Alfred North Whitehead

Mathematician

  • Born: February 15, 1861
  • Birthplace: Ramsgate, Isle of Thanet, Kent, England
  • Died: December 30, 1947
  • Place of death: Cambridge, Massachusetts

British philosopher

Striving for a more comprehensive and unified system of human knowledge, Whitehead made major contributions to mathematical logic and produced a wholly original and modern metaphysics.

Areas of achievement Philosophy, mathematics

Early Life

Alfred North Whitehead was the last of four children born to Alfred Whitehead, a schoolmaster and clergyman, and Maria Sarah Buckmaster. Whitehead’s father was a typical Victorian country vicar who tirelessly tended to the needs of the people of the Isle of Thanet and was well loved by them. His grandfather, Thomas Whitehead, was more remarkable intellectually. The son of a prosperous farmer, he had single-handedly created a successful boys’ school at Ramsgate, unusual for its time in its emphasis on mathematics and science.

Ramsgate was a small, close-knit community in which history was a physical presence in the form of many ancient ruins, including Norman and medieval churches and Richborough Castle, built by the Romans when they occupied Britain. The surrounding waters were notoriously treacherous, and Whitehead remembered as a child hearing at night the booming of cannon and seeing rockets rise in the night sky, signaling a ship in distress. He believed that over the generations this environment instilled in the people an obstinacy and a tendency toward lonely thought.

Because he was small for his age and appeared frail, young Whitehead was not allowed to attend school or participate in children’s games. Instead, his father tutored him in Latin, Greek, and mathematics. Whitehead learned his lessons quickly and had free time for periods of solitary thought and rambles through the wild coastal countryside with its mysterious ruins.

In 1875, Whitehead left home and entered Sherborne in Dorsetshire, a well-regarded public school from which both of his brothers had been graduated. He had grown to love mathematics, and he excelled at it enough to be excused from some of the standard courses in classical languages and literature to study it more deeply. Ignoring his “frailty” he took up Rugby, developing his athletic skills with seriousness and tenacity. As captain of the team he compensated for his size with intelligence and leadership and became one of the best forwards in the history of the school. Later in life he said that being tackled in a Rugby game was an excellent paradigm for the “Real” as he meant the term philosophically.

Before his last year at Sherborne, he chose to take the grueling six-day scholarship examination for Trinity College, Cambridge, an examination that would determine not only entry and the needed financial assistance but, more important, eligibility for a fellowship and, therefore, his hopes for a career in mathematics. Whitehead took the examination a year earlier than he needed to, and passed.

Whitehead entered Trinity College in the autumn of 1880 as a participant in a special honors program that allowed him to study in his area of specialty, mathematics, exclusively for the full three years of undergraduate work. In the Cambridge of that time, however, perhaps more than today, important education also took place outside the classroom in lively, spontaneous discussions with other students, an experience that Whitehead described as being like “a daily Platonic Dialogue,” and that sometimes ran late into the night and into the early morning, ranging over politics, history, philosophy, science, and the arts. For a time, Whitehead became intensely interested in Immanuel Kant’s Critique of Pure Reason (1781), in which one of Kant’s primary aims was to explain how arithmetic and geometry, which appear to be self-consistent deductive systems without need of empirical verification, can yet give knowledge that can be reliably applied in the real world. This question was a central theme in much of Whitehead’s own work, though he became disenchanted with Kant’s explanations.

While his mathematics teachers were all of the highest caliber, one in particular, William Davidson Niven, significantly influenced Whitehead’s development by introducing him to the physics of James Clerk Maxwell, whose theories about electromagnetism called into question the all-encompassing explanatory power of the then-reigning Newtonian physics, opening the way to modern physics.

Life’s Work

Whitehead’s high scores on final examinations and his dissertation on Maxwell’s Treatise on Electricity and Magnetism (1873) won for him a six-year fellowship, allowing him free room and board at Cambridge and unlimited freedom for mathematical research.

Unlike most research fellows, however, Whitehead did not become immediately productive. By character he was not a piecemeal problem solver who worked in ever narrower and more refined areas of a subject, but rather an explorer seeking a wider and more unified perspective. He discovered and was impressed with the works of Hermann Günther Grassman, an all but forgotten German mathematician who had developed a new kind of algebra. Grassman’s Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844), along with George Boole’s The Mathematical Analysis of Logic (1847) and William Hamilton’s The Elements of Quaternions (1866), seemed to Whitehead to portend a whole new field of algebras of logic not limited to number and quantity and with exciting unexplored applications. Whitehead envisioned a work in which all these ideas would be brought together in a general theory that would include giving a spatial interpretation to logic, which would provide a more powerful general theory of geometry.

