Meaning in Language: An Introduction to Semantics and Pragmatics

LOGIC AND MEANING

Chapter 2

Features some property to an entity or a relation between two or more entities.

It is either true or false

Truth or falsehood shows at least one proposition made

The same proposition may be expressed by an indefinite and large number of sentences.

PROPOSITIONS

Sentences: type-level entity where definite referring expressions have to be assigned referents

Statements: must be energized illocutionary force

Utterances: token-level entity where multiple utterances can be produced from one sentence

How Propositions Relate

Negative Operator:

Switches truth value

Implication:

"P and/or Q": PvQ is true as long as at least one of the two propositions P and Q is true. The order of the propositions is significant for this relation.

Logical Operators

Conjunction:

P&Q is true only if both P and Q are true.

The order of the propositions is irrelevant.

Disjunction

"P and/or Q": PvQ is true as long as at least one of the two propositions P and Q is true. T

The order of the propositions is irrelevant.

Equivalence

P"Q is true only if both P and Q have the same truth value.

The order of the propositions is irrelevant.

Logical Operators

Entailment:

Relation which holds between the propositions listed under P and the corresponding propositions under Q

Equivalence:

mutual entailment

Contrariety:

may not be simultaneously true

may be simultaneously false.

Contradiction:

must have opposite truth values in every circumstance

Natural Language Application

truth values vary independently of one another

May be both true, both false, or one true and the other false

relations described have an important role in the analysis of meaning relations between words

COMPATIBILITY

Known as second-order logic

Predicate Calculus:

system of representing the structure of propositions

INNER STRUCTURE OF PROPOSITIONS

closely linked pair of concepts

absolutely fundamental to both logic and semantics are argument and predicate.

Argument: designates some entity or group of entities

Predicate: attributes some property to the entity denoted by the argument

ARGUMENTS AND PREDICATES

The number of arguments a predicate takes is known as its valency

Logical Valency: determined by the number of arguments for it to be logically complete

Valency

Paradoxical:

Automatically express false propositions

Synthetic propositions:

Truth values made up by their correspondence or otherwise with the facts

Analytic:

they automatically express true propositions

Paradoxical, analytic and Synthetic Propositions

Quantification: requires a quantifier, a restriction, and a scope.

Existential Quantifier

Universal Quantifier

Quantifiers and Quantification

Downward Entailing: the valid entailment goes from less specific to more specific

Upward Entailing: the valid entailment goes from more specific to less specific

Directional Entailingness

Directional entailment properties correlate with negative polarity items (negpols).

Only normal in certain types of environment

typically contains a negative element of some kind.

Negative Polarity

Useful set of concepts drawn from logic of classes:

Identity

Inclusion

Disjunction

Intersection

Union

Class Relations

Mapping

Logic of Classes

Truth is assumed to be common knowledge shared by speaker and addressee.

Speaker presupposes knowledge about listener

Presuppositions

Russell:

believed that the presupposition of a sentence should be explicitly represented in a representation of the sentence's meaning.

Strawson:

presupposition is a relation between propositions

Accounting for Presuppositions

Reference: things in the world referred to by a particular expression

Denotation: word denotes a specific point of reference

Sense: word is associated with some kind of mental representation

Useful Distinctions to Remember