Russell’s Logicism Through Kantian Spectacles

russell: the Journal of Bertrand Russell Studies n.s. 34 (summer 2014): 79–94 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\kenneth\documents\type3401\rj 3401 193 red.docx 2014-05-14 8:54 PM oeviews RUSSELL’S LOGICISM THROUGH KANTIAN SPECTACLES Kevin C. Klement Philosophy / U. Massachusetts–Amherst Amherst, ma 01003, usa klement@philos.umass.edu Anssi Korhonen. Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context. (History of Analytic Philosophy series) Basingstoke, uk, and New York: Palgrave Macmillan, 2013. Pp. x + 277. isbn: 978-0-23057700 -8. £55; us$85. his new contribution to Palgrave Macmillan’s popular History of Analytical Philosophy series (edited by Michael Beaney) aims to outline the distinguishing philosophical outlook of Bertrand Russell’s early logicist period, exemplified most notably by Russell’s classic The Principles of Mathematics of 1903. The key themes of the book are Russell’s views in mathematical methodology and mathematical ontology, the universal applicability and nature of logic, and the relationship of logical and mathematical knowledge to the distinction between form and content in ontology and semantics. Throughout, Russell’s views are contrasted with the views of Kant and like-minded philosophers , who in many ways dominated the philosophical landscape prior to the emergence of analytic philosophy. The first chapter, “Russell’s Early Logicism: What Was It About?”, aims to differentiate how Russell understood his logicist project from the rather different aims of other philosophers with whom Russell is often lumped: Frege and logical empiricists such as A. J. Ayer and the members of the Vienna Circle . Korhonen notes aptly that while these thinkers were all in some sense logicists, their logicist aims were quite different: “there were in fact as many logicisms as there were logicists” (p. 21). In contrast to others, it was not principally important for Russell that mathematics be shown to be analytic. Russell gave different accounts of analyticity in different places. When employing a purely Kantian notion of analyticity on which analytic truths must be non-informative, Russell concluded that mathematics and logic were both synthetic à priori. When operating instead with a more Fregean notion of q= 80 Reviews c:\users\kenneth\documents\type3401\rj 3401 193 red.docx 2014-05-14 8:54 PM analyticity, on which all of modern logic counts as analytic, Russell claimed instead that mathematics is analytic. It was important for Russell that the “logic” to which mathematics could be shown to be reduced was the sophisticated and rich symbolic logic developed only at the end of the nineteenth century, not the more sterile syllogistic logics that had come before. Korhonen sees Russell’s project as a natural outgrowth in the increase in rigour brought about in nineteenth-century mathematics by its expansion into such areas as non-Euclidean geometry, and the increased interest in foundational aspects of other areas, such as real analysis. According to Korhonen, the importance of this increase in rigour in mathematics was not exclusively epistemological, but semantic, in that it made it easier to see how best to define certain mathematical concepts, allowing for the first time the definitions in terms of logical constants given by Russell. The relationship between Russell’s philosophy of mathematics and Kant’s looms large in the next two chapters. Chapter 2 delves into the Kantian and Russellian notions of mathematical methodology. Korhonen stresses an often overlooked similarity between Russell and Kant: both believed that the forms of judgment and reasoning used in traditional logic were inadequate to capture the semantic content and distinctive reasoning patterns necessary for mathematics. Citing, for example, the need for “construction postulates” in Euclidean geometry, Kant came to adopt what Korhonen dubs a “construction semantics”: the distinctive meaning or semantic content of mathematical concepts derives from the constructibility of instances of such concepts in pure intuition. Russell’s criticism of Kant’s philosophy of mathematics is often portrayed merely as the observation that more recent researches have shown that spatial diagrams are not necessary in mathematical proof. As Korhonen interprets Kant, however, mathematics requires an appeal to intuition not just in reasoning but for the very meaningfulness of its...

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