Philosophy and Logical Syntax by Rudolf Carnap

First published: 1935

Type of Philosophy: Epistemology, logic, philosophy of language

Context

Rudolf Carnap’s Philosophy and Logical Syntax is the substance of three lectures that he gave at the University of London in 1934. As a result, the book is short, outlining the essentials of the logical positivism of the Vienna Circle from the viewpoint of probably the best known and perhaps the most influential member of the group.

Logical positivism had its origin in a seminar conducted in the 1920’s by Moritz Schlick at the University of Vienna. A number of the members of this group, the original Vienna Circle, were scientists reacting against those idealist philosophers who pontificated, sometimes in almost complete ignorance, about the aim and function of science. Part of positivism’s program was the explicit rejection of this kind of irresponsible philosophizing. Another characteristic concern of the group was a strong interest in logic, an interest that grew out of its members’ admiration for the work that had been done on the foundations of mathematics toward the close of the nineteenth century and in the early twentieth century, particularly the work of Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (1910-1913). These interests quite naturally led the Vienna group to deliberate regarding philosophy’s proper business. They decided that philosophy is properly the analysis and clarification of meaningful language. By meaningful language, they meant the language of empirical science together with the language of mathematics; all other language, they held, lacked cognitive meaning. The Vienna Circle philosophers gave expression to this conviction in their criterion of empirical meaning, a widely known and vigorously debated tenet of logical positivism.

Verifiability Criterion

Carnap spends the first chapter of Philosophy and Logical Syntax discussing the implications of the verifiability criterion. At one point he states that only the propositions of mathematics and empirical science “have sense” and that all other propositions are without theoretical sense. However, he does not do much with mathematical propositions—with “analytic” propositions, as positivists sometimes labeled the propositions of logic and mathematics. He spends most of his time with “synthetic” propositions; that is, with propositions whose truth value cannot be determined simply by referring to their logical form. As examples of this analytic-synthetic distinction, consider the two propositions: “The ball is red,” and “Either the ball is red or the ball is not red.” One cannot know whether the first one is true or false without in fact examining the ball, but one can know that the second proposition is true without looking at the ball. It is true by virtue of its logical form. A sentence that is true or false by virtue of its form alone is analytic; a sentence whose truth value is determined by the (nonlinguistic) facts is synthetic.

Carnap holds the view that the only synthetic propositions that make sense are those propositions whose truth value can be determined by consulting the evidence of sense. These propositions, he further believes, are all to be found within the domain of empirical science. He uses the word “verification” in the usual logical positivist sense; that is to say, a proposition is verifiable if its truth value can be determined by reference to sense experience. The only synthetic propositions that make sense, then, are verifiable propositions, and these are all scientific propositions. This is the verifiability criterion of empirical meaning.

A Definition of Philosophy

It is Carnap’s view, then, that philosophy is the logical analysis of meaningful language, and meaningful language is restricted either to analytic propositions (logic and mathematics) or to empirically verifiable propositions (natural science). This theory implies that certain traditional areas of philosophy are no longer to be regarded as legitimate. Carnap rejects what he calls traditional metaphysics because it is made up of propositions that he feels are neither analytic nor empirically verifiable. As examples of metaphysical sentences, he mentions sentences about “the real essence of things,” “things in themselves,” and “the absolute.” In addition, Carnap rejects traditional philosophical ethics. He believes the usual utterances of ethical philosophers—such as “Killing is wrong”—mislead people by virtue of their grammatical form. They look like propositions, and so philosophers have given arguments to show that they are either true or false. Carnap, however, believes that what is grammatically an assertion, “Killing is wrong,” is logically not an assertion at all, but rather a disguised command, “Do not kill.” However, commands are neither true nor false and hence cannot be propositions. Ethics, then, is necessarily ruled out of the domain of philosophy.

Ethics and metaphysics are thus ruled out of philosophy proper. However, there must be something to them; otherwise why have people been so concerned about them? Here Carnap also has a simple answer. Metaphysical and ethical utterances express deep feelings and emotions, and that is why people are so concerned about them. However, Carnap points out, although these utterances resemble those of the lyric poet in that they express emotion and evoke a profound response in the reader, they nevertheless do not make theoretical or cognitive sense—they are meaningless from a philosophical and scientific point of view.

However, not only metaphysics and ethics suffer from Carnap’s determination to rid philosophy of the burden it has borne. Epistemology and psychology also suffer as a result of his reforming zeal. Psychology’s legitimacy lies in its being an empirical science, and, as such, it is not the philosopher’s concern. Epistemology is, Carnap suspects, a hybrid of psychology and logic. Philosophers must continue to do the logic, but they should give over the psychology to the behaviorists. The proper domain of the philosopher, after rejecting metaphysics, ethics, psychology, and epistemology, is to perform logical analysis on the language of the scientist. There can be no misunderstanding of Carnap’s intention here, for he writes, “The only proper task of Philosophy is Logical Analysis.”

