Semantics

Semantics

1. Kinds of Meaning: Lectures 1-2

   • PRINCIPLE OF COMPOSITIONALITY:
     • Not all linguistic expressions are compositional e.g. idioms
     • Local and structure-dependent: determiners and head nouns need to be able to compose together, just like verbs and their arguments
     • Based on syntax
     • Meaning of linguistic expression is determined by the meaning of its subparts, and the rules that combine them
   • DENOTATIONS
     • Ostensive definition: what it points to
     • Denotations pick out relevant sets
     • Bare nouns are predicates - they denote properties and can occur in the copula construction
     • Predicates denote sets of individuals that have the property ascribed
   • TRUTH CONDITIONS
     • What the world would have to be like in order for the proposition to be true
     • Intensions are a more accurate representation of word meaning
     • Presuppositions: A proposition X presupposes Y if Y is assumed to be true by anyone who expresses X
   • OPPOSITES
     • Extension - thing picked out in actual world Intension - thing picked out in all possible worlds
     • Literal (sentence) - derived from linguistic expression, independent of context. Inferred (utterance) - everything else
     • Tautology - necessarily true in all worlds Contradiction - necessarily false in all worlds
   • ENTAILMENTS
     • Useful to make reference to truth relations between statements, like the relation of entailment
     • Part of its encoded meaning, but not encoded directly
     • Uttering a sentence makes you committed to the truth of the sentence and the entailment
     • A statement A entails a statement B if wherever A is true, B must also be true
     • Upward
       • Entailment towards the superset, e.g. John likes blue cheese entails that he likes cheese. (towards the GENERAL)
     • Downward
       • Entailment towards the subset, e.g. Every dog barked entails that every small dog barked. (towards the SPECIFIC)

2. Logic: Lectures 3-6

   • PROPOSITIONAL
     • Treats propositions as atoms and provides a way of representing the constructing of complex propositions with connectives
     • Conjunction ^ - typically represented by 'and'. Order doesn't matter, only true when T+T, all others false
       • Loss of meaning in translation: sequential elements, and the distinction of 'but'
     • Disjunction v - typically represented by 'or', only true if p is true.
     • Negation ¬ - Opposites apply
     • Material implication -> - Partially resembles 'if...then', order matters, the antecedent 'if' must occur first. Only false if when T+F
       • Loss of meaning in translation: logic doesn't represent the causation implication
     • Equivalence <-> - Expressed as 'if and only if', order is irrelevant, true when T+T and F+F
       • Equivalences in logic are known as De Morgan's Law
     • Exclusive disjunction - Often what is expressed by 'or', but exclusivity may be an implicature
       • Can also be derived by adding 'but not both'
     • The Key: Match key to variables, propositions must not decompose any operators (negation), full propositions only, order implications correctly
   • PREDICATE
     • Represents the inner structure of propositions in terms of arguments, predicates and quantifiers
     • Form: Melissa is tall = TALL (m) Order of Obliqueness: Subject > Indirect Object > Direct Object
     • Prepositions left out, which alters meaning, e.g. the distinction between in/on
     • Quantifiers
       • Universal - variable bound by the universal quantifier e.g. ∀x(ILLUMINATED(x))
       • Existential - variable bound by the existential quantifier e.g. ∃x(ILLUMINATED(x))
       • Scope is read from the formula left-to-right, and is typically reflected by hierarchical relations
       • Restricted quantification - quantificational determiner exists with a noun that restricts it Universals require the implication symbol, and existentials require conjunctions e.g. ∀x(BOOK(x) -> READ(s,x)) and ∃x(BOOK(x) ^ READ(s,x))
     • Argument positions can be occupied by complex expressions like embedded sentences e.g. SAY(s(BARK(m)))
   • GENERALIZED QUANTIFIER THEORY (GQT)
     • Need to generalize quantifiers because a number of quantifiers fail to translate into the predicate logic system
     • All quantifiers can be recast as relations between sets e.g. [Every x: CIRCLE(x)] RED(x)
     • These are sensible ostensive definitions, they point to two sets [the main predicate and the nominal restriction], and say something numerical about the relation between them

