The (current) extension of for Words and Phrases current French king Set theory in 2 minutes (and without is the set of all current French kings – i.e., the empty set. tears)
Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 24 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell to Psychol- ogism However, the extension of
Extensions for Words and the current king of France Phrases
Set theory in 2 minutes would have to be the current French king (and without tears) ... but there is no such (existing) person! Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 25 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Principle
A Farewell SO: unlike to Psychol- ogism
Extensions current king of France (whose extension is ∅), for Words and Phrases
Set theory the current king of France in 2 minutes (and without tears) appears to have no extension.
Extensions for Words We will henceforth ignore such void descriptions. (Read chapter 9 for more and Phrases on this ...) Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s Not all nouns are count nouns — some are: Principle
A Farewell to Psychol- ogism mass nouns: milk, information,... Extensions for Words Hallmark: no plural (without meaning shift) and Phrases
Set theory relational nouns: brother, copy,... in 2 minutes (and Hallmark: possessives receive “special” meaning without tears)
Extensions functional nouns: father, surface,... for Words and Hallmark: relational plus inherent uniqueness Phrases
Truth Values as Extensions of Mass nouns will be ignored in the following. Sentences
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From Proposi- tions to Intensions Extensions for Words and Phrases
Frege’s The extensions of relational and functional nouns can be identified with sets Principle of (ordered pairs) of individuals. A Farewell to Psychol- ogism
Extensions Relational examples: for Words and Phrases (5)
Set theory in 2 minutes brother: (and without tears) {hEthan, Joeli, hJoel, Ethani, hDeborah,Joeli, hDeborah, Ethani,... } Extensions for Words and Phrases arm:
Truth Values as Extensions {hLudwig, Ludwig’s right armi, hLudwig, Ludwig’s left armi, hPaul, Paul’s of left armi,... } Sentences
Intensions Cases and idea: Proposi- 28 / 44 tions 2 Logical {hAlbert, E = mc i, hRené, COGITO i, hBertie,R ∈ R ⇔ R ∈/ R i,... } Space
From Proposi- tions to Intensions Extensions for Words and Phrases
Functional examples:
Frege’s (6) Principle A Farewell birthplace: to Psychol- ogism
Extensions {hAdam, Paradisei, hEve, Paradisei, hJohn, Liverpooli, hYoko, Tokyoi, for Words and ... } Phrases
Set theory in 2 minutes mother: (and without tears) {hCain, Evei, hAbel, Evei, hStella, Lindai, hSean, Yokoi,... } Extensions for Words and Phrases surface: Truth Values as Extensions {hMars, Mars’s surfacei, hEarth, Earth’s surfacei,... } of Sentences Intensions In addition to being relational, the extensions f of functional nouns in (6) are Cases and functions, i.e., they satisfy a uniqueness condition: Proposi- 29 / 44 tions
Logical (7) If both ha, v1 i ∈ f and ha, v2 i ∈ f , then v1 = v2. Space
From Proposi- tions to Intensions The extension of a functional noun is a function mapping individuals to individuals. Extensions for Words and Phrases: Taking stock
Frege’s The extension of a referential expression is an individual. Principle
A Farewell to Psychol- ogism
Extensions for Words The extension of a count noun (or intersective adjective) is a set of and Phrases individuals.
