Ten brilliant essays on logic appear in this collection, the work of one of the world’s best-known authorities on logic. In these thought-provoking arguments and meditations, Nobel Prize winner Bertrand Russell challenges the romantic mysticism of the 19th century, positing instead his theory of logical atomism. These essays are categorized by Russell as "entirely popular" and "somewhat more technical." The former include the well-known title essay plus "A Free Man’s Worship" and "The Place of Science in a Liberal Education"; the (...) latter comprise "On the Notion of Cause" and "Knowledge by Acquaintance and Knowledge by Description," along with other essays written in the cogent and witty style for which their author is justly renowned. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

According to Kant, “mathematical knowledge is the knowledge gained by reason from the construction of concepts.” In this paper, I shall make a few suggestions as to how this characterization of the mathematical method is to be understood.

By way of a reply to Charles Parsons's paper in the Nagel Festschrift, Kant's notion of intuition (Anschauung) is examined. It is argued that for Kant the immediate relation which an intuition has to its object is a mere corollary to its singularity. It does not presuppose (as Parsons suggests) any presence of the object to the mind. This is shown, e.g., by the Prolegomena § 8, where the objects of intuitions a priori are denied by Kant to be so (...) present. They yield knowledge, not in virtue of their immediacy but in virtue of their ideality. (shrink)

By what process of development he came to this opinion, though in itself an important and interesting question, is logically irrelevant to the inquiry how far the opinion itself is correct ; and among his opinions, when these have been ascertained, it becomes desirable to prune away such as seem inconsistent with his main doctrines, before those doctrines themselves are subjected to a critical scrutiny. Philosophic truth and falsehood, in short, rather than historical fact, are what primarily demand our attention (...) in this inquiry. (shrink)

Gegen die vielfach vertretene Auffassung, Frege habe die Hilbertsche Axiomatik nicht verstanden, wird nachzuweisen versucht, daß Frege die neue Methode nicht nur verstanden, sondem auch begrifflich präzise analysiert hat. Er definiert eine formale Theorie im Hilbertschen Sinn als eine Klasse von logisch beweisbaren Wenn-dann-Sätzen, die freie Variable enthalten und deren Wenn-Satz eine Konjunktion der Axiome im Hilbertschen Sinn ist. Er untersucht ferner das Verhältnis zwischen einer Hilbertschen Theorie und ihren Modellen (Anwendungen) und wendet seine allgemeinen Ergebnisse in erhellender Weise auf (...) Hilberts Grundlagen der Geometrie an. (shrink)