Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

The great influence of Georg Cantor's theory of sets and transfinite arithmetic has led to a considerable interest in his life. It is well known that he had a remarkable and unusual personality, and that he suffered from attacks of mental illness; but the ‘popular’ account of his life is richer in falsehood and distortion than in factual content. This paper attempts to correct these misrepresentations by drawing on a wide variety of manuscript sources concerning Cantor's life and career, including (...) the texts of some important documents. An appendix describes the most important collection of missing manuscripts, whose location would help further the preparation of a biographical study of Cantor. (shrink)

A survey such as this by one of the world's leading thinkers of his entire philosophical canon, is clearly as important as it is fascinating.

E. Husserl, Logik und allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, mit ergänzenden Texten aus der ersten Fassung 1910/11. (Husserliana, 30.) Introduction by U. Panzer. Dordrecht:Kluwer, 1996. lxii + 554 pp. £130. ISBN0 792 33731 X D. Jacquette, Meinongian logic. The semantics of existence and nonexistence. Berlin and New York:Walter de Gruyter, 1996. xiii + 297 pp. DM 198. ISBN 3 11 014865 X M. Beaney (ed. and introduced), The Frege Reader. Blackwell Publishers, 1997. xv + 409 pp. £14.99/$21.95 (pbk). ISBN 0 631 (...) 194 452 Elliott Mendelson, Introduction to formal logic, fourth edition. London:Chapman & Hall, 1997. x + 440 pp. £45.00. ISBN 1 412 808307 Samuel Guttenplan, The languages of logic. An introduction to formal logic, second edition. Oxford:Blackwell, 1997. x + 429 pp. No price stated. ISBN 1 55786 988 X A.C. Grayling, An introduction to philosophical logic, third edition. Oxford:Blackwell, 1997. vii + 343 pp. £15.99/$27.99. ISBN 0 631 19982 9 Lewis Carroll, Das Spiel der Logik. Edited with an afterword by P. Good. Translated by M.Zöllner. Cologne:Propen Verlag/frommann-holzboog, 1997. 120pp. 32 DM. ISBN 3 7728 1998 2. (shrink)

E. Husserl, Logik und allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, mit ergänzenden Texten aus der ersten Fassung 1910/11. (Husserliana, 30.) Introduction by U. Panzer. Dordrecht:Kluwer, 1996. lxii + 554 pp. £130. ISBN0 792 33731 X D. Jacquette, Meinongian logic. The semantics of existence and nonexistence. Berlin and New York:Walter de Gruyter, 1996. xiii + 297 pp. DM 198. ISBN 3 11 014865 X M. Beaney (ed. and introduced), The Frege Reader. Blackwell Publishers, 1997. xv + 409 pp. £14.99/$21.95 (pbk). ISBN 0 631 (...) 194 452 Elliott Mendelson, Introduction to formal logic, fourth edition. London:Chapman & Hall, 1997. x + 440 pp. £45.00. ISBN 1 412 808307 Samuel Guttenplan, The languages of logic. An introduction to formal logic, second edition. Oxford:Blackwell, 1997. x + 429 pp. No price stated. ISBN 1 55786 988 X A.C. Grayling, An introduction to philosophical logic, third edition. Oxford:Blackwell, 1997. vii + 343 pp. £15.99/$27.99. ISBN 0 631 19982 9 Lewis Carroll, Das Spiel der Logik. Edited with an afterword by P. Good. Translated by M.Zöllner. Cologne:Propen Verlag/frommann-holzboog, 1997. 120pp. 32 DM. ISBN 3 7728 1998 2. (shrink)

This paper is concerned with the influence that the set theory of Georg Cantor bore upon the mathematical logic of Bertrand Russell. In some respects the influence is positive, and stems directly from Cantor's writings or through intermediary figures such as Peano; but in various ways negative influence is evident, for Russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, six sections compare and contrast their views on matters of common interest; irrational (...) numbers, infinitesimals, cardinal and ordinal numbers, the axiom of infinity, the paradoxes, and the axioms of choice. Two further sections compare the two men over more general questions: the role of logic and the philosophy of mathematics. In a final section I draw some conclusions. (shrink)

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...

This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly.

Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and 'Russell's paradox'.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory and to develop (...) his own theory of manifolds. I define certain issues involved and discuss how Husserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl's theories about sets and manifolds out of the realm of abstract theorizing and prompt further exploration of uncharted philosophical territory rich in philosophical implications. (shrink)

Few have entertained the idea that Georg Cantor, the creator of set theory, might have influenced Edmund Husserl, the founder of the phenomenological movement. Yet an exchange of ideas took place between them when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which his ideas were particularly malleable and changed considerably and definitively. Here their writings are examined to show how Husserl's and Cantor's ideas overlapped and crisscrossed in the (...) areas of philosophy and mathematics, arithmetization, abstraction, consciousness and pure logic, psychologism, metaphysical idealism, new numbers, and sets and manifolds. (shrink)

The usual objections to infinite numbers, and classes, and series, and the notion that the infinite as such is self-contradictory, may... be dismissed as groundless. There remains, however, a very grave difficulty, connected with the contradiction [of the class of all classes not members of themselves]. This difficulty does not concern the infinite as such, but only certain very large infinite classes.

One hundred years ago Gottlob Frege published a damaging, abusive review of Edmund Husserl’s Philosophy of Arithmetic. Although rather a lot has now been written abound Frege’s review and the role it might have played in the development of Husserl’s thought, much still remains to be rectified regarding Frege’s assessment of the book and the credence his review has been accorded. Philosophers have generally been all too willing to trust Frege’s judgment, and so all too ready to dismiss Husserl’s book (...) as irredeemably muddled. (shrink)