Semantics_1

Semantics_1

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

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)
     • Prepositions left out, which alters meaning, e.g. the distinction between in/on