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.
1. 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.
2. Thought and Writings
a. 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.
b. The Early Mathematical Works
Whitehead's first major publication was his A Treatise on Universal
Algebra with Applications ("UA," 1898.) (Whenever appropriate, common
abbreviations will be given, along with the year of publication, for
Whitehead's major works.) Originally intended as a two-volume work,
the second volume never appeared as Whitehead's thinking on the
subject continued to evolve, and as the plans for Principia
Mathematica eventually came to incorporate many of the objectives of
this volume. Despite the "algebra" in the title, the work is primarily
on the foundations of geometry and formal spatial relations. UA offers
little in the way of original research by Whitehead. Rather, the work
is primarily expository in character, drawing together a number of
previously divergent and scattered themes of mathematical
investigation into the nature of spatial relations and their
underlying logic, and presenting them in a systematic form.
While the book helped establish Whitehead's reputation as a scholar
and was the basis of his election as a Fellow of the Royal Society, UA
had little direct impact on mathematical research either then or
later. Part of the problem was the timing and approach of Whitehead's
method. For while he was very explicit about the need for the rigorous
development of symbolic logic, Whitehead's logic was "algebraic" in
character. That is to say, Whitehead's focus was on relational systems
of order and structure preserving transformations. In contrast, the
approaches of Giuseppe Peano and Gottlob Frege, with their emphasis on
proof and semantic relations, soon became the focus of mathematical
attention. While these techniques were soon to become of central
importance for Whitehead's own work, the centrality of algebraic
methods to Whitehead's thinking is always in evidence, especially in
his philosophy of nature and metaphysics. The emphasis on structural
relations in these works is a key component to understanding his
arguments.
In addition, UA itself was one in a rising chorus of voices that had
begun to take the work of Hermann Grassmann seriously. Grassmann
algebras would come to play a vital role in tensor analysis and
general relativity. Finally, the opening discussion of UA regarding
the importance and uses of formal symbolism remains of philosophical
interest, both in its own right and as an important element in
Whitehead's later thought.
Other early works by Whitehead include his two short books, the Axioms
of Projective Geometry (1906) and the Axioms of Descriptive Geometry
(1907). These works take a much more explicitly logical approach to
their subject matter, as opposed to the algebraic techniques of
Whitehead's first book. However, it remains the case that these two
works are not about presenting cutting edge research so much as they
are about the clear and systematic development of existing materials.
As suggested by their titles, the approach is axiomatic, with the
axioms chosen for their illustrative and intuitive value, rather than
their strictly logical parsimony. As such, these books continue to
serve as clear and concise introductions to their subject matters.
Even as he was writing the two Axioms books, Whitehead was well into
the collaboration with Bertrand Russell that would lead to the three
volumes of the Principia Mathematica. Although most of the Principia
was written by Russell, the work itself was a truly collaborative
endeavor, as is demonstrated by the extant correspondence between the
two. The intention of the Principia was to deduce the whole of
arithmetic from absolutely fundamental logical principles. But
Whitehead's role in the project, besides working with Russell on the
vast array of details in the first three volumes, was to be the
principal author of a fourth volume whose focus would be the logical
foundations of geometry. Thus, what Whitehead had originally intended
to be the second volume of UA had transformed into the fourth volume
of the Principia Mathematica, and like that earlier planned volume,
the fourth part of Principia Mathematica never appeared. It would not
be until Whitehead's published work on the theory of extension, work
that never appeared independently but always as a part of a larger
philosophical enterprise, that his research into the foundations of
geometry would finally pay off.
c. Writings on Education
By the time the Principia was published, Whitehead had left his
teaching position at Trinity, and eventually secured a lectureship at
London's University College. It was in these London years that
Whitehead published a number of essays and addresses on the theory of
education. But it would be a mistake to suppose that his concern with
education began with the more teaching-oriented (as opposed to
research-oriented) positions he occupied after departing Cambridge.
Whitehead had long been noted as an exceptional lecturer by his
students at Cambridge. He also took on less popular teaching duties,
such as teaching at the non-degree conferring women's institutions
associated with Cambridge of Girton and Newham colleges.
