语言学教案Chapter 5 Meaning(7)

Token: M(s)

Note: A simple proposition is seen as a function (函数) of its argument. The truth value of a proposition varies with the argument.

M(s) =1, M(c) =0

E.g. John loves Mary. L (j, m)

John gave Mary a book. G (j, m, b)

kill: CAUSE (x, (BECOME (y, (～ALIVE (y)))))

C (x, (B (y, (～A (y)))))

All men are rational.

1. All is the universal quantifier and symbolized by an upturned A— in logic.

2. The argument men does not refer to any particular entity, which is known as a variable and symbolized as x, y.

Notation: x (M(x) R(x))

“For all x, it is the case that, if x is a man, then x is rational.”

Some men are clever.

Some is the existential quantifier and symbolized by a reversed E—

Notation: x (M(x) & C(x))

C.f. Universal quantifier & existential quantifier

1. Quantifiers

2. Implication connective

E.g.

All men are rational.

There is no man who is not rational. Notation: x (M(x R(x)) ≡～ x (M(x) & ～R(x))

(1) x (P(x))≡～ x (～P(x))

～ x (P(x))≡ x (～P(x))

x (P(x)) ≡～ x (～P(x))

～ x (P(x)) ≡ x (～P(x))

(2) x (M(x) R(x))

M(s)

∴R(s)

(3) x (M(x R(x))

R(s)

∴R(s)

(4) x (M(x) & C(x))

M(s)

∴C(s)