The Ways of Paradox and Other Essays
Selected Logic Papers
Modern analytic philosophy is descended from a fertile if temporary union between the revived formal logic of our age and empiricist philosophy. In the last decades of the nineteenth century logic underwent, at the hands of Frege, its most important developments since Aristotle started it off as a systematic discipline. Frege’s work seemed to realize the prophetic dreams of Leibniz. With it formal logic came to cover a vastly wider field than the syllogistic logic of Aristotle had ever done. Where the logic of Aristotle was largely confined to the study of inferences owing their validity to the way the words “all,” “some,” and “not” occurred in them (as in the old favorite: all men are mortal, all Greeks are men, so all Greeks are mortal), the logic of Frege also covered inferences hinging on “and,” “or,” and “if.” Aristotle’s theory of the syllogism turned out to be a rather small, elementary segment of the second main part of Frege’s system. Frege’s logic was expressed with unprecedented rigor, and as a crowning achievement, seemed to afford a basis of indubitable certainties from which the whole of mathematics could be derived, effecting a unification of the two disciplines.
At much the same time Mach in Austria, and W. K. Clifford and Karl Pearson in England, were adapting features of the traditional empiricism of Mill to the interpretation of physics, a science that Mill knew only as an intelligent general reader. For this new philosophy of science the basis of all knowledge of fact was the reports of immediate, subjective sense-experience. All the statements of common observation and scientific theory owed their significance and truth to these basic assertions, of which they were held to be convenient abbreviations. Concepts of ordinary material things and of the theoretical entities of science were understood as shorthand for the concepts of direct perception: color patches in the visual field, felt pressures and so forth. Science in this view was an application of Mach’s principle of the economy of thought, a concise and convenient notation for the common patterns and regularities to be found in the streams of individual sense-experience.
The union of logic and empiricism was solemnized in the first really independent philosophical writings of the first man to combine the requisite logical and philosophical expertise, in Our Knowledge of the External World (1914) and Philosophy of Logical Atomism (1918) of Bertrand Russell. In these works the world is seen as an array of individual events of sense-experience, some related so as to constitute minds, some (including many of the previous group) as material things. For Russell the task of philosophy was to use the new resources of logic to analyze the stock of received knowledge, to reveal its ultimate constitution in basic empirical terms where this was possible, and to discard it as illusion where no such reduction could be effected.
WITTGENSTEIN’S Tractatus Logico-Philosophicus (1922) was the first brilliant wayward child of the marriage, but the parental lineaments …