6.4 Predicate logic 195
individual who is remembered by everyone: in a universe consisting of Nina, Andrew, Tom, Harry and Briony, Tom might be remembered by Nina, Andrew, Harry and Briony. (44), by contrast, says that every person remembers at least one person. This single person remembered by eve-rybody may well differ from person to person: Briony may remember Harry, Nina may remember Andrew, Andrew may remember Tom. In (44), the existential quantifier is said to be in the scope of the universal quantifier. To take another example of scope differences, consider the two-place predicate F ‘is the father of in the following two propositions (see Allwood et al. 1977: 67 for discussion):
(45) (Vy) (3x) Fx, y For every y, there is an x such that x is the father of y. Everyone has a father.
(46) (3x) (Vy) Fx, y. There is at least one x, such that for every y, x is the father of y. Someone is the father of everyone.
The first proposition, (45), is true, the second, (46), is not. Yet the differ-ence between them consists solely in the order of the existential and universal quantifier, and the consequent scope differences between the two. Predicate logic notation can be used to precisely represent ambiguities in natural language. Sentence (47a), for example, has, among other read-ings, (47b) and (47c):
(47) a. Everyone here works for two companies. b. Everyone works for the same two companies. c. Everyone works for two companies, which may or may not be the same.
We can represent this difference concisely using the constant p for a per-son and c for a pair of companies, and the predicate W ‘work for’: (48) a. (3c) (Vp) Wp, c There is at least one pair of companies c, such that for every person p, p works for c Everyone works for the same two companies. b. (Vp) (3c) Wp, c For every person p, there is at least one pair of companies c such that p works for c. Everyone works for two companies (which may or may not be the same). QUESTION Using the abbreviations supplied, (i) translate the following logical formulae into idiomatic English:
P is a poet T is talented S is a simpleton
N is a novelist W is a prize winner