On a visit to his parents in Broadstairs in June of 1890, at a time when his great work did not seem to be going anywhere and he was contemplating conversion to Roman Catholicism, Whitehead was introduced to Evelyn Wade and fell in love. She was twenty-three years old, with black eyes and auburn hair and a vibrant personality. Though English, she spoke French as her native language, having been reared in a convent at Angers. Whitehead wasted no time and proposed to her romantically in a cave under the garden in his father’s vicarage. They were married in December of 1891. Their marriage was to produce three children. The youngest would be tragically killed in aerial combat in 1918. Evelyn loved and cared for Alfred and always made a place where he could work without interruption wherever they lived, but she had no interest in science or mathematics. However, she perfectly complemented his analytic temperament with a deep interest in people and a wonderful aesthetic sense. Her example, according to Whitehead, taught him that “beauty, moral and aesthetic, is the aim of existence: and that kindness, and love, and artistic satisfaction are among its modes of attainment” logic and science being important because they are useful in providing the conditions for periods of great art and literature. Whitehead’s later worldview incorporated these ideas.

Marriage was good for Whitehead. He soon began work in earnest on his project, the first volume of which was published in 1898 as A Treatise on Universal Algebra. The second volume was never written, partly because of another momentous event that occurred in the same year as Whitehead’s marriage: In 1890, Bertrand Russell entered Cambridge.

Whitehead, who happened to be reading examinations at the time, recognized Russell’s potential and, even though Russell’s scores were disappointingly low, saw to it some say by burning the scores that Russell received a scholarship. Their future collaboration on Principia Mathematica (1910-1913) was to be one of the most fruitful in the history of mathematics.

By 1903, Russell and Whitehead were colleagues. Russell had won a fellowship to Trinity College with a dissertation on the foundations of geometry. The two men found their individual interests and aims increasingly converging. With their wives, they attended the First International Congress of Philosophy in Paris in 1900 and met the great mathematician Giuseppe Peano, who had devised a symbolic notation that he was applying to the clarification of the foundations of mathematics. Russell, in his own work, had extended some of Peano’s ideas and in 1903 published Principles of Mathematics, in which he attempted to demonstrate that all mathematics, including geometry, could be deductively derived from a few concepts of logic. At the same time, Whitehead was working along similar lines in his projected second volume to his A Treatise on Universal Algebra. Their friendship and their intellectual excitement with what seemed to be a revolution in mathematics led inevitably toward collaboration, and they spent more and more time together.

At one point, the Russells even moved in with the Whiteheads. This, however, did not work out. Russell fell secretly and unrequitedly in love with Evelyn Whitehead he was by then very unhappy with his own wife and the Russells, without anything coming into the open, moved out amiably. The collaboration, however, was unaffected by this turn of events. The life of the mind was the greater passion for both men, and their work was proceeding well.

In 1903, they decided, rather than publish two separate additions to their own works, that they would concentrate on one joint work. This would become the monumental Principia Mathematica. They originally believed that it would take only about a year to complete. It took approximately nine. The manuscript ran to more than four thousand pages and required a four-wheeler to transport it to Cambridge Press. Whitehead, almost fifty, was now stooped from leaning over his desk for long periods. During the work on Principia Mathematica, Whitehead found time to write a short work that he considered to be his most original, “On Mathematical Concepts of the Material World.” Published in 1906, it is concerned with “the possible relations to space of the ultimate entities which (in ordinary language) constitute the ’stuff’ of space.” Anticipating Albert Einstein’s general theory of relativity, he criticized the classical concept of an absolute space occupied by pointlike atoms, defending instead a relativistic view that space is not independent of the things in it but is rather dependent for its structure on objects within it. Further, he proposed that the fundamental constituents of matter are not pointlike particles but are more complex entities such as lines of force, with particles being the result of the interactions of these lines. Neither this work nor Principia Mathematica met with great success when first published, being considered too philosophical by specialists.

In 1910, Whitehead rather mysteriously left his assured position at Trinity College and moved to London, where he had no position. Whitehead may have simply found himself in a rut; the reasons, however, are probably more complex. For one thing, he had become politically active in his last few years at Cambridge, speaking out for women’s rights and adopting a liberal position that outraged the university elite with their bias toward the rich and titled he and his wife were once pelted with oranges and rotten eggs while sitting behind a Labour Party speaker. A clue to his leaving Cambridge may also be found elsewhere. Years before, in 1887, as a member of the prestigious Cambridge Apostles discussion group, Whitehead had responded to the topic question, which asked which was more important in life, “Study or Marketplace?” with the terse comment, “Study with windows.” Whitehead probably had begun to sense that he could not commit himself to the ivory tower life of a don without trying to make some connection between his work and the wider world.

Indeed, his subsequent actions bear out this inference. Soon after settling in London, he wrote a popular exposition of mathematics for the layperson, An Introduction to Mathematics, which was published in 1911. From 1911 to 1914, he taught at University College, London, and from 1914 to 1924 he held a professorship at the Imperial College of Science and Technology in Kensington, all the while serving on various committees and councils setting the policies for London education. The aim of these institutions was to bring education to the masses, rationally adapting it to their needs and circumstances. Whitehead believed that the old elitist structure of the university must give way to new forms and that no less than the salvation of civilization was at stake. He compared this enterprise of mass education to the activities of the monasteries of the Middle Ages. His ideas on this subject appeared later in his books The Aims of Education, and Other Essays, published in 1929, and Essays in Science and Philosophy, published in 1947.

