Book Reviews Everything that Linguists have Always Wanted to Know about Logic 
Everything that Linguists have 
Always Wanted to Know about Logic* 
*but were ashamed to ask 
James D. McCawley 
The University of Chicago Press, Chicago, 1981, 
508 pp., Paperback, $12.50, ISBN 0-226-55618-2. 
Most introductory courses on logic teach only the 
syntax of first-order predicate calculus and give a few 
simple proofs, usually of theorems in arithmetic. Ad- 
vanced courses are taught in mathematics departments, 
where they lead to topics that have little or no applica- 
tion to linguistics. In one of the standard textbooks, 
Schoenfield (1967) explicitly states "Mathematical 
logic has always been closely connected with the phi- 
losophy of mathematics. I have generally avoided 
philosophical issues except when they were closely 
connected with the mathematical material" (p. iii). 
Schoenfield dismisses the relationship between lan- 
guage and logic with a few terse comments like "we 
introduce the symbol & to mean and" (p. 10). Given 
such logic books and courses, people studying natural 
language would find it hard to see any relevance to 
their interests. With this book, McCawley has done a 
great service in bringing together a wealth of material 
on the applications of logic to linguistics and philoso- 
phy. 
The first third of the book introduces the standard 
topics of propositional calculus, predicate calculus, 
proofs, sets, and models. Unlike mathematical texts 
that skip over the mapping from language to logic as 
quickly as possible, McCawley illuminates it with 
pointed examples. He counters the common claim that 
"If A, then B" is synonymous with "A only if B," by 
citing examples like the following: 
If butter is heated, it melts. 
Butter is heated only if it melts. 
After covering the standard topics, McCawley spends 
the remaining two thirds on important issues that are 
rarely mentioned in introductory texts: definite de- 
scriptions, comparatives, speech acts, conversational 
implicature, presupposition, modal logic, relevance 
logic, counterfactual conditionals, possible worlds, 
many-valued logic, fuzzy logic, lambda calculus, 
Montague's intensional logic, and nonstandard quanti- 
fication. 
The book does have some shortcomings, many of 
which stem from the same source as some of its 
strengths--McCawley's idiosyncratic approach to the 
subject matter. As might be expected from one who 
views English as a VSO language, McCawley adopts a 
prefix notation, writing = (AAB,C) instead of the more 
common AAB=C. He also replaces the standard 
terms conjunction and disjunction with the terms and- 
conjunction and or-conjunction. He deliberately blurs 
the distinctions between axioms, rules of inference, 
and meaning postulates: "I maintain that the differ- 
ence between 'axiom' and 'rule of inference' is best 
regarded as one of detail rather than one of general 
nature: axioms are merely rules of inference that in- 
volve no premises" (p. 45); "The distinction between 
meaning postulate and rule of inference is only as 
good as the difference between 'nonlogical element' 
and 'logical element,' which is to say that it is far from 
clear that the difference has any substance" (p. 46). 
Although some people might agree with McCawley, 
others believe that those distinctions are important for 
a semantic theory or a knowledge representation lan- 
guage. In a book as general as this one, he should at 
least have given a more sympathetic treatment of the 
distinctions. Besides controversial stands, the book 
also makes some statements that are wrong or at least 
misleading. In discussing branching quantifiers, for 
example, McCawley says that they extend "the combi- 
natory possibilities of first-order quantifiers in such a 
way as to match the expressive power of second-order 
quantifiers" (p. 450). In fact, branching quantifiers 
provide only a subset of the power of second-order 
logic, not all of it (Walkoe 1976). 
Despite some flaws, this book provides a good cov- 
erage of logic and its use in clarifying semantic issues. 
Since McCawley wrote it for an introductory course, 
he does not assume that the reader is fluent in juggling 
the symbolism and provides extensive commentary on 
the formal operations. Even though it is an introduc- 
tory text, a reader who has not had previous exposure 
to symbolic logic may find it rather difficult for self 
study. Logic teachers who do not adopt it as a prima- 
ry textbook will still find it an excellent source of ex- 
amples. Readers who would like a quick review of 
logic should also consider Logic in Linguistics by All- 
wood et al. (1977); it is not as comprehensive as 
McCawley's book, but its terminology is more stand- 
ard. 
John F. Sowa, IBM Systems Research Institute 

References 
Allwood, Jens, Lars-Gunnar Andersson, Osten Dahl (1977) Logic 
in Linguistics, Cambridge University Press, Cambridge. 
Schoenfield, Joseph R. (1967) Mathematical Logic, Addison-Wesley, 
Reading, MA. 
Walkoe, Wilbur, Jr. (1976) "A Small Step Backwards," American 
Mathematical Monthly, vol. 83, pp. 338-344. 
