Semantics

Semantics

1. LECTURE 1 + 2 Meaning & Truth

   • MEANING
     • SENTENCE v. UTTERANCE
       • SENTENCE = LITERAL MEANING
         • UTTERANCE = INFERRED MEANING
     • COMPOSITIONALITY
       • COMPOSITIONALITY = MEANING OF AN EXPRESSION IS DETERMINED ENTIRELY ON ITS SUBPARTS AND THE RULES THAT COMBINE THE SUBPARTS
       • LOCAL AND STRUCTURE- DEPENDENT
       • EXPLAINS HOW WE UNDERSTAND SENTENCES WE HAVE NEVER HEARD BEFORE
     • DENOTATIONS
       • WHAT A WORD IDENTIFIES IN WORLD = DEFINITION
         • WHAT A WORD POINTS TO = DENOTATION
       • DENOTATIONS POINT TO THINGS WITH PROPERTIES
   • TRUTH
     • TRUTH & FALSITY
       • MEANING OF A SENTENCE = TRUTH CONDITIONS
         • DENOTATION OF SENTENCE = TRUTH VALUE
     • EXTENSION & INTENSION
       • EXTENSION = THING PICKED OUT BY THE EXPRESSION IN ACTUAL WORLD - TRUTH CONDITIONS
       • INTENSION = THING PICKED OUT BY THE EXPRESSION IN ALL POSSIBLE WORLDS - TRUTH VALUE
     • POSSIBLE WORLDS
       • HYPOTHETICAL STATE OF AFFAIRS CONSIDERING THE WAY THINGS MIGHT HAVE BEEN
       • INCLUDES THE WORLD WE ARE IN NOW
       • INTENSION (TRUTH CONDITIONS) OF A SENTENCE IS CLOSER TO THE TRUE MEANING
     • TRUTH CONDITIONS & TRUTH VALUE
       • EXAMPLE: DANIEL GRAHAM IS ENGLISH
       • TO KNOW THE MEANING OF THE SENTENCE, YOU DON'T NEED TO KNOW IF IT'S TRUE IN THE ACTUAL WORLD (TRUTH VALUE)
     • ENTAILMENTS
       • A STATEMENT (A) ENTAILS (B) IF WHEREVER (A) IS TRUE, (B) MUST ALSO BE TRUE
         • THE DOOR IS OPEN ENTAILS THE DOOR IS NOT CLOSED
           • PART OF ENCODED MEANING

2. LECTURE 3 - 6 LOGIC

   • PROPOSITIONAL LOGIC
     • TREATS PREPOSITIONS AS ATOMS AND DESCRIBES MEANING RELATING AT SENTENCE LEVEL
     • USES THE TOOLS ^ FOR CONJUNCTION V FOR DISJUNCTION ¬ FOR NEGATION --> FOR MATERIAL IMPLICATION AND <-> FOR EQUIVALENCE
     • EQUIVALENCES ARE PROVEN IN TRUTH TABLES
   • PREDICATE LOGIC
     • LOGIC WHICH PROVIDES REPRESENTATION OF INNER STRUCTURE OF PROPOSITIONS IN TERMS OF PREDICATES AND ARGUMENTS
     • ORDER IS: SUBJECT --> iO --> dO
     • INFORMATION IS OFTEN LOST THROUGH LOGIC
     • UNIVERSAL QUANTIFICATION DEALS WITH EVERY
       • IS DEALT WITH BY USING THE LOGIC FORMULA FOR EVERY
         • USES CONDITIONAL --> IN FORMULA
     • EXISTENTIAL QUANTIFICATION DEALS WITH SOMETHING
       • IS DEALT WITH BY USING THE LOGIC FORMULA FOR SOMETHING
         • USES CONJUNCTION ^ IN FORMULA
   • GQT
     • GENERALIZED QUANTIFIER THEORY
     • RECASTS ALL QUANTIFIERS AS RELATIONS BETWEEN SETS
     • MOST X:
       • EVERY X:
         • NO X:
     • EXAMPLE: [EVERY X: CIRCLE (X)] RED (X)

3. DEFINITIONS

   • write them down

4. LECTURE 8 - 9 QUANTIFIERS

   • SET THEORY
     • SETS : COLLECTIONS OF THINGS
       • SET THEORY: ALGEBRAS OF SETS OF THINGS
     • USES SET THEORY NOTIONS TO DESCRIBE RELATIONS
   • SYMMETRICAL & ASYMMETRICAL Q'S
     • ASYMMETRIC QUANTIFIERS
       • DESCRIBE PROPORTIONS OF SETS IN INTERSECTIONS
       • PROPORTIONAL
       • LICENSE NPIs IN MOST CASES
       • DOWNWARD ENTAILING
     • SYMMETRIC QUANTIFIERS
       • COUNT ELEMENTS IN INTERSECTIONS
       • CARDINAL
         • DONT COME WITH EXISTENCE PRESUPPOSITION
       • DON'T LICENSE NPIs
       • UPWARD ENTAILING
   • ENTAILMENTS
     • DOWNWARD ENTAILMENT
       • TOWARDS SUBSET
         • EVERY DOG BARKED
     • UPWARD ENTAILMENT
       • TOWARDS SUPERSET
         • JOHN LIKES BLUE CHEESE

5. LECTURE 9 - 10 DEFINITES

   • DEFINITE DESCRIPTIONS
     • LIKE NAMES
     • REFER TO INDIVIDUAL IN ACTUAL WORLD
     • RIGID DESIGNATORS
       • INTENSION IS RICHER THAN PROPER NAMES
   • RUSSELL'S PROPOSAL
     • DEFINITE DESCRIPTIONS ASSERT TWO THINGS:
       • 1: EXISTENCE - THERE MUST BE AN INDIVIDUAL ACCURATELY DESCRIBED BY THE EXPRESSION
         • 2: UNIQUENESS - THERE MUST BE EXACTLY ONE INDIVIDUAL SATISFYING THIS DESCRIPTIOS
   • SUBSTITUTIVITY
     • IF 'A=B' IS TRUE, AND S1 IS A STATEMENT CONTAINING THE EXPRESSION 'A' AND S2 IS A STATEMENT IDENTICAL TO S1 EXCEPT THAT THE EXPRESSION 'B' APPEARS INSTEAD OF 'A' THEN S1 AND S2 HAVE THE SAME TRUTH VALUE
     • OPAQUE CONTEXTS:
       • MODALISED SENTENCES
         • COMPLEMENT OF PROPOSITIONAL ATTITUDE PREDICATES LIKE WANT OR BELIEVE

6. LECTURES 11 - 12 MODALITY

   • EPISTEMIC MODALITY
     • WHAT IS NECESSARILY/ POSSIBLY TRUE/ FALSE
       • GIVEN WHAT IS KNOWN
     • CONTEXT - DEPENDENT
   • DEONTIC MODALITY
     • CONCERNS WHAT IS NECESSARILY/ POSSIBLY TRUE/ FALSE
       • ACCORDING TO A SET OF RULES/LAWS
   • LEARN THE LOGIC IN MODALITY