Moreover, the concern for the conveyance of ideas is evident from the
earliest of Whitehead's writings. The very opening pages of UA are
devoted to a discussion of the reasons and economies of well-chosen
symbols as aids to the advancement of thought. Or again, the intention
underlying the two Axioms books was not so much the advancement of
research as the communication of achieved developments in mathematics.
Whitehead's book, An Introduction to Mathematics (1911), published in
the midst of the effort to get the Principia out, had no research
agenda per se. This book was again entirely devoted toward introducing
students to the character of mathematical thought, to the methods of
abstraction, the nature of variables and functions, and to offer some
sense of the power and generality of these formalisms.
Whitehead's essays that specifically address education often do so
with the explicit desire to revise the teaching of mathematics in
England. But they also argue, both explicitly and implicitly, for a
balance of liberal education devoted to the opening of the mind, with
technical education intended to facilitate the vocational aptitudes of
the student. Education for Whitehead was never just the mere
memorization of ancient stories and empty abstractions, any more than
it was just the technical training of the working class. It always
entailed the growth of the student as a fully functioning human being.
In this respect, as well as others, Whitehead's arguments compare
favorably with those of John Dewey [[hyperlink]].
Whitehead never systematized his educational thought the way Dewey
did, so these ideas must be gleaned from his various essays and looked
for as an implicit foundation to such larger works as his Adventures
of Ideas (see below). Many of Whitehead's essays on education were
collected together in The Aims of Education, published in 1929, as
well as his Essays in Science and Philosophy, published in 1948.
d. The Philosophy of Nature
Whitehead's interest in the problem of space was, at least from his
days as a graduate student at Cambridge, more than just an interest in
the purely formal or mathematical aspects of geometry. It is to be
recalled that his dissertation was on Maxwell's theory of
electromagnetism, which was a major development in the ideas that led
to Einstein's theories of special and general relativity. The famous
Michelson-Morely experiment to measure the so-called "Ether drift" was
a response to Maxwell's theory of electromagnetism. Einstein himself
offers only a generic nod toward the experiments regarding space and
light in his 1905 paper on special relativity. The problem Einstein
specifically cites in that paper is the lack of symmetry then to be
found in theories of space and the behavior of electromagnetic
phenomena. By 1910, when the first volume of the Principia Mathematica
was being published, Hermann Minkowski had reorganized the mathematics
of Einstein's special relativity into a four-dimensional non-Euclidean
manifold. By 1914, two years before the publication of Einstein's
paper on general relativity, theoretical developments had advanced to
the extent that an expedition to the Crimea was planned to observe the
predicted bending of stellar light around the sun during an eclipse.
This expedition was cancelled with the eruption of the First World
War.
These developments helped conspire to prevent Whitehead's planned
fourth volume of the Principia from ever appearing. A few papers
appeared during the war years, in which a relational theory of space
begins to emerge. What is perhaps most notable about these papers is
that they are no longer specifically mathematical in nature, but are
explicitly philosophical. Finally, in 1919 and 1920, Whitehead's
thought appeared in print with the publications of two books, An
Enquiry into the Principles of Natural Knowledge ("PNK," 1919) and The
Concept of Nature ("CN," 1920).
While PNK is much more formally technical than CN, both books share a
common and radical view of nature and science that rejects the
identification of nature with the mathematical tools used to
characterize its relational structures. Nature for Whitehead is that
which is experienced through the senses. For this reason, Whitehead
argues that there are no such things as "points" of either time or
space. An infinitesimal point is a high abstraction with no
experiential reality, while time and space are irreducibly extensional
in character.
To account for the effectiveness of mathematical abstractions in their
application to natural knowledge, Whitehead introduced his theory of
"extensive abstraction." By using the logical and topological
structures of concentric part-whole relations, Whitehead argued that
abstract entities such as geometric points could be derived from the
concrete, extensive relations of space and time. These abstract
entities, in their turn, could be shown to be significant of the
nature they had been abstractively derived from. Moreover, since these
abstract entities were formally easier to use, their significance of
nature could be retained through their various deductive relations,
thereby giving evidence for further natural significances by this
detour through purely abstract relations.
