Meaning and Necessity

Meaning and Necessity: A Study in Semantics and Modal Logic (1947; enlarged edition 1956) is a book about semantics and modal logic by the philosopher Rudolf Carnap. The book, in which Carnap discusses the nature of linguistic expressions, was a continuation of his previous work in semantics in Introduction to Semantics (1942) and Formalization of Logic (1943). Considered an important discussion of semantics, it was influential and provided a basis for further developments in modal logic.

Meaning and Necessity: A Study in Semantics and Modal Logic

Cover of the first edition
Author	Rudolf Carnap
Language	English
Series	Studies in Semantics
Subjects	Semantics Modal logic
Publisher	University of Chicago Press
Publication date	1947
Publication place	United States
Media type	Print (Hardcover and Paperback)
Pages	258 (1964 fourth impression)
ISBN	978-0226093475

A particularly famous further development in semantics and modal logic, Saul Kripke's Naming and Necessity, is titled as a reference to Carnap's book.^[1]

Summary

Carnap writes that his main purpose is the development of a new method for "the semantical analysis of meaning", which he understands as analyzing and describing the meanings of linguistic expressions. He refers to this method as "the method of extension and intension", and explains that it is based on modification and extension of concepts such as those of class and property. He contrasts it with semantical methods that "regard an expression in a language as a name of a concrete or abstract entity", observing that unlike them, it "takes an expression, not as naming anything, but as possessing an intension and an extension." He presents Meaning and Necessity as the third volume of "Studies in Semantics", which includes previous volumes such as Introduction to Semantics (1942) and Formalization of Logic (1943).^[2] According to commentators, the book continues Carnap's shift from a purely syntactic approach in The Logical Syntax of Language (1934) to a framework in which semantics and proof theory are treated as complementary parts of the logical analysis of language.^[3]

Within this framework Carnap treats sentences, predicates and individual constants as "designators" and assigns to each of them both an extension and an intension. The extension of a sentence is its truth-value, the extension of a predicate is the class (or relation) of objects that satisfy it, and the extension of an individual constant is the individual to which it refers; the corresponding intensions are, respectively, propositions, properties or relations, and individual concepts.^[3] The intension of a linguistic expression is determined solely by the semantic rules of the language, while its actual extension is obtained by applying those rules together with the "true" or "actual" state-description (the actual possible world).^[3] Extensions may therefore depend on empirical facts, whereas intensions are fixed by the linguistic framework. On this basis Carnap defines semantic notions such as truth, logical truth and logical consequence, treating logic as a special part of semantics concerned with what he calls L-truth and L-falsehood.^[3]

The term "state-description" is used by Carnap to refer to a class of sentences which "contains for every atomic sentence either this sentence or its negation, but not both, and no other sentences". He considers the term justified because a state-description "obviously gives a complete description of a possible state of the universe of individuals with respect to all properties and relations expressed by predicates of the system."^[4] In his intensional semantics, state-descriptions function like possible worlds: for a given formal language they represent complete ways the universe of discourse might be, one state-description corresponds to the actual state of the universe, and a sentence is simply true (in the ordinary sense) if and only if it holds in that actual state-description.^[3] This framework allows Carnap to define the extension of a sentence as its truth-value at the actual state-description and to reconstruct propositions as sets of state-descriptions (the "range" of a sentence), though he treats this identification as a convenient explication rather than a strict analysis of propositions.^[3]

On the basis of state-descriptions, Carnap defines the central intensional notions of the book. A sentence is L-true (logically true or analytic) when it holds in every state-description, and L-false when its negation holds in every state-description; sentences that are true or false without being L-true or L-false are factually true or false.^[3] Logical necessity is expressed in the object language by an operator N (read "it is necessary that"), which is defined so that N(A) holds in a state-description s if and only if A holds in every state-description; the corresponding possibility operator is then introduced in the usual way as ¬N¬.^[3] In this way Meaning and Necessity provides an intensional semantics for modal logics at least as strong as C. I. Lewis's system S5 and identifies logical necessity with truth in all state-descriptions, rather than with a separate metaphysical modality.^[5]

