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Creteling 2017 Architecture of the grammar and Winfried Lechner the syntax-semantics interface INTRO: INTENSIONALITY Topics & Goals " Basic facts about intensionality (referential opacity, propositional attitudes) " Modeling intensionality " Review of some formal techniques (λ-calculus, composition interpretation) " Initial evidence for object language worlds/situation variables 1. INTENSIONALITY The intensional contexts that will be of interest are environments that violate Leibniz’ Law (aka ‘Principle of Substitution salva veritate’ or ‘Principle of Indiscernibility of Identicals’): (1) Leibniz’ Law [Gottfried Leibniz, quote from around 1686] Substitution of coextensional expressions preserves truth. (Eadem vel Coincidentia sunt quae sibi ubique substitutui possunt salva veritate) Extensionally, (2)a and (2)b are synonymous. Still, they do not mean the same: (2)a is a tautology while (2)b is cognitively significant. (2) a. The Morning Star is the Morning Star. b. The Morning Star is the Evening Star. I. Intensional operators. Embedding under intensional operators exposes truth conditional difference. Substituting co-extensive terms under modals affects meaning: (3) a. It is possible that the Morning Star is not the Evening Star. (true) b. / It is possible that the Morning Star is not the Morning Star. (false) (4) Opaque context For any syntactic environment ε and ε’ and expressions α and β such that ε contains α and ε’ is just like ε except that α has been substituted by β: a. ε is opaque iff ε =/ ε’ b. ε is transparent otherwise II. Intensional Transitive Verbs. Object position of ITV-verbs (want, need, seek, desire, lack, admire, own, offer, buy, paint, imagine,...) is opaque. Suppose the speaker knows that Clark Kent is Superman. (5) a. Lois Lane killed Clark Kent. b. Lois Lane killed Superman. (6) a. Lois Lane is looking for Clark Kent. b. / Lois Lane is looking for Superman. III. Propositional Attitudes. Propositional attitudes express relations between sentient individuals and propositions. Embedding under propositional attitude predicates leads to opacity. (7) Supposition: Dimitris is a Russian athlete who won a stage of the Tour the France. John has been watching the race, but mistakenly believes that Dimitris is Greek because all Dimitrides he knows are Greek. No other Russian took part in the race. (8) a. Dimitris won the race. b. The Russian athlete won the race. (9) a. John believes that Dimitris won the race. b. / John believes that the Russian athlete won the race. (10) Supposition: All and only those animals that have a heart (cordates) also have a liver. John is not aware of this fact, though. Also, for religious reasons, he does not eat animals with a liver. (11) a. John has eaten an animal with a heart. b. John has eaten an animal with a liver. (12) a. John does not want to eat animals with a liver. (true) b. / John does not want to eat animals with a heart. (false) All fours statements in (13) can be simultaneously true (from SEP entry on Propositional Attitude Reports): (13) a. Superman is Clark Kent. b. John believes that Superman is invincible. c. John does not believe that Clark Kent is invincible. (Neg-raising: (13)c (13)d) d. John believes that Clark Kent is not invincible. IV. Intensional adverbs. Some adverbs fail to preserve meaning. (14) Supposition: All and only those who ate at a fish restaurant X on 15th Nov 1999 had food poisoning. [Robin Cooper 2005, lecture notes] (15) a. John ate a fish in restaurant X on 15th Nov 1999. b. John had food poisoning on 15th Nov 1999. (16) a. John voluntarily ate a fish in restaurant X on 15th Nov 1999. b. / John voluntarily had a food poisoning X on 15th Nov 1999. (17) Supposition: The doctors are the violinists. (18) a. John allegedly is a doctor. b. / John allegedly is a violinist. V. Intensional adjectives. non-intersective (skillful, good, typical,...) and intensional non-subsective APs (former, alleged, fake,...) create opaque contexts (Siegel 1976; Larson 2000, among many others). (19) Supposition: Mr. Perry murdered both Smith and Jones. (20) a. Sam met the murderer of Smith. b. Sam met the murderer of Jones. (21) a. Sam met the alleged murderer of Smith. b. / Sam met the alleged murderer of Jones. (22) Supposition: The doctors are the violinists. (23) a. Sam knows the doctors. b. Sam knows the violinists. (24) a. Sam knows the skillful doctors. b. / Sam knows the skillful violinists. 