Whitehead also rejected "objects" as abstractions, and argued that the
fundamental realities of both experience and nature are events. Events
are themselves irreducibly extended entities, where the temporal /
durational extension is primary. "Objects" are the idealized
significances that retain a stable meaning through an event or family
of events.
It is important to note here that Whitehead is arguing for a kind of
empiricism. But, as Victor Lowe has noted, this empiricism is more
akin to the ideas of William James than it is to the logical
positivism of Whitehead's day. In other words, Whitehead is arguing
for a kind of Jamesian "radical empiricism," in which sense-data are
abstractions, and the basic deliverances of raw experience include
such things as relations and complex events.
These ideas were further developed with the publication of Whitehead's
The Principles of Relativity with Applications to Natural Science
("R," 1922). Here Whitehead proposed an alternative physical theory of
space and gravity to Einstein's general relativity. Whitehead's theory
has commonly been classified as "quasi-linear" in the physics
literature, when it should properly be describes as "bimetric."
Einstein's theory collapses the physical and the spatial into a single
metric, so that gravity and space are essentially identified.
Whitehead pointed out that this then loses the logical relations
necessary to make meaningful cosmological measurements. In order to
make meaningful measurements of space, we must know the geometry of
that space so that the congruence relations of our measurement
instruments can be projected through that space while retaining their
significance. Since Einstein's theory loses the distinction between
the physical and the geometrical, the only way we can know the
geometry of the space we are trying to measure is if we first know the
distributions of matter and energy throughout the cosmos that affect
that geometry. But we can only know these distributions if we can
first make accurate measurements of space. Thus, as Whitehead argued,
we are left in the position of first having to know everything before
we can know anything.
Whitehead argued that the solution to this problem was to separate the
necessary relations of geometry from the contingent relations of
physics, so that one's theory of space and gravity is "bimetric," or
is built from the two metrics of geometry and physics. Unfortunately,
Whitehead never used the term "bimetric," and his theory has often
been misinterpreted. Questions of the viability of Whitehead's
specific theory have needlessly distracted both philosophers and
physicists from the real issue of the class of theories of space and
gravity that Whitehead was arguing for. Numerous viable bimetric
alternatives to Einstein's theory of relativity are currently known in
the physics literature. But because Whitehead's theory has been
misclassified and its central arguments poorly understood, the
connections between Whitehead's philosophical arguments and these
physical theories have largely gone unnoticed.
e. The Metaphysical Works
The problems Whitehead had engaged with his triad of works on the
philosophy of nature and science required a complete re-evaluation of
the assumptions of modern science. To this end, Whitehead published
Science in the Modern World ("SMW," 1925). This work had both a
critical and a constructive aspect, although the critical themes
occupied most of Whitehead's attention. Central to those critical
themes was Whitehead's challenge to dogmatic scientific materialism
developed through an analysis of the historical developments and
contingencies of that belief. In addition, he continued with the
themes of his earlier triad, arguing that objects in general, and
matter in particular, are abstractions. What are most real are events
and their mutual involvements in relational structures.
Already in PNK, Whitehead had characterized electromagnetic phenomena
by saying that while such phenomena could be related to specific
vector quantities at each specific point of space, they express "at
all points one definite physical fact" (PNK, 29). Physical facts such
as electromagnetic phenomena are single, relational wholes, but they
are spread out across the cosmos. In SMW Whitehead called the failure
to appreciate this holism and the relational connectedness of reality,
"the fallacy of simple location." According to Whitehead, much of
contemporary science, driven as it was by the dogma of materialism,
was committed to the fallacy that only such things as could be
localized at a mathematically simple "point" of space and time were
genuinely real. Relations and connections were, in this dogmatic view,
secondary to and parasitic upon such simply located entities.
Whitehead saw this as reversing the facts of nature and experience,
and devoted considerable space in SMW to criticizing it.
A second and related fallacy of contemporary science was what
Whitehead identified in SMW as, "the fallacy of misplaced
concreteness." While misplaced concreteness could include treating
entities with a simple location as more real than those of a field of
relations, it also went beyond this. Misplaced concreteness included
treating "points" of space or time as more real than the extensional
relations that are the genuine deliverances of experience. Thus, this
fallacy resulted in treating abstractions as though they were
concretely real. In Whitehead's view, all of contemporary physics was
infected by this fallacy, and the resultant philosophy of nature had
reversed the roles of the concrete and the abstract.
