Semantics

Semantics

Kinds of Meaning: Lectures 1-2
1. PRINCIPLE OF COMPOSITIONALITY:
  1. Not all linguistic expressions are compositional e.g. idioms
  2. Local and structure-dependent: determiners and head nouns need to be able to compose together, just like verbs and their arguments
  3. Based on syntax
  4. Meaning of linguistic expression is determined by the meaning of its subparts, and the rules that combine them
2. DENOTATIONS
  1. Ostensive definition: what it points to
  2. Denotations pick out relevant sets
  3. Bare nouns are predicates - they denote properties and can occur in the copula construction
  4. Predicates denote sets of individuals that have the property ascribed
3. TRUTH CONDITIONS
  1. What the world would have to be like in order for the proposition to be true
  2. Intensions are a more accurate representation of word meaning
  3. Presuppositions: A proposition X presupposes Y if Y is assumed to be true by anyone who expresses X
4. OPPOSITES
  1. Extension - thing picked out in actual world Intension - thing picked out in all possible worlds
  2. Literal (sentence) - derived from linguistic expression, independent of context. Inferred (utterance) - everything else
  3. Tautology - necessarily true in all worlds Contradiction - necessarily false in all worlds
5. ENTAILMENTS
  1. Useful to make reference to truth relations between statements, like the relation of entailment
  2. Part of its encoded meaning, but not encoded directly
  3. Uttering a sentence makes you committed to the truth of the sentence and the entailment
  4. A statement A entails a statement B if wherever A is true, B must also be true
  5. Upward
    1. Entailment towards the superset, e.g. John likes blue cheese entails that he likes cheese. (towards the GENERAL)
  6. Downward
    1. Entailment towards the subset, e.g. Every dog barked entails that every small dog barked. (towards the SPECIFIC)
Logic: Lectures 3-6
1. PROPOSITIONAL
  1. Treats propositions as atoms and provides a way of representing the constructing of complex propositions with connectives
  2. Conjunction ^ - typically represented by 'and'. Order doesn't matter, only true when T+T, all others false
    1. Loss of meaning in translation: sequential elements, and the distinction of 'but'
  3. Disjunction v - typically represented by 'or', only true if p is true.
  4. Negation ¬ - Opposites apply
  5. Material implication -> - Partially resembles 'if...then', order matters, the antecedent 'if' must occur first. Only false if when T+F
    1. Loss of meaning in translation: logic doesn't represent the causation implication
  6. Equivalence <-> - Expressed as 'if and only if', order is irrelevant, true when T+T and F+F
    1. Equivalences in logic are known as De Morgan's Law
  7. Exclusive disjunction - Often what is expressed by 'or', but exclusivity may be an implicature
    1. Can also be derived by adding 'but not both'
  8. The Key: Match key to variables, propositions must not decompose any operators (negation), full propositions only, order implications correctly
2. PREDICATE
  1. Represents the inner structure of propositions in terms of arguments, predicates and quantifiers
  2. Form: Melissa is tall = TALL (m) Order of Obliqueness: Subject > Indirect Object > Direct Object
  3. Prepositions left out, which alters meaning, e.g. the distinction between in/on
  4. Quantifiers
    1. Universal - variable bound by the universal quantifier e.g. ∀x(ILLUMINATED(x))
    2. Existential - variable bound by the existential quantifier e.g. ∃x(ILLUMINATED(x))
    3. Scope is read from the formula left-to-right, and is typically reflected by hierarchical relations
    4. 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))
  5. Argument positions can be occupied by complex expressions like embedded sentences e.g. SAY(s(BARK(m)))
3. GENERALIZED QUANTIFIER THEORY (GQT)
  1. Need to generalize quantifiers because a number of quantifiers fail to translate into the predicate logic system
  2. All quantifiers can be recast as relations between sets e.g. [Every x: CIRCLE(x)] RED(x)
  3. 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
Quantifiers: Lectures 7-9
1. SET THEORY
  1. Sets - collections of things Set theory - algebras of set things
  2. Notation
    1. 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
  3. Asymmetric Quantifiers
    1. Most, few, every
