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Whitehead, Alfred Northlocked

  • E. T. Whittaker
  • , revised by I. Grattan-Guinness

Alfred North Whitehead (1861–1947)

by Walter Stoneman, 1917

Whitehead, Alfred North (1861–1947), mathematician and philosopher, was born at Ramsgate on 15 February 1861, the last of the four children of the Revd Alfred Whitehead (1827–1898), at that time headmaster of a private school in Ramsgate, and later vicar of St Peter's, Isle of Thanet, and honorary canon of Canterbury, and his wife, Maria Sarah (1832–1924), daughter of William Buckmaster, a prosperous military tailor. An elder brother, Henry Whitehead, became ultimately bishop of Madras; his only child, Alfred's nephew, was John Henry Constantine Whitehead FRS (1904–1960), Waynflete professor of pure mathematics in Oxford University.

At Sherborne School, Whitehead won the Digby prize for mathematics and science three years in succession and in his last year was head of the school and captain of football and cricket. He proceeded in 1880 to Trinity College, Cambridge, where he was a scholar, and where he remained for the next thirty years. In the mathematical tripos of 1883 he was bracketed fourth wrangler, the next year he was elected a fellow of his college, and a few months afterwards was put on the staff as an assistant lecturer. He was also elected to the Apostles that year, but resigned three years later. On 16 December 1890 he married Evelyn Ada Maud Rice (1865–1950), daughter of Captain Arthur Robert Willoughby-Wade of the Seaforth Highlanders and niece of the Chinese scholar and diplomat Sir T. F. Wade. They had a daughter, Jessie, and two sons, North and Eric. Evelyn Whitehead formed a close but chaste friendship with Bertrand Russell, especially in 1900–01.

Systems of symbolic logic

Whitehead's first considerable work was published in 1898 under the title of A Treatise on Universal Algebra, with Applications. Its purpose was to investigate systems of symbolic reasoning allied to ordinary algebra, such as Hermann Grassmann's calculus of extension (the main influence on him), the quaternions of Sir W. R. Hamilton, and symbolic logic; the latter subject was treated very fully, the system described being based largely upon that devised by George Boole in 1854. The book was highly original, and gave Whitehead a reputation which led to his election as FRS in 1903.

One of Whitehead's pupils at Trinity, Bertrand Russell, became a specially attached disciple. In 1900 Whitehead and Russell went together to Paris to attend the international congress on philosophy, where they heard lectures by Giuseppe Peano of Turin and his followers, who had recently developed a new ideography for use in symbolic logic. Boole had used only the ordinary algebraic symbols, but Peano introduced symbols to represent logical notions such as 'is contained in', 'the set of all x's such that', 'there exists', 'is a', and 'the only'. Peano's ideograms represent constitutive elements of all the other notions in logic, just as the chemical atoms are the constitutive elements of all substances in chemistry, and they provide the basis of a formal language. Whitehead and Russell immediately recognized the superiority of this ideography and resolved to devote themselves to its development, and in particular to attempt thereby to settle the vexed question of the foundations of mathematics. They arrived at the ‘logicist’ position, that mathematics is a part of logic, so that a separate philosophy of mathematics does not exist, a view contradicting the Kantian doctrine that mathematical proofs depend on a priori forms of intuition. The investigation was published in the three colossal volumes of Principia mathematica which appeared in 1910–13, and which formed the greatest single contribution to symbolic logic for the time. The revisions and additions of the second edition of 1925–7 were produced solely by Russell, as Whitehead reported rather testily in Mind. There was to have been a fourth volume of the Principia, written by Whitehead and treating of geometries. He had made considerable progress with it; but the death in action of his son Eric in 1918 during the First World War seems to have destroyed his will to complete work of this kind.

In any case, logicism occupied only an (important) intermediate position in Whitehead's conception of mathematics in general, broader than that encompassed by logicism in admitting enquiry into creative and imaginative aspects and applications to the physical world. By contrast, for Russell logicism was the final philosophical position sought for mathematics. While Principia mathematica was Whitehead's main occupation during the 1900s, he wrote a remarkable paper, 'Mathematical concepts of the material world', published in the Philosophical Transactions of the Royal Society (1906). In this he was feeling his way to a general philosophy of nature: as the ultimate existents, he rejected particles of matter and points of space (thereby severing himself completely from classical physics), and in their stead postulated what he called linear objective reals. Some of the principles of his later philosophy first appear here.