The critical aspects of SMW were ideas that Whitehead had already
expressed (in different forms) in his previous publications, only now
with more refined clarity and persuasiveness. On the other hand, the
constructive arguments in SMW are astonishing in their scope and
subtlety, and are the first presentation of his mature metaphysical
thinking. For example, the word "prehension," which Whitehead defines
as "uncognitive apprehension" (SMW 69) makes its first systematic
appearance in Whitehead's writings as he refines and develops the
kinds and layers of relational connections between people and the
surrounding world. As the "uncognitive" in the above is intended to
show, these relations are not always or exclusively knowledge based,
yet they are a form of "grasping" of aspects of the world. Our
connection to the world begins with a "pre-epistemic" prehension of
it, from which the process of abstraction is able to distill valid
knowledge of the world. But that knowledge is abstract and only
significant of the world; it does not stand in any simple one-to-one
relation with the world. In particular, this pre-epistemic grasp of
the world is the source of our quasi- a priori knowledge of space
which enables us to know of those uniformities that make cosmological
measurements, and the general conduct of science, possible.
SMW goes far beyond the purely epistemic program of Whitehead's
philosophy of nature. The final three chapters, entitled "God,"
"Religion and Science," and "Requisites for Social Progress," clearly
announce the explicit emergence of the second major thematic strand of
Whitehead's thought, the "problem of history" or "the accretion of
value." Moreover, these topics are engaged with the same thoroughly
relational approach that Whitehead previously used with nature and
science.
Despite the foreshadowing of these last chapters of SMW, Whitehead's
next book may well have come as a surprise to his academic colleagues.
Whitehead's brief Religion in the Making ("RM," 1926) tackles no part
of his earlier thematic problem of space, but instead focuses entirely
on the second thematic of history and value. Whitehead defines
religion as "what the individual does with his own solitariness" (RM
16). Yet it is still Whitehead the algebraist who is constructing this
definition. Solitariness is understood as a multi-layered relational
modality of the individual in and toward the world. In addition, this
relational mode cannot be understood in separation from its history.
On this point, Whitehead compares religion with arithmetic. Thus, an
understanding of the latter makes no essential reference to its
history, whereas for religion such a reference is vital. Moreover, as
Whitehead states, "You use arithmetic, but you are religious" (RM 15).
Whitehead also argues that, "The purpose of God is the attainment of
value in the temporal world," and "Value is inherent in actuality
itself" (RM 100). Whitehead's use of the word "God" in the foregoing
invites a wide range of habitual assumptions about his meaning, most,
if not all, of which will probably be mistaken. The key element for
Whitehead is value. God, like arithmetic, is discussed in terms of
something which has a purpose. On the other hand, value is like being
religious in that it is inherent. It is something that is rather than
something that is used.
Shortly after this work, there appeared another book whose brevity
betrays its importance, Symbolism its Meaning and Effect ("S," 1927).
Whitehead's explicit interest in symbols was present in his earliest
publication. But in conjunction with his theory of prehension, the
theory of symbols came to take on an even greater importance for him.
Our "uncognitive" sense-perceptions are directly caught up in our
symbolic awareness as is shown by the immediacy with which we move
beyond what is directly given to our senses. Whitehead uses the
example of a puppy dog that sees a chair as a chair rather than as a
patch of color, even though the latter is all that impinges on the
dog's retina. (Whitehead may not have known that dogs are color blind,
but this does not significantly affect his example.) Thus, this work
further develops Whitehead's theories of perception and awareness, and
does so in a manner that is relatively non-technical. Because of the
centrality of the theory of symbols and perception to Whitehead's
later philosophy, this clarity of exposition makes this book a vital
stepping stone to what followed.