3 Lechner: Architecture of the grammar VI. Conditionals. Antecedent of conditionals is opaque. (25) a. If Lois Lane starts dating Clark Kent, she will be dating an office mate. b. / If Lois Lane starts dating Superman, she will be dating an office mate. VII. Quotation. Quotations are opaque. Additional indicator of opacity is indexical shift inside quotations from speaker in context to ‘quoting authority’. (26) a. Lois Lane said: “I like Clark Kent”. b. / Lois Lane said: “I like Superman”. (27) a. Lois Lane said, that I liked Clark Kent. (I denotes in context c speaker in c) b. / Lois Lane said: “I like Clark Kent”. (I denotes in context c Lois Lane) 2. INTENSIONAL SEMANTICS 2.1. LAMBDA CALCULUS (28) a. Syntax If φ is an expression of type δ, and α is a variable of type ε, then λα.φ is an expression of type <ε,δ>. b. Semantics [Heim and Kratzer 1998] i. λα.φ =Def the smallest function which maps α to φ ii. λα.φ =Def the function which maps α to 1 if φ, and to 0 otherwise (29) a. f(x) = x+2 b. λx.x+2 ‘the smallest function which maps arbitrary x to x+2’ c. λx.Prime(x) ‘the smallest function which returns 1 (T) if arbitrary x is a prime’ (30) a. λx.love(x)(John) ‘the individuals John loves’ b. λx.love(John)(x) ‘the individuals loved by John’ c. λx.λy.love(x)(y) ‘diadic relation between lovers and loved ones’ = love 2.2. MODELING INTENSIONALITY Standard analysis of failed inferences (Frege 1882): " Natural language expressions have two different denotations: an extension and an intension (Carnap 1947; reference and sense in Frege 1882) " Leibniz’ Law applies to extensions only. " Intensional contexts combine with intensions. Interpretation relative to a possible world or situation: (31) Intension of α relative to an assignment g (world/situation independent denotation of α) a. =def the function f from possible worlds w to denotations of type α which assigns to each w the extension of α in w. w, g b. =def λw.α (32) Extension of α relative to an assignment g and a world w (denotation evaluated in w) a. =def the result of evaluating at w the function f from possible worlds w to denotations of type α which assigns to each w the extension of α in w w, g b. =def α #1: Intro: Intensionality 4 The terms ‘situation’ and ‘world’ will be used as if they were interchangeable salva veritate. Strictly speaking, this is not true - worlds are more like maximal situations (Kratzer 2011). Natural language semantics specifies recursive definitions of values for each expression relative to a model, an assignment function for variables/pronouns and a world/situation. (33) A Model is a structure <D, I> in which a. D is the domain of entities (aka universe or ontology) b. I is the interpretation function from constants of type τ to elements of Dτ (34) Interpretation relative to model, assignment and world (index) αM, g, w = denotation of α relative to M, assignment g and world w (35) g is an assignment function from variables of type τ to entities of Dτ (36) Semantic values of simple expressions (terms) a. If α is a constant, αM,g = I(α) M,g b. If α is a variable, α1 = g(α1) = g(1) [the latter convention] (37) Notational convention: superscripts for M and g will be ommitted unless ambiguity arises. (38) Intensional Model a. Set of possible worlds/situations b. Domains of individuals in each world c. Interpretation function (for constants, i.e. lexical items) the Lexicon d. Assignment function (for variables) e. Accessibility relation Extensional vs. intensional systems: In intensional system, natural language is interpreted relative to a world/situation parameter. This the world/situation, can be bound and manipulated by metalanguage operators (e.g. IFA below). In extensional system, world/situations are part of object language. (39) Intensional language: interpretation relative to worlds as atoms of logical meta language. dogw, g = λx.x is a dog in w dog is of type <e,t> (40) Extensional language: worlds are part of object language. [Gallin 1975 Ty2; Cresswell 1990] a. dogg = λw.λx.x is a dog in w dog is of type <s,<e,t>> b. dogg = λxλw.x is a dog in w dog is of type <e,<s,t>> 2.2.1. Definitions 1. Types: Recursive definition of semantic types of object language expressions that correspond to the syntactic categories of the metalanguage: (41) Intensional: the set of types T is the smallest set such that a. e T b. t T c. If τ T and υ T, then <τ,υ> T d. If τ T, then <s, τ> T (s is not an atomic type) (42) Extensional (Ty2; Gallin 1975) a. e T b. t T c. s T (s is an atomic type) d. If τ T and υ T, then <τ,υ> T 5 Lechner: Architecture of the grammar 2. Domain: recursive definition of possible denotations for each type τ. (43) Domains a. De = D (the set of all possible individuals) b. Dt = {0,1} c. Ds = domain of situations (mereological structure) d. D<τ,υ> = set of all functions from Dτ to Dυ ({f | f: Dτ Dυ}, for any type τ, υ e.
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