    2. Asymmetric quantifiers describe what proportion of the nominal restriction is in the intersection
    3. Most circles are red ≠ Most red things are circles
    4. PROPORTIONAL QUANTIFIERS
  4. Symmetric Quantifiers
    1. Numbers
    2. Symmetric quantifiers just count subsets
    3. CARDINAL QUANTIFIERS (do not come with an existence presupposition)
2. NEGATIVE POLARITY ITEMS
  1. Words that seem to need to be in the scope of a negative element e.g. ever and anything
  2. NPIs are licensed in non-negative sentences with PROPORTIONAL quantifiers that have downward entailments
  3. CARDINAL quantifiers do not license NPIs at all
  4. No: downward entailing on restriction and main predicate so NPIs licensed in both positions = neg + NPI
  5. Every: downward entailing only on restriction, only licenses NPIs here
  6. Three: not downward entailing on either argument, so NPIs not licensed anywhere
3. EXISTENTIAL SENTENCES
  1. THERE+BE+NP
  2. Only some quantifiers can be in the subject of such sentences, e.g. some, many, four
  3. 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
Presuppositions, Definites & Opacity: Lectures 9-11
1. PRESUPPOSITIONS
  1. Only propositions can give rise to entailments, but lexical items can give rise to presuppositions
  2. Tests
    1. Negation test: presuppositions are retained under negation, but entailments are not
    2. Interruption test: "I didn't know P" is an appropriate interruption
  3. Kinds of presuppositions
    1. Existential: presupposes the existence of a given identity
    2. Factive: presupposes the truth of a following proposition
    3. Counterfactual: presupposes the falsity of a following proposition
    4. Lexical/aspectual: presupposes another concept with the use of a given expression, typically related to structured sequence of events
2. DEFINITE DESCRIPTIONS
  1. 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
  2. Russell's proposal
    1. 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)
    2. 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)))
  3. Alternative: GQT + Benefits
    1. Makes 'the' a proportional quantifier, ensures it comes with an existence presupposition
    2. Accounts for familiarity effect with 'the'
    3. Easily amended to account for plural definites
3. OPACITY
  1. Principle of Substitutivity
    1. Identical expressions have the same truth value
    2. Does not hold opaque sentences like "often been an Italian"
  2. Opaque contexts: modalized sentences; the complement of propositional attitude predicates like 'want'
  3. Adverbs
    1. 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
    2. 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
4. INDEFINITES
  1. Specific reading: a particular individual
  2. Non-specific reading: any individual
Modality: Lectures 11-13
1. Modal expressions: auxiliaries, adverbs, adjectives, constructions
2. LOGICAL MODALITY
  1. 4 logical states of modality: necessarily true/false ◻ (non-contingent) & possibly true/false ⋄ (contingent)
3. EPISTEMIC MODALITY
  1. What is necessary/possible, given WHAT IS KNOWN (context-dependent). Involves quantification over worlds which are compatible with what we know (epistemically possible worlds)
  2. Necessary
    1. Must/can't
    2. ∀we
  3. Possible
    1. Might/could be
    2. ∃we
4. DEONTIC MODALITY
  1. 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)
  2. Necessary
    1. Must/required to
    2. ∀wpo
  3. Possible
    1. Can/may/allowed to
    2. ∃wpo
5. POSSIBLE WORLDS
  1. 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
  2. Possible to quantify over these worlds using ∀w - all possible worlds & ∃w - at least one possible world
6. RESTRICTION
  1. If modals quantify over possible worlds, the modal flavour is a restriction of this quantification. This is know as the modal base
  2. 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).
  3. Approaches
    1. VARIABLE STRENGTH APPROACH: different strengths require different quantifications over possible worlds. Stronger the modal - the more accessible the world is
    2. VARIABLE RESTRICTION APPROACH: concentrating on different worlds. The narrower the restriction, the more accessible
  4. Pragmatics
    1. Modal "must" cannot be used when we have direct evidence, because it comes with an evidential presupposition.
    2. Ambiguities in specific/non-specific interpretations

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