In 1910 Whitehead resigned from his senior lectureship in mathematics at Trinity College (though not from his fellowship) and moved to London. This action was partly in protest against Trinity's acceptance of the resignation of the mathematician Andrew Forsyth who had eloped with a married woman, but it also reflected his desire to move into a fresh arena where his fairly progressive views on education might find expression. Later, in 1929 he published The Aims of Education and other Essays, in which he discusses such issues as the roles of classical and technical education, the mathematical curriculum, and the function of the universities. At first, having no teaching appointment, he wrote the short Introduction to Mathematics (1911). From that year to 1914 he was on the staff of University College, London, and from 1914 to 1924 he held a chair of applied mathematics at the Imperial College of Science and Technology.

Epistemology and metaphysics

From this time onwards Whitehead became more and more involved in questions which really belonged to epistemology and metaphysics. The discovery of the special theory of relativity in 1904 had opened up new prospects in the philosophy of nature. In 1915–17 he published several papers of a philosophical character, which were followed by two books, An Enquiry Concerning the Principles of Natural Knowledge (1919) and The Concept of Nature (1920). He now developed his own version of process philosophies associated with the names of H. L. Bergson, Samuel Alexander, and C. L. Morgan, and put forward the doctrine that the ultimate components of reality are events. An event is never instantaneous, it always lasts over a certain (although perhaps very short) duration of time: the notions of an 'instant' of time and a 'point' of space were not, in his scheme, accepted as primitive, but were obtained by a limiting process which he called the 'method of extensive abstraction'.

While Whitehead was engaged in his development of process metaphysics in 1914–19, the theory of general relativity was announced, in which the physical phenomenon of gravitation was expressed by a curvature of space-time, varying according to the physical situation from point to point over the whole universe. Whitehead criticized it, and devised an alternative theory which he set forth in a book, The Principle of Relativity, in 1922; his work did not, however, win general acceptance.

Philosophy at Harvard

In 1924 Whitehead resigned his chair at the Imperial College in order to accept a professorship in the department of philosophy of Harvard University, which he occupied until his final retirement in 1937. One of Whitehead's first public acts was to deliver the Lowell lectures at Boston in 1925; the expanded printed version came out later that year as Science and the Modern World, and sold very widely. Here he wedded his emerging philosophy of science to a historical survey of the development of the physical sciences.

In the session 1927–8 Whitehead returned to Britain in order to deliver the Gifford lectures at Edinburgh University. These, which were published in 1929 under the title Process and Reality, an Essay in Cosmology, may be regarded as the definitive exposition of his mature philosophy, to which he gave the name 'philosophy of organism' but which is commonly referred to as 'process philosophy'. Process philosophy contrasts with the tradition of substance philosophy which began with Descartes and which, characterized by the dualism of mind and matter, made knowledge problematic and thus brought epistemology to the centre of philosophical discussion. Whitehead challenges this centrality when he says that problems which are apparently epistemological have their origin in the Cartesian metaphysics of substance which, influenced as it was by the physics of its day, needs to be reassessed in the light of twentieth-century scientific thought. In Process and Reality, as in his earlier works, the beginning is made with events. Those events which are 'the final real things of which the world is made up' were now called 'actual entities'. Thus the category of 'actual entities' plays the same fundamental part in the philosophy of organism as the category of 'substance' plays in many older philosophies; but whereas the term 'substance' is associated with the notion of something that endures, an 'actual entity' according to Whitehead has no permanence. In order to emphasize the difference between his philosophy and the philosophies of substance, Whitehead described an actual entity not as a 'subject' but as a 'superject', a term designed to suggest its emergence from antecedent entities to itself. He accounted for the permanence that is discovered amid the flux of events by postulating what he called 'eternal objects', which have some resemblance to the 'forms' or 'ideas' of Plato; they have a potentiality of ingression into the becoming of actual entities, thereby contributing definiteness of character to them.