Set theory in 2 minutes (and without tears)
Extensions The extension of a relational noun is a binary relation among [= set of for Words and ordered pairs of] individuals. Phrases
Truth Values as Extensions of Sentences The extension of a functional noun is a function mapping individuals to Intensions individuals. Cases and Proposi- 30 / 44 tions
Logical Space
From Proposi- tions to Intensions Extensions for Words and Phrases: verbal constituents
Frege’s Principle
A Farewell Extensions of verbs and verb phrases to Psychol- ogism (8) Extensions for Words and sleep: the set of sleepers Phrases
Set theory in 2 minutes (and without kiss: a relation between kissers and kissees, i.e., the set of pairs hx, y i such tears) that x kisses y Extensions for Words and Phrases donate: a three-place relation, a set of triples Truth Values as Extensions of Sentences
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Cases and Proposi- 31 / 44 tions
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From Proposi- tions to Intensions Extensions for Words and Phrases: verbal constituents
Frege’s Principle
A Farewell to Psychol- (9) ogism
Extensions for Words type of expression type of extension example extension and intransitive verb set of individuals sleep the set of sleepers Phrases transitive verb set of pairs eat the set of pairs Set theory in 2 minutes of individuals heater, eateni (and ditransitive verb set of triples donate the set of triples without tears) of individuals hdonator, recipient, Extensions for Words donationi and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 32 / 44 tions
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From Proposi- tions to Intensions Truth Values as Extensions of Sentences
Frege’s Principle
A Farewell to Psychol- ogism
Extensions for Words and (10) Parallelism between valency and type of extension: Phrases The extension of an n-place verb is always a set of n-tuples. Set theory in 2 minutes (and without tears)
Extensions for Words and Phrases
Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Truth Values as Extensions of Sentences
(11) The Pope shows the President the Vatican Palace
Frege’s Principle A Farewell (12) verb or verb phrase valency extension to Psychol- ogism shows 3 the triples ha, b, c i Extensions where a shows b to c for Words and shows 2 the pairs ha, b i Phrases the President where a shows b to the President Set theory in 2 minutes shows 1 the 1-tuples hai (and without the President where a shows the Vatican Palace tears) the Vatican Palace to the President Extensions for Words and (13) sentence valency extension Phrases The Pope shows the 0 the 0-tuples h i Truth Values as President the where the Pope shows the Extensions of Vatican Palace Vatican Palace to the president Sentences
Intensions
Cases and Proposi- 34 / 44 tions
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From Proposi- tions to Intensions Truth Values as Extensions of Sentences
(14) sentence valency extension The Pope shows the 0 the 0-tuples h i Frege’s President the where the Pope shows the Principle Vatican Palace Vatican Palace to the president A Farewell to Psychol- ogism
Extensions for Words Standard Assumption 1 and Phrases Set theory There is precisely one zero-tuple, viz., the empty set ∅. in 2 minutes (and without tears) Two cases: Extensions for Words and IF the Pope does NOT show the Vatican Palace to the president, then Phrases NO zero-tuple satisfies the condition that the Pope shows the Vatican Truth Values as Palace to the president Extensions of and so the extension in (14) is empty, i.e.: ∅. Sentences
Intensions IF the Pope DOES show the Vatican Palace to the president, then ANY Cases and Proposi- zero-tuple satisfies the condition that the Pope shows the Vatican 35 / 44 tions Palace to the president Logical Space and so the extension in (14) is the set of all 0-tuples, i.e.: {∅}.
From Proposi- tions to Intensions Truth Values as Extensions of Sentences
Frege’s Two cases: Principle
A Farewell to Psychol- If the Pope does not show the Vatican Palace to the president, then the ogism extension in (14) is: ∅. Extensions for Words and Phrases If the Pope does show the Vatican Palace to the president, then the Set theory extension in (14) is: {∅}. in 2 minutes (and without tears) (Wildly) generalizing: Extensions for Words and If a (declarative) sentence is false, its extension is: ∅. Phrases
Truth If a (declarative) sentence is true, its extension is: {∅}. Values as Extensions of Sentences
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From Proposi- tions to Intensions Truth Values as Extensions of Sentences
(Wildly) generalizing: Frege’s Principle
A Farewell If a (declarative) sentence is false, its extension is: ∅. to Psychol- ogism If a (declarative) sentence is true, its extension is: {∅}. Extensions for Words and Phrases
Set theory in 2 minutes Standard Assumption 2 (and without tears) ∅ = 0, {∅} = 1. Extensions for Words and Phrases
Truth Values as (15) Frege’s Generalization Extensions The extension of a sentence S is its truth value, i.e., 1 if S is true and of Sentences 0 if S is false. Intensions
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From Proposi- tions to Intensions Intensions
REMINDER Frege’s Principle
A Farewell to Psychol- The meaning of any expressions has (at least) two components, viz. its: ogism
Extensions for Words intension ≈ its contribution to the content of expressions in which it and Phrases occurs
Set theory in 2 minutes extension: ≈ its contribution to the reference of expressions in which it (and occurs without tears) . . . and maybe more (but not in this course) Extensions for Words and Phrases In the simplest cases:
Truth Values as Extensions Intension is content. of Sentences Extension is reference.