Pragmatics, Semantics, and Syntax

In other writings, Carnap has taken some pains to identify what he means by logical syntax. In the Foundations of Logic and Mathematics (1939), he has perhaps made the distinctions most clearly. In this work, he distinguishes pragmatics, semantics, and syntax as parts of the general philosophical concern with language that he calls “semiotic.” The first distinction that needs to be made here is between language that is about language and language that is not about language. One might, for example, assert the proposition: “The ball is red.” In this case, one would be using language to talk about the nonlinguistic world, to talk about a ball. However, one might then go on to talk about the proposition that refers to the red ball; one might say: “The proposition The ball is red’ has four words in it.” In this case, the proposition is not about objects (such as red balls) but about language itself. Such language about language is called “metalanguage”; language about objects is called “object language.” The general theory of an object language, stated in a metalanguage, is what Carnap means by “semiotic.” However, semiotics has three branches: pragmatics, semantics, and syntax. Pragmatics is an empirical study of three elements that can be distinguished in the use of a language—linguistic signs, the meanings (Carnap calls them “designata”) of the signs, and the users of the signs. Pragmatics studies all three elements. Oversimplifying, pragmatics may be likened to the activity of an anthropologist constructing a dictionary for a tribe he or she is studying. The anthropologist studies and records how the tribespeople use words, how the words are spelled and combined, and what the words indicate.

Semantics is an abstraction from pragmatics. The semanticist (in the Carnapian sense) restricts his concern to the words or signs and their designata or meanings. He abstracts from users to focus solely on the signs and their designata. There are two kinds of semantics: descriptive and pure. Descriptive semantics is an empirical study of signs and their matter-of-fact meanings in popular usage; pure semantics, on the other hand, is not an empirical study but a normative one that lays down rules regarding the signs and what their proper designata are. A pure semantical system is an artificial language consisting of rules specifying designata for a collection of linguistic signs. An example of a pure semantical sentence might be: “The predicate word large’ designates the property of being large in a physical sense.” This specifies how the word “large” is to be used in a given artificial language, and it implies that such common language expressions as “That’s a large order” are incorrect in the semantical system in which the rule occurs.

Syntax represents yet another level of abstraction. Pragmatics includes signs, designata, and users. Semantics ignores the users and focuses its attention solely on signs and their designata. Syntax ignores the designata of the signs as well as ignoring the users. It is concerned only with the signs and the rules in accordance with which they can be combined and manipulated. Again, one may oversimplify and say that the subject matter of syntax is the traditional rules of logical deduction, provided one adds that the rules are formulated in a more abstract and formal way than is customary. Very roughly speaking, then, pragmatics may be likened to making a dictionary of usage; semantics may be likened to specifying the exact and unambiguous definitions of words in, say, a technical treatise; and syntax may be likened to constructing a formal set of rules of logic.

Formation and Transformation Rules

In his second chapter, Carnap attempts to characterize and illustrate logical syntax somewhat more fully. He says syntax is a “formal” theory, meaning that syntax abstracts from all concerned with the sense or meaning of the signs and confines itself strictly to the forms of the signs or words. It consists entirely of rules specifying how signs—regarded simply as shapes or designs or sounds—may be combined and manipulated. Within this formal theory, there are formation and transformation rules. The formation rules, in effect, define what is to be regarded as a proper sentence. The ordinary person’s rejection of Russell’s well-known example of an ill-formed sentence—”Quadruplicity drinks procrastination”—is made by virtue of an appeal to the implicit formation rules of the English language. Ordinarily, of course, people abide by the implicit formation rules of English. Carnap’s formation rules are intended to make explicit these implicit rules that people follow. The other group of rules, the transformation rules, specify what manipulations can be performed on the well-formed sentences identified by the formation rules. The transformation rules are the rules of logical deduction expressed in syntactical terms. Carnap states that the two primitive terms in a logical syntax are “sentence” and “direct consequence.” That is to say, syntax attempts to identify what are proper sentences and also to specify how people are to draw their logical consequences.