Whitehead also introduced a concept which he called 'creativity', corresponding more or less to Plato's chōra, or Aristotle's prōtē hylē or to the 'neutral stuff' of the 'neutral monists'. It is an ultimate, behind all forms, without a character of its own; particular eternal objects can, however, infuse their own character into it, thereby constituting actual entities. Thus it is by creativity that the actual world has its character of passage into novelty. Order is another essential notion, since for him the world is layered in various kinds of ordering.

It will be seen that Whitehead's writing abounded in new words, and new senses of old words; he had indeed the conviction that ordinary speech, which, as he had shown in Principia mathematica, is inadequate for the purposes of logic, is still more inadequate for the purposes of metaphysics. A new term 'prehension' signified that one actual entity grasps other actual entities into a unity. This word made it possible to express the nature of an actual entity very simply: 'The essence of an actual entity consists solely in the fact that it is a prehending thing.' The word 'concretion' or 'concrescence' is another novelty: it means that togetherness or unity that comes to exist as a result of the prehension. Every event originates as a unity of concrescent prehensions: the process of concrescence is Being. He pursued some educational corollaries in the collection of essays entitled The Aims of Education (1929), and the metaphysical and metaphorical elements of this approach in Adventures of Ideas (1933). These aspects of Whitehead's philosophy have made perhaps the greatest impact, as a major constituent of process philosophy, which is practised with most vigour in the USA.

Metaphysical principles, in Whitehead's view, are truths about the nature of God. His God, however, is not omnipotent, and cannot be identified with the God of the Christian religion: he is a non-temporal 'actual entity'. This philosophical theism, which is developed further in Religion in the Making (1926), replaced an earlier agnosticism which had itself been the successor to a brief involvement with Roman Catholicism in the 1890s and an Anglican upbringing. It has been the aspect of his thought which has attracted the most interest in the decades following his death. Even before his retirement in 1937 many philosophers at Harvard turned towards logical positivism and the philosophy of Wittgenstein, and among British philosophers Whitehead's later thought has never been popular. But theologians, as well as the philosopher Charles Hartshorne, have developed a 'process theology' which, centred in southern California, has given rise to numerous publications, by Anglicans, Catholics, Methodists, and those of other denominations.

Recognition and death

In his later years Whitehead was acknowledged as one of the greatest living philosophers, and was the recipient of many distinctions. In 1922 he was the first recipient of the James Scott prize of the Royal Society of Edinburgh; in 1925 he received the Sylvester medal of the Royal Society; and in 1930 the Butler medal of Columbia University. In 1931 he attained the honour of combining his fellowship of the British Academy with fellowship of the Royal Society, and in 1945 he was appointed to the Order of Merit. He died at Cambridge, Massachusetts, on 30 December 1947. He was cremated and his ashes scattered in Harvard Memorial Church on 6 January 1948. His widow destroyed all his manuscripts, as he had expressly desired.


  • V. Lowe, Alfred North Whitehead: the man and his work, 2 vols. (1985–90)
  • P. A. Schlipp, ed., The philosophy of Alfred North Whitehead, 2nd edn (1951)
  • R. M. Palter, Whitehead's philosophy of science (1960)
  • M. Code, Order and organism (1985)
  • I. Grattan-Guinness, ‘Review of V. Lowe, Alfred North Whitehead, vol. 1’, Transactions of the C. S. Peirce Society, 22 (1986), 61–8
  • D. W. Sherburne, ‘Whitehead, Alfred North’, The Cambridge dictionary of philosophy, ed. R. Audi (1995)
  • personal knowledge (1959)
  • private information (1959)
  • I. Grattan-Guinness, ‘Algebras, projective geometry, mathematical logic, and constructing the world: intersections in the philosophy of mathematics of A. N. Whitehead’, Historia Mathematica, 29 (2002), 427–62


  • CUL, Turnbull MSS, letters to G. E. Moore
  • McMaster University, Ontario, Hamilton, corresp. with Bertrand Russell


  • W. Stoneman, photograph, 1917, NPG [see illus.]
  • P. Drury, pencil drawing, 1928, Trinity Cam.