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Logic. by Robert Baum; Quantificational Logic. by David T. Wieck Review by: Nelson Pole The Journal of Symbolic Logic, Vol. 42, No. 3 (Sep., 1977), pp. 424-425 Published by: Association for Symbolic Logic Stable URL: http://www.jstor.org/stable/2272874 . Accessed: 10/06/2014 11:22 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Symbolic Logic. http://www.jstor.org This content downloaded from 193.105.154.3 on Tue, 10 Jun 2014 11:22:31 AM All use subject to JSTOR Terms and Conditions

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Logic. by Robert Baum; Quantificational Logic. by David T. WieckReview by: Nelson PoleThe Journal of Symbolic Logic, Vol. 42, No. 3 (Sep., 1977), pp. 424-425Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2272874 .

Accessed: 10/06/2014 11:22

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

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Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to TheJournal of Symbolic Logic.

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424 REVIEWS

ROBERT BAUM. Logic.' Holt, Rinehart and Winston, Inc., New York, etc., 1975, xii + 516 pp.

DAVID T. WIECK. Quantificational logic. Therein, pp. 238-281. This is another general-purpose introductory textbook. Unlike most others, this one

should become a fixture in the syllabi. Its merits are not in extending our knowledge of logic. Rather, it will earn its place by its successful use of educational psychology. According to my non-scientific sampling of philosophers, introductory logic is the most

popular course offered by philosophy departments! It is annoying that until now there have appeared few logic texts that follow such basic practices as providing a summary for each chapter, illustration of both correct and incorrect uses of concepts, strategies for using rules, and realistic exercises. This is the happy exception.

The book is divided into four parts: Syllogistic logic, Symbolic logic, Induction, and

Language. Though language seems to come last, it is the key to the whole work. Each

part centers on how symbolic apparatus affects our understanding of natural language. The Introduction states that "To identify and evaluate arguments expressed in ordinary language requires skill which can only be acquired through practice" (p. 30). In general, the book follows its own advice. (But see p. 20.) It tries to convey that logical procedures require interpretation. Decision procedures may be available for formal systems, but

they are not yet available for natural languages. One of the best places where this comes across is in the chapter on informal fallacies (pp. 462-491). Instead of presenting the usual labels as unappealable indictments, it suggests that informal arguments are

enthymemes whose missing premiss may be questionable (p. 464). This approach should

foreclose, for example, dismissing Berkeley merely because his central argument

(objects are mind dependent because their qualities are) seems to be guilty of composition.

There are errors in the text, but they are usually minor. Some serious

exceptions: On page 148 a truth-functionally compound sentence (containing the

operator "not") is mistakenly asserted to be not compound, because it is not a truth function of what appears to be a sentence component. On page 206 it is claimed that it is easier to make a mistake in a shortened truth-table proof of validity than in its method of deduction (which employs a standard natural deduction scheme for propositional logic). Perhaps the author's students have different difficulties than do my students. The

quantification rules do not contain errors, but they are very conservative. The book does

not use a conditional proof (CP) procedure for introducing existential instantiation (El).

Nevertheless, some straightforward arguments require CP or indirect proof because of

the system's conservatism, e.g. (y)(3x)(Fy - Gx), . * . (y)Fy. The rule of universal general- ization (UG) presented could be modified to permit UG on a constant free in a line

introduced by El, when the line to which UG is to be applied does not contain free the

constant first introduced by El. Allowing for this is one of the motivations behind the

alternative approach of introducing El by means of CP. In summary, this book is a useful work for those introductory courses that teach a

little of everything. Errata: On page 26, line 13 from below should read: "Therefore, Paris is in

Europe." On page 130, line 12 from below, the syllogistic form is "AAI-1." On page 148, line 6 from below should end in "compound." On page 162, the fifth English line, delete the first "only." On page 194, the second premiss from below should read: "It is

not the case both that the Republicans will nominate Gerald Ford and that George Wallace will run as an Independent." On page 204, row 11 should end with T. On page 217, the first word in the second line under the schema should be "Disjunctive." On

page 232, in the first example there should be a solid line from step 2 to step 7. On page 239, the second premiss in the form should be "q* t." On page 493, Exercise 8, no. 3, the

premisses are true and the argument is sound; Exercise 10, no. 9, (b) and (c) are

interchanged. On page 499, Exercise 3-5, no. 25, the last F should be - F; Exercise 3-6, no. 13, the last column should contain only T's. On page 500, Exercise 3-9, no. 13 is a

tautology. On page 502, Exercise 4-2, no. 21, row 5, column 6 should contain T; no. 25,