There are other important syntactical terms in addition to “sentence” and “direct consequence,” however. Carnap spends a fair amount of time in the second chapter defining and illustrating these additional syntactical terms. He defines “valid” as the property a sentence has if it is a direct consequence of the null class of premises. Putting this into a different logical terminology, one could say that a proposition that is validly inferred from tautologies is itself a tautology; Carnap means by “valid” what is often called “tautologous.” Carnap then defines “contravalid” so that it corresponds to the usual notion of self-contradiction. These two classes of sentences, the valid and the contravalid, make up the class of “determinate” sentences; all other sentences (sometimes called “contingent sentences” by other logicians) are called “indeterminate.”

The syntactical transformation rules serve to isolate the valid and contravalid sentences. These rules are called “L-rules” by Carnap. However, one may make other inferences that depend not on these logical rules but on certain laws of natural science; for example, Newton’s laws or the laws of thermodynamics. Scientific laws such as these, which also serve to justify drawing the consequences of sentences, Carnap calls “P-rules” to distinguish them from the L-rules. Carnap is then able to distinguish additional kinds of sentences; namely, P-valid and P-contravalid sentences.

Additional terms are defined in this second chapter. Enough have been mentioned here, however, to enable us to see what it is that Carnap is trying to do. He is making many of the usual distinctions and defining many of the usual terms of traditional logic. However, he is doing it in a slightly different way from that characteristic of traditional logic. He has avoided the usual basic logical terms “true” and “false,” since they depend on the question of the meaning of the propositions that are said to be either true or false. He has also avoided the usual logical term “implication,” and has replaced it with “direct consequence.” All of this is intentional and novel. Carnap sees it as being implied by his definition of syntax as a formal theory. He can describe a language and lay down rules for manipulating it without ever dealing with the question of the meaning of the words and sentences, and, consequently, without ever worrying about the subject matter with which the language deals. He is not doing physics or chemistry or biology; rather, he is manipulating symbols, symbols that might be assigned meanings later on so that they become words and sentences in a theory of chemistry, physics, or biology. However, as Carnap sees it, he has sharply separated the work of the philosopher-logician from the work of the scientist. Furthermore, abstracting from the meanings of the words and sentences enables the philosopher-logician to concentrate on the properly logical matters and avoid the tangles that often impede progress in the sciences. Best of all, the philosopher-logician has a legitimate activity in which to engage, one that benefits the scientist and that also circumvents the morasses of much traditional philosophy.

Pseudo-object Sentences

Just how Carnap feels he has avoided the morasses of traditional philosophy is best seen by looking at his discussion of what he calls “pseudo-object sentences.” Carnap feels that many times philosophers have combined syntactical predicates with nonsyntactical subjects. The result is neither one thing nor another; they are not statements in the object language nor are they statements in the metalanguage. They are, however, responsible for many of the disputes of traditional metaphysics about the reality or nonreality of entities such as universals. One example will perhaps illustrate Carnap’s distinction fairly clearly. He distinguishes three sentences:

The rose is red.

The rose is a thing.

The word “rose” is a thing-word.

No disputes arise over the first sentence, which Carnap defines as a real object-sentence in the material mode of speech. It is a sensible sentence that everyone understands and knows how to handle. Nor do disputes arise over the third sentence, which Carnap describes as a syntactical sentence in the formal mode of speech. Most people do not speak this way, but when they do (that is, when they are philosophical syntacticians), they make sense and avoid confusion. Unfortunately, philosophers have too often spoken in the manner of the second sentence, which Carnap calls a pseudo-object sentence. They then believe they are speaking about roses, and they begin debating and defining, getting further and further mired in the morass of bogus entities. One should speak either with the vulgar about red roses or with the sophisticated about thing-words. However, one should beware of speaking with the metaphysicians about rose-things.

Pseudo-object sentences are likely to give rise to pseudo-questions. This is the burden of the final chapter of Carnap’s book. Logical positivism offers hope, he feels, for genuine progress in philosophy because it identifies the errors of earlier philosophies, and it provides a technique for avoiding them. The problem of universals, for example, is not a real problem; it is a pseudo-problem that results from confusing the “formal mode” of speech and the “material mode” of speech, from being deceived by pseudo-object sentences such as “The rose is a thing.” People should speak in the formal mode about “predicate words” and not in the material mode about universals as things.