Carnap also gives a systematic account of intensionality and synonymy within this framework. He distinguishes extensional from intensional linguistic contexts, and proposes that in intensional contexts expressions may be intersubstituted salva veritate only when they have not merely the same extension but the same intension. To explicate sameness of intension he introduces the notion of "intensional isomorphism": roughly, two expressions are synonymous when their associated intensions have the same internal structure, not merely the same range of state-descriptions.^[3] This allows him to draw a distinction between merely coextensive expressions and expressions that are genuinely equivalent in meaning, and to treat intensional constructions such as belief and propositional attitude reports, which he takes to be neither purely extensional nor adequately handled by earlier semantic theories.^[3]

In the later chapters Carnap applies the method of extension and intension to modal logic in full predicate form. He develops a modal predicate logic (often referred to as system C) containing the necessity operator N, and provides a corresponding semantic theory in which formulas are evaluated at state-descriptions.^[5] Whereas in his earlier work on modality he interpreted first-order quantifiers substitutionally, in Meaning and Necessity he allows quantifiers to range, intensionally, over "individual concepts", understood as functions from state-descriptions to individual constants; this device is intended to make sense of quantified modal statements while avoiding certain problematic commitments about necessary identity and substitution in modal contexts.^[3] Carnap uses this system to respond to objections to quantified modal logic raised by philosophers such as W. V. O. Quine, arguing that necessity can be treated as a logical notion explicated within a suitably chosen linguistic framework rather than as a primitive metaphysical relation.^[5]

The enlarged edition of Meaning and Necessity includes previously published papers replying to criticism of Carnap by the philosophers Gilbert Ryle, Ernest Nagel, and Alonzo Church.^[6] In these additions Carnap defends his use of intensional entities such as propositions and individual concepts, and clarifies how his semantic framework is compatible with a deflationary attitude toward metaphysical questions about the "existence" of abstract objects.^[3]

Publication history

Meaning and Necessity was first published in 1947 by the University of Chicago Press. An enlarged edition was published in 1956. In 1964, a fourth impression was published.^[7]

Reception

Meaning and Necessity received a positive review from Marie Hochmuth in the Quarterly Journal of Speech and a negative review from Ryle in Philosophy.^[8][9]

Hochmuth wrote that Carnap's work, like that of other members of the Vienna Circle, had "inspired the search for a neutral system of symbols, free from the dross of historical languages." She credited Carnap with drawing attention to "the urgent need for a system of theoretical pragmatics, not only for psychology and linguistics, but also for analytic philosophy." However, she noted that the first edition of the work had been criticized for "Carnap's claims for the simplicity and the scientific purity of his system."^[8]

Discussions of Meaning and Necessity include those by Carnap in Revue Internationale de Philosophie,^[10] the philosopher Nathan Salmon in The Philosophical Review,^[11] Bernard Linsky in History & Philosophy of Logic,^[12] Amélie Gheerbrant and Marcin Mostowski in Mathematical Logic Quarterly,^[13] and Juan José Acero in Teorema.^[14] Linsky suggested that Carnap had independently rediscovered points first made about logic by the philosopher Leon Chwistek in 1924.^[12]

The philosopher A. J. Ayer considered Meaning and Necessity more important than Carnap's other books on semantics, Introduction to Semantics and Formalization of Logic. However, he criticized the work, arguing that there is only a nominal distinction between Carnap's view that linguistic expressions have intensions and extensions and the traditional view that they "name concrete or abstract entities". He also suggested that despite Carnap's claim that every designation refers to both an intension and an extension, his system "provides only for the designation of intensional entities".^[15] The philosopher Dagfinn Føllesdal wrote that while Carnap admitted that he ignored complications with his proposed system of modal logic, he failed to explain what they were. He criticized Carnap for this, and suggested that Carnap was unaware of some of the problems with his views.^[16]

The philosopher E. J. Lowe wrote that Meaning and Necessity was "important and influential", and laid the foundations of much subsequent work in the semantics of modal logic. According to Lowe, the book was the culmination of Carnap's concern with the semantics of natural and formal languages, which developed subsequent to his publication of The Logical Syntax of Language (1934).^[17] The philosopher Henry E. Kyburg Jr. wrote that Meaning and Necessity provided the basis for a new form of modal logic. He considered Carnap's concept of the state-description one of his most important contributions.^[18]