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REVIEWS 425

the conclusion is mistakenly labeled "Premise" and row 6 should end with T. On page 503, Exercise 4-4, no. 9, line 5 is by "M.T., 2, 4." On page 505, Exercise 4-7, no. 5, line 8 is by "Trans., 3." NELSON POLE

M. J. CRESSWELL. Logics and languages. Methuen & Co Ltd, London 1973, xi+ 273 pp.

The goal of this book is to outline a set-theoretic analysis of natural language semantics, following ideas introduced by Montague (under whom the author studied briefly, in 1970). The technical development is relieved by frequent excursions into philosophy and linguistics, and the reader unfamiliar with Montague semantics will find this volume a useful introduction to the field.

Parts I and II give an account of certain formal languages, which are used in Parts III and IV to provide the "deep structure" for sentences of English. The richest of these are the so-called A -categorial languages Y', syntactically similar to Church's type theory except for the presence of functors of several arguments. The types, or "syntactic categories," include 0 (sentences), 1 (names), and derived types (,r, *,, *, ,,r) (functors from things of types o,, * - *, o,, to things of type r). Complex expressions are generated from constants and variables of various types by functor-application and A -abstraction. A model for Y'A specifies a domain D, for each type or, a distinguished subset T of Do, and a value V(8) e D, for each constant 8 of type or. For derived types oa =

(Ir, -,, o -*, Un), D, is some set of functions, total or partial, from D, X * - - X Don into D,. DO is the set of propositions, T the set of true ones, D1 the set of things. The value function V is extended as usual to closed expressions (it may be undefined for some of them).

Cresswell devotes a lengthy discussion to the metaphysics of propositions. In an indexical model propositions are sets of "possible worlds," and T consists of those that contain a distinguished "real world." A possible world, however, is itself a complex entity; precisely, a set of "basic particular situations"-space-time points, perhaps. To avoid the problems of propositional identity versus logical equivalence, Cresswell later redefines propositions, this time as sets of sets of sets of possible worlds. The "things," or elements of D1, are no less complex, comprising not only individuals (in something like the usual sense) but also individual concepts, concepts of concepts, etc. Indeed, in the intended models everything is a thing; i.e., D, C D1 for every type Oc. This innovation takes some getting used to, since it robs the higher domains of most of their functions. Whatever its inherent appeal, it proves to have many applications, e.g. in the analysis of self-reference, context-dependence, and the semantics of collective nominals.

Cresswell argues that his proposed semantics, while strictly set-theoretic in nature, is not inconsistent with a doctrine of innate ideas or natural kinds. It is doubtful, though, whether his "meaning algebras" are enough to bridge the gap; they will surely not carry his claim (pp. 56-57) that a "universal dictionary of all languages" might be forthcoming.

In analyzing the semantics of English, Cresswell follows Montague in taking nominals (John, everyone, someone) to be constants having type (0,(0, 1)), i.e., designating properties of properties of things. Common count nouns (man) and intransitive verbs (runs) are of type (0, 1); transitive verbs (loves) are of type (0, 1, 1). Similarly, one can assign appropriate types to determiners (every, a, the), abstract and mass nouns, adverbs, adjectives, and prepositions. The "deep structure" of the English sentence everyone runs is then the A-categorial sentence (everyone, runs), whose value is the proposition that being a running thing has the property of being true of everyone. The sentence (1) everyone loves someone has as one of its deep structures the A -categorial sentence (2) (everyone, (Ax(someone, (Ay (loves, x, y))))),where x, y are variables of type 1. Since Cresswell allows us to interchange the order of a functor and its arguments in 2A, (2) can be written as (everyone, (Ax ((Ay (loves, x, y)), someone))), from which the surface structure (1) can be recaptured by deleting all symbols except the constants. Cresswell proposes that, in general, the surface structure of an English sentence-or at least a "shallow structure" quite close to it-is merely the result of deleting A's,

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