In 1923, another major shift occurred in Whitehead’s life. While still at the Imperial College of Science and Technology, Whitehead received an invitation to come to Harvard University to join the philosophy department. This invitation was no doubt based on his reputation as a philosopher of science. Whitehead was then sixty-two years old, an age when most people are thinking of retirement. Whitehead, however, had never taught philosophy and liked the idea, and his wife wholeheartedly supported the move. It turned out to be the beginning of a massive creative surge in a new direction, reaching far beyond the specialized boundaries of the philosophy of science.

Beginning with Science and the Modern World, based on the Lowell lectures he gave in 1925 and published that year, Whitehead called into question the view that values have nothing to do with the basic constituents of nature, which, according to the prevailing view that he called “scientific materialism,” consisted really only of matter in motion. In 1929, continuing this trend toward an all-inclusive worldview, there followed Process and Reality, which is considered to be one of the greatest works of metaphysics of all time, as well as one of the most forbidding. It propounds what Whitehead called “the philosophy of organism,” in a novel terminology. Adventures of Ideas, published in 1933, was his last major work and probably his most accessible book on philosophy, with extensive explorations of sociology, cosmology, philosophy, and civilization as revealed from the perspective of his new metaphysical views.

Whitehead’s reception in the United States was warm, and it provided him with an audience for the products of his far-ranging and independent intellect that he perhaps could not have had in his native England. He is remembered fondly by students and faculty as rosy-cheeked and cherubic, giving freely of his time, meeting with students often on Sunday evenings, and lecturing widely at eastern and midwestern universities. His last work, a small, lucid, and accessible work titled Modes of Thought (1938), was based on lectures he gave at Wellesley College and the University of Chicago. Whitehead died at Cambridge, Massachusetts, on December 30, 1947.

Significance

For more than fifty years, Whitehead applied his unique intellectual gifts successively to mathematics, education, and speculative philosophy and cosmology, always striving for an understanding of the nature of reality that could be applied to the betterment of humankind. Where he saw value in the ideas of others, he unselfishly helped those ideas to reach fruition. As a teacher, he brought out the best in his students, always with kindness and respect for their distinctive gifts. His later metaphysics is unique in the field for its scientific sophistication, yet it is free of the dogmatic rejection of the preeminence of human value in the world often found in the natural sciences.

Bibliography

Emmet, Dorothy M. “Whitehead, Alfred North.” Vol. 7 in The Encyclopedia of Philosophy, edited by Paul Edwards. New York: Macmillan, 1967. An excellent topical overview of Whitehead’s philosophy.

Epperson, Michael. Quantum Mechanics and the Philosophy of Alfred North Whitehead. New York: Fordham University Press, 2004. Examines the relationship between relativity theory, quantum mechanics, and Whitehead’s view of the cosmos, describing how his ideas incorporate science and philosophy.

Lowe, Victor. Alfred North Whitehead: The Man and His Work. 2 vols. Baltimore: Johns Hopkins University Press, 1985-1990. The fullest available account of Whitehead’s life through his tenure at Cambridge. Volume 2 covers Whitehead’s life in London and at Harvard. Lowe was a student of Whitehead and is an eminent authority on his work.

Malone-France, Derek. Deep Empiricism: Kant, Whitehead, and the Necessity of Philosophical Theism. Lanham, Md.: Lexington Books, 2007. Malone-France finds critical comparisons between Immanuel Kant’s transcendental realism and Whitehead’s organic realism.

Rose, Philip. On Whitehead. Belmont, Calif.: Wadsworth/Thomson Learning, 2002. A concise overview of Whitehead’s ideas, one in a series of books designed to provide students and other readers an introduction to the thoughts of significant philosophers.

Russell, Bertrand. The Autobiography of Bertrand Russell: 1872-1914. Boston: Little, Brown, 1951. Valuable for its account of the writing of Principia Mathematica, even though it is related from Russell’s somewhat biased point of view.

Schilpp, Paul Arthur, ed. The Philosophy of Alfred North Whitehead. 2d ed. New York: Tudor, 1951. A collection of critical essays on Whitehead that includes Whitehead’s autobiographical sketch and Lowe’s insightful essay “The Development of Whitehead’s Philosophy.” Contains complete bibliography of Whitehead’s works.

Whitehead, Alfred North. Alfred North Whitehead: An Anthology. Compiled by F. S. C. Northrop and Mason W. Gross. New York: Macmillan, 1953. Contains selections from all Whitehead’s major works and is thus an excellent starting point for anyone wishing to become familiar with his ideas.

‗‗‗‗‗‗‗. An Introduction to Mathematics. London: Williams and Norgate, 1911. Rev. ed. London: Oxford University Press, 1948. For anyone interested in Whitehead or in an exposition of the power of mathematics.

1901-1940: June 16, 1902: Russell Discovers the “Great Paradox”; 1904-1907: Brouwer Develops Intuitionist Foundations of Mathematics; 1907: Publication of James’s Pragmatism; 1910-1913: Principia Mathematica Defines the Logistic Movement; 1913: Husserl Advances Phenomenology; 1921: Wittgenstein Emerges as an Important Philosopher; 1922: First Meeting of the Vienna Circle.