Alfred North Whitehead, who lived from 1861 to 1947, is chiefly remembered in England as Bertrand Russell’s collaborator in the three volumes of Principia Mathematica. He was, however, not only a professional mathematician – which Russell ceased to be after coming out joint seventh Wrangler in the first part of the Cambridge Tripos in 1893 – but a philosopher in his own right. It was as a philosopher that he was invited to occupy a Chair at Harvard in 1924, after retiring from the Chair of Applied Mathematics at the Imperial College of Science in the University of London. He retained his professorship at Harvard until 1937 and continued to live in Cambridge, Massachusetts until his death. His association with the English Cambridge lasted from 1880, when he came up to Trinity as a mathematical scholar from Sherborne, until 1910, when he resigned the Fellowship at Trinity which he had held for 26 years.
Professor Lowe was a pupil of Whitehead’s at Harvard and has remained a great admirer both of the man and of his work. He confesses in the preface that the research for this volume occupied him for nearly twenty years. The principal reason why it took so long was the almost total lack of any documents relating to Whitehead’s private life. Whitehead wrote very few letters and the few that he kept were destroyed by his widow, in accordance with his will, together with all his letters to her as well as all his manuscripts. The only letters on which Professor Lowe was able to draw were a small number written to Whitehead’s eldest son in the Twenties and a large number written to Bertrand Russell in the course of their ten years’ collaboration on Principia Mathematica. Professor Lowe was indebted to Russell, not only for the opportunity to read these letters, but also for Russell’s personal recollections of Whitehead, communicated in an interview when Russell was aged 93, for the information contained in the first two volumes of Russell’s Autobiography and most of all for the charming memoir of Whitehead which Russell included in Portraits from Memory.
The Isle of Thanet dominated the Whitehead that I knew. His grandfather had migrated to it from the lsle of Sheppey and, according to Whitehead, was said by his friends to have composed a hymn containing the following sublime stanza:
Lord of the Lambkin and the Lion
Lord of Jerusalem and Mount Zion,
Lord of the Comet and the Planet,
Lord of Sheppey and the Isle of Thanet.
Professor Lowe quotes this stanza in a chapter devoted to an account of Whitehead’s forbears, many of whom, on his father’s side, were schoolmasters or Anglican clergymen. Whitehead’s own father was both. The Thomas Whitehead to whom the quatrain was attributed took over a derelict school called Chatham House in Ramsgate in 1810 and within ten years, according to Professor Lowe, ‘made it one of the best schools in England’. I do not know what led Lowe to believe that ‘the great public schools that drew pupils from all over England came later.’
Whitehead went to Sherborne at the age of 15 and in due course became head of the school, a member of the cricket eleven and captain of the rugby fifteen. Professor Lowe’s conception of the old-fashioned public school system is exceedingly idyllic. ‘The light touch in giving orders, habits of courtesy and moderation, and appeals to fair play, “good form”, loyalty, and the good of the group became the most effective characteristics of prefectorial regimes.’ I fear that hardly anyone who attended an English public school at any time before the last world war would assent to this description. His account of the game of rugby football is almost equally implausible. It is possible that in Whitehead’s day not merely eight, but nine or ten, of the fifteen were forwards, but I find it hard to believe that every player except the ‘full back’ was ‘constantly in motion’.
In his fourth year at Cambridge, a few months before he obtained his Fellowship, Whitehead was elected an Apostle. Here Professor Lowe has had the advantage of being able to consult one of Whitehead’s successors in the brotherhood, Professor Richard Braithwaite, who allowed him to read the relevant passages in the minute book. This was of less assistance than one might have expected since none of Whitehead’s papers or speeches were in the record. Professor Lowe has had to make what he can, and makes rather more than he should, of the implications of Whitehead’s votes on a number of the issues that came up for debate. Even so, he has been obliged to devote most of the chapter in question to descriptions of Whitehead’s fellow Apostles of the period. I found them interesting on the whole, and I think I see how one of these persons contrived to have himself ‘twice knighted’.
For a short period before his marriage to Evelyn Wade in 1890, Whitehead, who had been brought up as an Anglican, toyed with the idea of becoming a Roman Catholic. He became an agnostic instead. Much later he arrived at the curious opinion, which he shared with another distinguished metaphysician, Samuel Alexander, that God is in the process of becoming, or, to put it more crudely, that he does not yet exist. This is something that Professor Lowe will need to elucidate in his second volume.
From this volume one receives the impression that the Whiteheads’ marriage was not entirely happy, mainly because of Whitehead’s absorption in his work, partly because of Mrs Whitehead’s psychosomatic heart attacks. At several points Lowe displays a veiled hostility to Mrs Whitehead. He believes that it was her extravagance, not Whitehead’s, as Russell himself alleged, that made it necessary for Russell to contribute substantially and also secretly, in so far as Whitehead himself did not know of it, to their financial support. I am sure that Russell’s main motive was the desire that the work on Principia Mathematica should proceed smoothly. At the same time Professor Lowe makes it appear very probable that Russell fell in love with Evelyn Whitehead, at some time between his falling out of love with his first wife Alys Pearsall Smith and the beginning of his affair with Ottoline Morrell, that she returned his affection, but that the affair was not consummated.
The first of the three volumes of Principia Mathematica appeared in 1910, the second in 1912 and the third in 1913. It was intended that Whitehead should write a fourth volume on the foundations of geometry but he never completed it. Before 1910 his major work on mathematics was A Treatise on Universal Algebra, with Applications, which came out in 1898. Apart from that, he published two short books, The Axioms of Projective Geometry and The Axioms of Descriptive Geometry, and about a dozen articles in various mathematical journals. He might have produced more if he had not had to do a moderate amount of teaching at Trinity, besides having some administrative duties. His treatise on algebra procured him election to the Royal Society, though it did not greatly interest most of his fellow mathematicians. Neither, indeed, did Principia Mathematica, for the unhappy reason that mathematicians tended, and still tend, to be suspicious of enquiries into the logical foundations of their subject.
Professor Lowe’s treatment of Whitehead’s mathematical work and of Principia Mathematica itself falls between two stools. It is too technical for the general reader and not critical enough for the expert. For instance, he avoids any assessment of Russell’s Theory of Types, without which it is impossible to estimate the value of Prinicipia Mathematica. He should be more at ease in his second volume, where I hope that he will deal not only with Whitehead’s metaphysics but also with his valuable contributions to the philosophy of science.