What followed was Process and Reality ("PR," 1929). This book is
easily one of the most dense and difficult works in the entire Western
canon. The book is rife with technical terms of Whitehead's own
invention, necessitated by his struggle to push beyond the inherited
limits of the available concepts toward a comprehensive vision of the
logical structures of becoming. It is here that we see the problem of
space receive its ultimate payoff in Whitehead's thought. But this
payoff comes in the form of a fully relational metaphysical scheme
that draws upon his theory of symbols and perception in the most
essential manner possible. At the same time, PR plants the seeds for
the further engagement of the problem of the accretion of value that
is to come in his later work. Because each process of becoming must be
considered holistically as an essentially organic unity, Whitehead
often refers to his theory as the "philosophy of organism."
PR invites controversy while defying brief exposition. Many of the
relational ideas Whitehead develops are holistic in character, and
thus do not lend themselves to the linear presentation of language.
Moreover, the language Whitehead needs to build his holistic image of
the world is often biological or mentalistic in character, which can
be jarring when the topic being discussed is something like an
electron. Moreover, Whitehead the algebraist was an intrinsically
relational thinker, and explicitly characterized the subject /
predicate mode of language as a "high abstraction." Nevertheless,
there are some basic ideas which can be quickly set out.
The first of these is that PR is not about time per se. This has been
a subject of much confusion. But Whitehead himself points out that
physical time as such only comes about with "reflection" of the
"divisibility" of his two major relational types into one another (PR
288 – 9). Moreover, throughout PR, Whitehead continues to endorse the
theory of nature found in his earlier triad of books on the subject.
So the first step in gaining a handle on PR is to recognize that it is
better thought of as addressing the logic of becoming, whereas his
books from 1919 – 1922 address the "nature" of time.
The basic units of becoming for Whitehead are "actual occasions."
Actual occasions are "drops of experience," and relate to the world
into which they are emerging by "feeling" that relatedness and
translating it into the occasion's concrete reality. When first
encountered, this mode of expression is likely to seem peculiar if not
downright outrageous. One thing to note here is that Whitehead is not
talking about any sort of high-level cognition. When he speaks of
"feeling" he means an immediacy of concrete relatedness that is vastly
different from any sort of "knowing," yet which exists on a relational
spectrum where cognitive modes can emerge from sufficiently complex
collections of occasions that interrelate within a systematic whole.
Also, feeling is a far more basic form of relatedness than can be
represented by formal algebraic or geometrical schemata. These latter
are intrinsically abstract, and to take them as basic would be to
commit the fallacy of misplaced concreteness. But feeling is not
abstract. Rather, it is the first and most concrete manifestation of
an occasion's relational engagement with reality.
This focus on concrete modes of relatedness is essential because an
actual occasion is itself a coming into being of the concrete. The
nature of this "concrescence," using Whitehead's term, is a matter of
the occasion's creatively internalizing its relatedness to the rest of
the world by feeling that world, and in turn uniquely expressing its
concreteness through its extensive connectedness with that world. Thus
an electron in a field of forces "feels" the electrical charges acting
upon it, and translates this "experience" into its own electronic
modes of concreteness. Only later do we schematize these relations
with the abstract algebraic and geometrical forms of physical science.
For the electron, the interaction is irreducibly concrete.
Actual occasions are fundamentally atomic in character, which leads to
the next interpretive difficulty. In his previous works, events were
essentially extended and continuous. And when Whitehead speaks of an
"event" in PR without any other qualifying adjectives, he still means
the extensive variety found in his earlier works (PR 73). But PR deals
with a different set of problems from that previous triad, and it
cannot take such continuity for granted. For one thing, Whitehead
treats Zeno's Paradoxes very seriously and argues that one cannot
resolve these paradoxes if one starts from the assumption of
continuity, because it is then impossible to make sense of anything
coming immediately before or immediately after anything else. Between
any two points of a continuum such as the real number line there are
an infinite number of other points, thus rendering the concept of the
"next" point meaningless. But it is precisely this concept of the
"next occasion" that Whitehead requires to render intelligible the
relational structures of his metaphysics. If there are infinitely many
occasions between any two occasions, even ones that are nominally
"close" together, then it becomes impossible to say how it is that
later occasions feel their predecessors – there is an unbounded
infinity of other occasions intervening in such influences, and
changing it in what are now undeterminable ways. Therefore, Whitehead
argued, continuity is not something which is "given;" rather it is
something which is achieved. Each occasion makes itself continuous
with its past in the manner in which it feels that past and creatively
incorporates the past into its own concrescence, its coming into
being.
