Alfred North Whitehead The Man And His Work, Vol. I, 1861–1910 by Victor Lowe (review)

reference to the anarchic splendour of a civilisation that Burckhardt taught us to appreciate. We began this review by asking how one writes a history of Italian Renaissance art. Vasari suggested that the history of Renaissance painting evincessome kind of underlying ordering principle, and we all know the kind of organic metaphor, local patriotism and individual ambition that underlies his ordering, itself a frequent object of teaching in Renaissance studies. Burckhardt’s monumental study of The Civilization of theRenaissancein Italy was described by its author as an ‘essay’ in the sense of a “tentative effort, a first draft”. Certainly, any modern attempt at a survey needs to emphasize theprovisional nature of its attempt and to get its categories straight. It is the ordering principles of these three books which are most open to criticism. Perhaps, in the end, enough surveyhistories existalready and, in focusing on the usefulnessof such an attempt, we need to remember that the major contributions to the art history of the Renaissance have taken the form of short essays on particular objects or issues (Panofsky, Wind, Meiss)or partial studiesof particular periods(Meiss,Antal, Wellfin). Perhaps one should attempt no more at present. But the apparent capacity of Renaissance art to transcend its context in forms of unrivalled (and particularly sensual) ideality adds to the continuing historical challenge to find pattern within the diversity of such art and to make this amazing period less strange to us. Reviewed by Roger Cranshaw and Adrian Lewis, 2 Mead Villas Box, Avon, U.K. AlfredNorthWhitehead TheMan And His Work, Vol. I, 1861- 1910. Victor Lowe. The Johns Hopkins University Press, Baltimore, 1985. 351 pp. Victor Lowe is without doubt the greatest living authority on the life and work of Alfred North Whitehead. He was a student of Whitehead’s while a graduate at Harvard, and was so impressed by the man that his work has becomeassociated with a professionallifetimeof expounding Whitehead’s theories and ideas to the public. This book, therefore, is likely to be the definitive study on Whitehead. Whitehead’s career began conventionally enough. He was brought up in a stereotypical Victorian environment and was sent to Sherborne School, where he excelled at classicsand mathematics. He then attended Trinity College, Cambridge , where he was elected to the famous CambridgeConversazioneSociety of gifted undergraduates (the ‘Apostles’), graduated fourth wrangler in the mathematical tripos of 1884, and commenced lecturing almost immediately thereafter. Although as a Cambridge undergraduate he was trained to be a combined pure-applied mathematician, his personal inclinations veered towards large, general questions about fundamental ideas in mathematics which were off the beaten path. His early interest in the differential geometry of spatial manifolds led him almost naturally to consider complex quantities represented by special generalized forms of ordinary algebra. His Univetval Algebra published in 1898 was an attempt to show that all geometry could be unified by reference to a particular type of algebra, and that this algebra itself was merely an outgrowth of an even more universaltype of symbolism contained in the calculus of formal logic. It was therefore almost inevitable that he should be interested in and drawn towards the work of his former pupil, Bertrand Russell, and his work on the foundations of mathematics. An alliance was established to produce a work which they hoped would placeall mathematical reasoning on a solid foundation of logic and thus prove that mathematics could lay claim to being a perfectly consistent system based upon elementary rules of formal reasoning. This goal would in some measure fulfil two needs: clear up unsolved problems encountered in the theory of infinite series and satisfy the aesthetic desire of an abstract thinker for clarity and certainty. Their joint work PrincipiaMathematica (3 vols) was hailed as the greatest singlecontribution to logic since Aristotle. Unfortunately, not many years after the publication of their book its major thesis proved untenable, and even during its early appearance it was not widelyread andfailedto influencethe development of either pure or applied mathematics. The book, however, was a truly unique collaboration. Russell was basically a logician and not asskilledin mathematics as Whitehead. Whitehead’s primary task (it would seem) was to apply the logical results of Russell to their...