语言学教案Chapter 5 Meaning(6)

proposition≈ sentence meaning

Truth value: truth or false

Predicate logic (Pp 180)

p (simple proposition)

one-place connective: negation ～ or ﹁

two-place connective: conjunction &

disjunction ∨

implication

equivalence ≡ or

Connective conjunction: similar to the English “and”

Connective disjunction: similar to the English “or”

Connective implication/conditional implication: corresponds to the English “if…then” Connective equivalence/biconditional: corresponds to “iff…then”

C.f. Antonyms & “not”

With complementary antonyms, the denial of one is the assertion of the other. With gradable, that is not necessarily the case.

E.g. John isn’t old.

John is old.

C.f. Conjunction & “and”

Conjunction

E.g. He missed the train and arrived late.

“And”

E.g. He arrived late and missed the train.

*He missed the train and arrived late.

C.f. Implication & “if…then”

Implication

E.g. If he is an Englishman, he speaks English.

If snow is white, grass is green.

E.g. If snow is black, grass is green.

“If…then”

E.g.? If snow is white, grass is green.

*If snow is black, grass is green.

In sum, propositional logic, concerned with the semantic relation between propositions, treats a simple proposition as an unanalyzed whole.

E.g. All men are rational.

Socrates is a man.

Therefore, Socrates is rational.

PREDICATE LOGIC/PREDICATE CALCCULUS studies the internal structure of simple propositions.

Question: How to analyze Socrates is a man?

Argument (主目): a term which refers to some entity about which a statement is being made

Predicate (谓词): a term which ascribes some property, or relation, to the entity, or entities, referred to

Socrates is the argument, and man is the predicate.