Alfred North Whitehead

Alfred North Whitehead was a notable mathematician, logician, educator and philosopher. The staggering complexity of Whitehead’s thought, coupled with the extraordinary literary quality of his writing, have conspired to make Whitehead (in an oft-repeated saying) one of the most-quoted but least-read philosophers in the Western canon. While he is widely recognized for his collaborative work with Bertrand Russell on the Principia Mathematica, he also made highly innovative contributions to philosophy, especially in the area of process metaphysics. Whitehead was an Englishman by birth and a mathematician by formal education. He was highly regarded by his students as a teacher and noted as a conscientious and hard-working administrator. The volume of his mathematical publication was never great, and much of his work has been eclipsed by more contemporary developments in the fields in which he specialized. Yet many of his works continue to stand out as examples of expository clarity without ever sacrificing logical rigor, while his theory of “extensive abstraction” is considered to be foundational in contemporary field of formal spatial relations known as “mereotopology.”

Whitehead’s decades-long focus on the logical and algebraic issues of space and geometry which led to his work on extension, became an integral part of an explosion of profoundly original philosophical work He began publishing even as his career as an academic mathematician was reaching a close. The first wave of these philosophical works included his Enquiry into the Principles of Natural Knowledge, The Concept of Nature, and The Principle of Relativity, published between 1919 and 1922. These books address the philosophies of science and nature, and include an important critique of the problem of measurement raised by Albert Einstein’s general theory of relativity. They also present an alternative theory of space and gravity. Whitehead built his system around an event-based ontology that interpreted time as essentially extensive rather than point-like.

Facing mandatory retirement in England, Whitehead accepted a position at Harvard in 1924, where he continued his philosophical output. His Science and the Modern World offers a careful critique of orthodox scientific materialism and presents his first worked-out version of the related fallacies of “misplaced concreteness” and “simple location.” The first fallacy is the error of treating an abstraction as though it were concretely real. The second is the error of assuming that anything that is real must have a simple spatial location. But the pinnacle of Whitehead’s metaphysical work came with his monumental Process and Reality in 1929 and his Adventures of Ideas in 1933. The first of these books gives a comprehensive and multi-layered categoreal system of internal and external relations that analyzes the logic of becoming an extension within the context of a solution to the problem of the one and the many, while also providing a ground for his philosophy of nature. The second is an outline of a philosophy of history and culture within the framework of his metaphysical scheme.

Biography

Alfred North Whitehead was born on February 15th, 1861 at Ramsgate in Kent, England, to Alfred and Maria Whitehead. Thought by his parents to be too delicate for the rough and tumble world of the English public school system, young Alfred was initially tutored at home. Ironically, when he was finally placed in public school, Whitehead became both head boy of his house and captain of his school’s rugby team. Whitehead always looked upon his days as a boy as a rather idyllic time. The education he received at home was always congenial to his natural habit of thinking, and he was able to spend long periods of time walking about in English country settings that were rich with history.

While Whitehead always enjoyed the classics, his true strength was with mathematics. Because of both its quality, and the unique opportunity to take the entrance examinations early, Alfred tested for Trinity College, Cambridge, in 1879, a year before he would otherwise have been allowed to enter. Whitehead’s focus was in mathematics, as were those of about half the hopefuls that were taking the competitive exams that year. While not in the very top tier, Whitehead’s exam scores were nevertheless good enough to gain him entrance into Trinity for the school year beginning in 1880, along with a £50 scholarship. While the money was certainly important, the scholarship itself qualified Whitehead for further rewards and considerations, and set him on the path to eventually being elected a Fellow of Trinity.

This happened in 1884, with the completion of his undergraduate work and his high standing in the finals examinations in mathematics for that year. Whitehead’s early career was focused on teaching, and it is known that he taught at Trinity during every term from 1884 to 1910. He traveled to Germany during an off-season at Cambridge (probably 1885), in part to learn more of the work of such German mathematicians as Felix Klein. Whitehead was also an ongoing member of various intellectual groups at Cambridge during this period. But he published nothing of note, and while he was universally praised as a teacher, the youthful Alfred displayed little promise as a researcher.

In 1891, when he was thirty years of age, Whitehead married Evelyn Wade. Evelyn was in every respect the perfect wife and partner for Alfred. While not conventionally intellectual, Evelyn was still an extremely bright woman, fiercely protective of Alfred and his work, and a true home-maker in the finest sense of the term. Although Evelyn herself was never fully accepted into the social structures of Cambridge society, she always ensured that Alfred lived in a comfortable, tastefully appointed home, and saw to it that he had the space and opportunity to entertain fellow scholars and other Cambrians in a fashion that always reflected well upon the mathematician.