Intensions
Cases and Proposi- 38 / 44 tions
Logical Space
From Proposi- tions to Intensions Cases and Propositions
(3) Four fair coins are tossed (4) At least one of the 4 tossed coins lands heads up Frege’s (5) At least one of the 4 tossed coins lands heads down Principle (6) Exactly 2 of the 4 tossed coins land heads up A Farewell to Psychol- (7) Exactly 2 of the 4 tossed coins land heads down 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
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Cases and Proposi- 39 / 44 tions
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From Proposi- tions to Intensions Cases and Propositions
Frege’s Principle
A Farewell to Psychol- (3) Four fair coins are tossed ogism (4) At least one of the 4 tossed coins lands heads up Extensions for Words (5) At least one of the 4 tossed coins lands heads down and Phrases (6) Exactly 2 of the 4 tossed coins land heads up Set theory (7) Exactly 2 of the 4 tossed coins land heads down in 2 minutes (and without Definition [to be revised] tears) The proposition expressed by a sentence is the set of possible cases of Extensions for Words which that sentence is true. and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 40 / 44 tions
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From Proposi- tions to Intensions Cases and Propositions
Frege’s Principle
A Farewell to Psychol- ogism (16) possible cases c1 c2 c3 c4
Extensions 1 1 1 1 1 for Words and 2 1 1 1 0 Phrases 3 1 1 0 1 Set theory ...... in 2 minutes (and 14 0 0 1 0 without tears) 15 0 0 0 1 Extensions 16 0 0 0 0 for Words and Phrases
Truth Values as Extensions of Sentences
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From Proposi- tions to Intensions Logical Space
Frege’s Principle
A Farewell to Psychol- (17) a. Four coins were tossed when John coughed ogism b. Four coins were tossed when John coughed and it started to rain Extensions for Words c.... and Phrases (18) [Revised] Definition Set theory in 2 minutes a. The proposition ||S|| expressed by a sentence S is the set of (and without possible worlds of which that sentence is true. tears)
Extensions for Words A sentence S is true of a possible world w if and only if w ∈ ||S||. and Phrases
Truth Values as Extensions of Sentences
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Cases and Proposi- 42 / 44 tions
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From Proposi- tions to Intensions From Propositions to Intensions
Frege’s Principle world truth value A Farewell to Psychol- w1 1 ogism w2 0 Extensions for Words (19) w3 1 and ...... Phrases
Set theory wn 0 in 2 minutes ...... (and without tears)
Extensions for Words (20) Definition and The intension of an expression α is that function f such that for Phrases every possible world w, f (w) = α’s extension at w. Truth Values as Extensions of Sentences
Intensions
Cases and Proposi- 43 / 44 tions
Logical Space
From Proposi- tions to Intensions Frege’s Principle If you want to know more about this, read . . .
A Farewell to Psychol- ogism Textbook
In t roduc ti on Thomas Ede Zimmermann, Wolfgang Sternefeld Thomas Ede Zimmermann, Extensions This textbook introduces undergraduate students of language and linguis- 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 they have never come across before. Extensive English examples provide Introduction and ample illustration. o Seman ti c s ff Highly accessible introduction to elementary subfield of linguistics to Semantics Phrases ff Must-have for all first year students of linguistics world-wide The Essential Student’s Guide to Compositi- ff Requires no previous knowledge of formal logic on of Meaning ff Contains exercises plus answer key perfect for self-study and classroom use
ff Rich selection of English examples and phenomena
Set theory ff Exceptional in its extensive treatment of compositional semantics in 2 minutes (and without tears)
Extensions for Words www.degruyter.com 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- 44 / 44 tions
Logical Space
From Proposi- tions to Intensions