3. Quantifiers: Lectures 7-9

   • SET THEORY
     • Sets - collections of things Set theory - algebras of set things
     • Notation
       • 1. A=B: A is identical to B 2. A⊂B: A is a proper subset of B 3. A⊆B: A is a subset of B 4. |A|=2: The cardinality of A is 2; A has 2 members 5. |B>A|: B has more members than A 6. |B∩A|: The cardinality of the intersection of B and A is two 7. |B-A|>|A∩B|: The number of members in B that are not also in A is greater than the number of elements in both
     • Asymmetric Quantifiers
       • Most, few, every
       • Asymmetric quantifiers describe what proportion of the nominal restriction is in the intersection
       • Most circles are red ≠ Most red things are circles
       • PROPORTIONAL QUANTIFIERS
     • Symmetric Quantifiers
       • Numbers
       • Symmetric quantifiers just count subsets
       • CARDINAL QUANTIFIERS (do not come with an existence presupposition)
   • NEGATIVE POLARITY ITEMS
     • Words that seem to need to be in the scope of a negative element e.g. ever and anything
     • NPIs are licensed in non-negative sentences with PROPORTIONAL quantifiers that have downward entailments
     • CARDINAL quantifiers do not license NPIs at all
     • No: downward entailing on restriction and main predicate so NPIs licensed in both positions = neg + NPI
     • Every: downward entailing only on restriction, only licenses NPIs here
     • Three: not downward entailing on either argument, so NPIs not licensed anywhere
   • EXISTENTIAL SENTENCES
     • THERE+BE+NP
     • Only some quantifiers can be in the subject of such sentences, e.g. some, many, four
     • Proportional quantifiers resist these positions because they presuppose the existence of a background set, and it would sound odd to use them in an existential sentence, because existence is already ASSERTED by the quantifiers

4. Presuppositions, Definites & Opacity: Lectures 9-11

   • PRESUPPOSITIONS
     • Only propositions can give rise to entailments, but lexical items can give rise to presuppositions
     • Tests
       • Negation test: presuppositions are retained under negation, but entailments are not
       • Interruption test: "I didn't know P" is an appropriate interruption
     • Kinds of presuppositions
       • Existential: presupposes the existence of a given identity
       • Factive: presupposes the truth of a following proposition
       • Counterfactual: presupposes the falsity of a following proposition
       • Lexical/aspectual: presupposes another concept with the use of a given expression, typically related to structured sequence of events
   • DEFINITE DESCRIPTIONS
     • Refer to a single individual in the actual world, but definite descriptions are not rigid designators, because the intension of a definite description is richer than the name
     • Russell's proposal
       • Definite descriptions assert existence (there must be an individual accurately described by the expression), and uniqueness (there must be exactly one individual satisfying the descriptions)
       • Formula in classical predicate logic, using ∃ for existence and ∀ for uniqueness e.g. ∃x(KING-OF-FRANCE(x) & ∀y(KING-OF-FRANCE(y) -> y=x) & BALD (x)))
     • Alternative: GQT + Benefits
       • Makes 'the' a proportional quantifier, ensures it comes with an existence presupposition
       • Accounts for familiarity effect with 'the'
       • Easily amended to account for plural definites
   • OPACITY
     • Principle of Substitutivity
       • Identical expressions have the same truth value
       • Does not hold opaque sentences like "often been an Italian"
     • Opaque contexts: modalized sentences; the complement of propositional attitude predicates like 'want'
     • Adverbs
       • Adverbs like often are not just simple adjuncts, they are propositional operators that take scope, the issue is the scope of the adverb with respect to the definite expression
       • Weird scope reading: One individual cannot have a property like Italian-ness on and off, it's an individual level predicate which must hold through all contexts
   • INDEFINITES
     • Specific reading: a particular individual
     • Non-specific reading: any individual

5. Modality: Lectures 11-13

   • Modal expressions: auxiliaries, adverbs, adjectives, constructions
   • LOGICAL MODALITY
     • 4 logical states of modality: necessarily true/false ◻ (non-contingent) & possibly true/false ⋄ (contingent)
   • EPISTEMIC MODALITY
     • What is necessary/possible, given WHAT IS KNOWN (context-dependent). Involves quantification over worlds which are compatible with what we know (epistemically possible worlds)
     • Necessary
       • Must/can't
       • ∀we
     • Possible
       • Might/could be
       • ∃we
   • DEONTIC MODALITY
     • What is MORALLY/LEGALLY necessary/possible, according to some set of rules (contextually given). Involves quantification over the set of worlds in which the relevant codes of behaviour are adhered to (perfect obedience worlds)
     • Necessary
       • Must/required to
       • ∀wpo
     • Possible
       • Can/may/allowed to
       • ∃wpo
   • POSSIBLE WORLDS
     • Modalized sentences don't assert that the core proposition is true in the actual world, they say something about the set if worlds in which it would be true
     • Possible to quantify over these worlds using ∀w - all possible worlds & ∃w - at least one possible world
   • RESTRICTION
     • If modals quantify over possible worlds, the modal flavour is a restriction of this quantification. This is know as the modal base
     • Modal base is characterised as being accessible to the actual word, the restriction is specifying an accessible relation between the actual world and the set of possible worlds (epistemically/deontically accessible).
     • Approaches
       • VARIABLE STRENGTH APPROACH: different strengths require different quantifications over possible worlds. Stronger the modal - the more accessible the world is
       • VARIABLE RESTRICTION APPROACH: concentrating on different worlds. The narrower the restriction, the more accessible
     • Pragmatics
       • Modal "must" cannot be used when we have direct evidence, because it comes with an evidential presupposition.
       • Ambiguities in specific/non-specific interpretations