It is also in this period that Whitehead began work on his first major publication, his Treatise on Universal Algebra. Perhaps with his new status as a family man, Whitehead felt the need to better establish himself as a Cambridge scholar. The book would ultimately be of minimal influence in the mathematical community. Indeed, the mathematical discipline that goes by that name shares only its name with Whitehead’s work, and is otherwise a very different area of inquiry. Still, the book established Whitehead’s reputation as a scholar of note, and was the basis for his 1903 election as a Fellow of the Royal Society.

It was after the publication of this work that Whitehead began the lengthy collaboration with his student, and ultimately Trinity Fellow, Bertrand Russell, on that monumental work that would become the Principia Mathematica. However, the final stages of this collaboration would not occur within the precincts of Cambridge. By 1910, Whitehead had been at Trinity College for thirty years, and he felt his creativity was being stifled. But it was also in this year that Whitehead’s friend and colleague Andrew Forsyth’s long-time affair with a married woman turned into a public indiscretion. It was expected that Forsyth would lose his Cambridge professorship, but the school took the extra step of withdrawing his Trinity Fellowship as well. Publicly in protest of this extravagant action, Whitehead resigned his own professorship (though not his Fellowship) as well. Privately, it was the excuse he needed to shake up his own life.

At the age of 49 and lacking even the promise of a job, Whitehead moved his family to London, where he was unemployed for the academic year of 1910 – 11. It was Evelyn who borrowed or bullied the money from their acquaintances that kept the family afloat during that time. Alfred finally secured a lectureship at University College, but the position offered no chance of growth or advancement for him. Finally in 1914, the Imperial College of Science and Technology in London appointed him as a professor of applied Mathematics.

It was here that Whitehead’s initial burst of philosophical creativity occurred. His decades of research into logic and spatial reasoning expressed itself in a series of three profoundly original books on the subjects of science, nature, and Einstein’s theory of relativity. At the same time, Whitehead maintained his teaching load while also assuming an increasing number of significant administrative duties. He was universally praised for his skill in all three of these general activities. However, by 1921 Whitehead was sixty years old and facing mandatory retirement within the English academic system. He would only be permitted to work until his sixty-fifth birthday, and then only with an annual dispensation from Imperial College. So it was that in 1924, Whitehead accepted an appointment as a professor of philosophy at Harvard University.

While Whitehead’s work at Imperial College is impressive, the explosion of works that came during his Harvard years is absolutely astounding. These publications include Science and the Modern World, Process and Reality, and Adventures of Ideas.

Whitehead continued to teach at Harvard until his retirement in 1937. He had been elected to the British Academy in 1931, and awarded the Order of Merit in 1945. He died peacefully on December 30th, 1947. Per the explicit instructions in his will, Evelyn Whitehead burned all of his unpublished papers. This action has been the source of boundless regret for Whitehead scholars, but it was Whitehead’s belief that evaluations of his thought should be based exclusively on his published work.

Major Thematic Structures

The thematic and historical analyses of Whitehead’s work largely coincide. However, these two approaches naturally lend themselves to slightly different emphases, and there are important historical overlaps of the dominating themes of his thought. So it is worthwhile to view these themes ahistorically prior to showing their temporal development.

The first of these thematic structures might reasonably be called “the problem of space.” The confluence of several trends in mathematical research set this problem at the very forefront of Whitehead’s own inquiries. James Clerk Maxwell’s Treatise on electromagnetism had been published in 1873, and Maxwell himself taught at Cambridge from 1871 until his death in 1879. The topic was a major subject of interest at Cambridge, and Whitehead wrote his Trinity Fellowship dissertation on Maxwell’s theory. During the same period, William Clifford in England, and Felix Klein and Wilhelm Killing in Germany were advancing the study of spaces of constant curvature. Whitehead was well aware of their work, as well as that of Hermann Grassmann, whose ideas would later become of central importance in tensor analysis.

The second major trend of Whitehead’s thought can be usefully abbreviated as “the problem of history,” although a more accurate descriptive phrase would be “the problem of the accretion of value.” Of the two themes, this one can be the more difficult to discern within Whitehead’s corpus, partly because it is often implicit and does not lend itself to formalized analysis. In its more obvious forms, this theme first appears in Whitehead’s writings on education. However, even in his earliest works, Whitehead’s concern with the function of symbolism as an instrument in the growth of knowledge shows a concern for the accretion of value. Nevertheless, it is primarily with his later philosophical work that this topic emerges as a central element and primary focus of his thought