The next important development in analytic philosophy was initiated when Russell published a series of articles entitled “Philosophy of Logical Atomism” (1918–19), in which he acknowledged a debt to Wittgenstein, who had studied with Russell before World War I. Wittgenstein’s own version of logical atomism, presented in his difficult work Tractatus Logico-Philosophicus (1922), was tremendously influential in the subsequent development of analytic philosophy.

Russell’s choice of the words logical atomism to describe this viewpoint was, in fact, particularly apt. By the word logical Russell meant to sustain the position, described above, that through analysis—particularly with the aid of symbolic logic—the underlying logical structure of language can be revealed and that this disclosure, in turn, would show the fundamental structure of that which language is used to describe. By the word atomism Russell meant to emphasize the particulate nature of the results that his analyses and those of Wittgenstein seemed to yield.

On the linguistic level, the atoms in question are atomic propositions, the simplest statements that it is possible to make about the world; and on the level of what language talks about, the atoms are the simplest atomic facts, those expressible by atomic propositions. More complex propositions, called molecular propositions, are built up out of atomic propositions via the logical connectives—such as “… or …,” “… and …,” and “… not …”—and the truth-value of the molecular proposition is in each case a function of the truth-values of its component atomic propositions.

Language, then, must break down, upon analysis, into propositions that cannot be analyzed into any other simpler propositions; and, insofar as language mirrors reality, the world must then be composed of facts that are not constituted of other simpler facts. Atomic propositions themselves, however, are composed of strings of names that function, as Russell explained, in the strict logical sense; and atomic facts are composed of simple objects, the things that can thus be named.

The details of logical atomism have fascinated philosophers because of the way in which they not only formed a coherent whole but also seemed to follow inexorably from the doctrine’s central assumptions. There are close connections between logical atomism, which was perhaps the most metaphysical theory in contemporary analytic philosophy, and traditional empiricism. The decomposition of language and the world into atomic elements, for example, was a significant feature of the work of the classical empiricists Locke, Berkeley, and Hume. The thesis that the structure of language mirrors the structure of reality has as a consequence that the meaning of a proposition is the particular fact to which it is isomorphic. This “picture theory” of meaning, as it came to be called, was adumbrated by Russell and stated explicitly in the Tractatus. Another theme of logical atomism is that the deductive sciences—mathematics and logic—are based solely on the way that language operates and cannot reveal any truths about the world, not even about a world of entities called numbers. Finally, logical atomism, in Wittgenstein’s thought as opposed to Russell’s, was at one and the same time metaphysical—in the sense of conveying via pure reasoning something about how the world is—and antimetaphysical. Wittgenstein’s Tractatus is unique in the history of empiricism in its acceptance of the fact that it is itself a piece of metaphysics, even though part of its metaphysics is that metaphysics is impossible: the Tractatus says of itself that what it says cannot be coherently said. Only empirical science, according to Wittgenstein, can tell us anything about the world as it is. Yet the Tractatus apparently tells us about, for example, the relationship between language and the facts of the world. For Wittgenstein the solution of this apparent paradox lies in his distinction between what can be said and what can only be shown. There are certain things that can somehow be seen to be so—in particular, the ways in which language is connected with the world—though they cannot be straightforwardly stated. Although metaphysics is not strictly expressible in any language, the attempt to say metaphysical things, if done in the right way, can show what it cannot coherently express.

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Western philosophy: Analytic philosophy

Logical positivism

Wittgenstein’s Tractatus was both a landmark in the history of contemporary analytic philosophy and perhaps its most aberrant example. Not only did it contain a highly sophisticated metaphysics, but it also was an important influence on the most antimetaphysical school of analytic philosophy, viz., logical positivism. The central doctrines of this school were developed by a group of philosophers, scientists, and logicians centred in Vienna who came to be known as the Vienna Circle. Among the members of this group, Rudolf Carnap (1891–1970) and Moritz Schlick (1882–1936) have perhaps had the most influence on Anglo-American philosophy, though it was an English philosopher, A.J. Ayer (1910–89), who introduced the ideas of logical positivism to English philosophy in his widely read work Language, Truth and Logic (1936). Its main tenets have struck sympathetic chords among many analytic philosophers and are still important today, even if sometimes in repudiation.

Above all else, logical positivism was antimetaphysical; nothing can be learned about the world, it held, except through the methods of the empirical sciences. The positivists sought a method that would (1) determine whether a theory that seems to be about the world is really metaphysical and (2) show that such a metaphysical theory is, in fact, meaningless. This they found in the principle of verification. In its positive form, the principle says that the meaning of any statement that is really about the world is given by the methods employed for verifying its truth or falsity—the only allowable methods being, ultimately, those of observation and experiment. In its negative form, the principle says that no statement can be about the world unless there is some method of verification attached to it. The negative form was the weapon used against metaphysics and as a vindication of science as the only possible source of knowledge about the world. The principle would thus class as meaningless many philosophical and religious theories that purport to say something about the world but provide no way of testing the truth of the statements of which the theory is composed. In religion, for example, it would render suspect the statement that God exists, which, being metaphysical, would be strictly speaking meaningless.

The principle of verification ran almost immediately into difficulties, most of which were first raised by the positivists themselves. The attempt to work out these difficulties belongs to a more detailed study of the movement. It is sufficient to note here that, as a result of these problems, most subsequent analytic philosophers have been wary of appealing directly to the principle. It has, however, influenced philosophical work in more subtle ways.

With the principle of verification in hand, the positivists thought that they could show a great many theories to be nonsense. There were several areas of discourse, however, that failed the test of the principle but that nevertheless were impossible to rule out in this fashion. Foremost among them were the disciplines of mathematics and ethics. Mathematics (and logic) could hardly be written off as nonsense. Yet mathematical theorems are not verifiable by observation and experiment; they are known, in fact, by pure a priori reasoning alone. The answer to this problem seemed to be provided in Wittgenstein’s Tractatus, which held that the propositions of mathematics and logic are, in Kantian terms, analytic; i.e., like the statement “All bachelors are unmarried,” they are true not because they correctly describe the world but because they are consistent with or follow logically from the conventions underlying the use of the symbols involved.

About ethics—or, more precisely, about any statement expressing a judgment of value—the positivist view was quite different, yet still of lasting importance. On this view value judgments are not, like mathematical truths, necessary adjuncts to science; nor, obviously, are they true by definition or linguistic convention. The usual view of the positivists, as mentioned briefly above, is that what look like statements of fact—e.g., that one should not tell lies—are really expressions of one’s feelings toward a certain action, in the same way that “Ouch!” is an expression of one’s pain. Value judgments, therefore, are not about the world, and they are not really true or false. This doctrine, known as emotivism, illustrates the positivists’ divorce of ethics from science and once again reflects an old empiricist theme. The same theme can be seen, for example, in Hume’s dictum that one cannot derive an “ought” from an “is”: from matters of fact one cannot derive a conclusion about what ought to be.