The position Carnap states in Philosophy and Logical Syntax has been stated much more fully in other of his works, especially in his earlier Logische Syntax der Sprache (1934; The Logical Syntax of Language, 1937). In some of his later works, he modified some of his earlier views—most notably, perhaps, by admitting semantics to philosophical legitimacy along with syntax. However, in its essentials, his position remained as stated in Philosophy and Logical Syntax. It is a view that has influenced contemporary philosophy greatly, and it is genuinely novel—a notable achievement in as ancient a discipline as philosophy. It probably has not had the influence outside philosophy that the intrinsic merit of the position deserves. This lack of widespread influence is quite probably the result of Carnap’s tendency, in his more extended writing, to use a formidable and forbidding battery of technical apparatus including strange terms and Gothic script. He unfortunately did not completely rid himself of a Germanic fascination with architectonics and a tendency to identify the profound with the unfamiliar. He also suffered from a tendency to oversimplify and trivialize the views he opposed. His rejection of the excesses of some idealist-philosophers is understandable, but less acceptable is his simple “resolution” of the problems with which the idealists wrestled by defining them out of existence as “pseudo-problems.” However, despite Carnap’s lack of understanding and sympathy for philosophical problems other than his own, he brought great skill to bear on the problems that did interest him. Carnap was a great innovator and an original thinker of enormous stature who strove to develop a logic that does not rest on any prior theory of meaning.

Principal Ideas Advanced

•Philosophy is the logical analysis of meaningful language.

•Meaningful language is either the language of logic and mathematics (involving analytic sentences) or the language of science (involving empirically verifiable synthetic sentences).

•Metaphysics and ethics are not legitimate parts of philosophy, for their language is meaningless.

•Logical analysis is logical syntax, and logical syntax is the study of the manipulation of signs in accordance with the rules of a language.

Bibliography

Ayer, A. J., ed. Logical Positivism. Glencoe, Ill.: Free Press, 1959. This anthology of writings by logical positivists contains three papers by Rudolf Carnap, others by his associates, and a useful introduction by the editor, who favored the movement.

Cirera, Ramon. Carnap and the Vienna Circle. Amsterdam: Rodopi, 1994. A vigorous survey and interpretation of the philosophical views of Carnap and his colleagues in the Vienna Circle.

Coffa, J. Alberto. The Semantic Tradition from Kant to Carnap. Cambridge, England: Cambridge University Press, 1991. This study traces connections between the views of Carnap and those of his predecessors regarding language and a priori knowledge.

Friedman, Michael. “Logical Truth and Analyticity in Carnap’s Logical Syntax of Language.” In History and Philosophy of Modern Mathematics, edited by William Asprey and Philip Kitcher. Volume 11 in Minnesota Studies in the Philosophy of Science. Minneapolis: University of Minnesota Press, 1988. In this article, Friedman, a leading philosopher of science, provides an incisive description and criticism of this central work of Carnap’s.

Goodman, Nelson. Ways of Worldmaking. Indianapolis, Ind.: Hackett, 1978. A discussion of the method of logical construction in philosophy by one of its practitioners.

Hintikka, Jaacko. Rudolf Carnap. Dordrecht: Reidel, 1975. A large collection of personal reminiscences of Carnap and discussions of his thought by colleagues and students who remember him with admiration.

Katz, Jerrold J. Cogitations. New York: Oxford University Press, 1986. Chapters 4, 5, and 6 present a view of analytic truth differing from Carnap’s yet not accepting Quine’s criticisms of Carnap.

Quine, Willard V. From a Logical Point of View. Cambridge, Mass.: Harvard University Press, 1953. The papers “On What There Is” and “Two Dogmas of Empiricism” contain explicit and implied criticisms of Carnap’s position.

Quine, Willard V. “Truth by Convention.” In Readings in Philosophical Analysis, edited by Herbert Feigl and Wilfred Sellars. New York: AppletonCentury-Crofts, 1949. An important early criticism of Carnap’s notion of analytic truth.

Richardson, Alan W. Carnap’s Construction of the World. Cambridge, England: Cambridge University Press, 1998. Richardson studies Carnap’s first major book and rejects the widespread interpretation that Carnap, in this book, aims to carry out Bertrand Russell’s epistemological program.

Schilpp, Paul, ed. The Philosophy of Rudolf Carnap. Volume 11 in The Library of Living Philosophers. La Salle, Ill.: Open Court, 1963. Contains Carnap’s autobiography, twenty-six substantial descriptive and critical essays by others, Carnap’s lengthy replies to these commentators, and a bibliography of Carnap’s writings.

Urmson, J. O. Philosophical Analysis: Its Development Between the Two World Wars. Oxford: Clarendon Press, 1956. Part 2 of this short, readable book describes logical positivism and criticizes its philosophical approach.

Weinberg, J. R. An Examination of Logical Positivism. London: Routledge, 1936. Weinberg’s survey of the then-very-new doctrines of logical positivism is for the most part breathlessly admiring although he has a few reservations.

Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. London: Routledge and Kegan Paul, 1922. The logical positivists borrowed several important doctrines from this dark but seminal work while rejecting its metaphysical aspect.