Thus, Whitehead argues against the "continuity of becoming" and in
favor of the "becoming of continuity" (PR 68 – 9). Occasions become
atomically, but once they have become they incorporate themselves into
the continuity of the universe by feeling the concreteness of what has
come before and making that concreteness a part of the occasion's own
internal makeup. The continuity of space and durations in Whitehead's
earlier triad does not conflict with his metaphysical atomism, because
those earlier works were dealing with physical nature in which
continuity has already come into being, while PR is dealing with
relational structures that are logically and metaphysically prior to
nature.
Most authors believe that the sense of "atomic" being used here is
similar to, if not synonymous with, "microscopic." However, there are
reasons why one might want to resist such an interpretation. To begin
with, it teeters on the edge of the fallacy of simple location to
assume that by "atomic" Whitehead means "very small." An electron,
which Whitehead often refers to as an "electronic occasion," may have
a tiny region of most highly focused effects. But the electromagnetic
field that spreads out from that electron reaches far beyond that
narrow focus. The electron "feels" and is "felt" throughout this field
of influence which is not spatially limited. Moreover, Whitehead
clearly states that space and time are derivative notions from
extension whereas, "To be an actual occasion in the physical world
means that the entity in question is a relatum in this scheme of
extensive connection" (PR 288 – 9). The quality of being microscopic
is something that only emerges after one has a fully developed notion
of space, while actual occasions are logically prior to space and a
part of the extensive relations from which space itself is derived.
Thus it is at least arguably the case that the sense of "atomic" that
Whitehead is employing hearkens back more to the original Greek
meaning of "irreducible" than to the microscopic sense that pervades
physical science. In other words, the "atomic" nature of what is
actual is directly connected to its relational holism.
The structure of PR is also worth attention, for each of the five
major parts offers a significant perspective on the whole. Part I
gives Whitehead's defense of speculative philosophy and sets out the
"categoreal scheme" underlying PR. The second part applies these
categories to a variety of historical and thematic topics. Part three
gives the theory of prehensions as these manifest themselves with and
through the categories, and is often called the "genetic account." The
theory of extension, or the "coordinate account," constitutes part
four and represents the ultimate development of Whitehead's rigorous
thought on the nature of space. The last and final part presents both
a theory of the dialectic of opposites, and the minimalist role of God
in Whitehead's system as the foundation of coherence in the world's
processes of becoming.
Two of the features of part I that stand out are Whitehead's defense
of speculative philosophy, and his proposed resolution of the
traditional problem of the One and the Many. "Speculative philosophy"
for Whitehead is a phrase he uses interchangeably with "metaphysics."
However, what Whitehead means is a speculative program in the most
scientifically honorific sense of the term. Rejecting any form of
dogmatism, Whitehead states that his purpose is to, "frame a coherent,
logical, necessary system of general ideas in terms of which every
element of our experience can be interpreted" (PR 3). The second
feature, the solution to the problem of the "one and the many," is
often summarized as, "The many become one, and increase by one." This
means that the many occasions of the universe that have already become
contribute their atomic reality to the becoming of a new occasion
("the many become one"). However, this occasion, upon fully realizing
in its own atomic character, now contributes that reality to the
previously achieved realities of the other occasions ("and increase by
one").
The atomic becoming of an actual occasion is achieved by that
occasion's "prehensive" relations and its "extensive" relations. An
actual occasion's holistically felt and non-sequentially internalized
concrete evaluations of its relationships to the rest of the world is
the subject matter of the theory of "prehension," part III of PR. This
is easily one of the most difficult and complex portions of that work.
The development that Whitehead is describing is so holistic and
anti-sequential that it might appropriately be compared to James
Joyce's Finnegan's Wake. An actual occasion "prehends" its world
(relationally takes that world in) by feeling the "objective data" of
past occasions which the new occasion utilizes in its own
concrescence. This data is prehended in an atemporal and nonlinear
manner, and is creatively combined into the occasion's own manifest
self-realization. This is to say that the becoming of the occasion is
also informed by a densely teleological sense of the occasion's own
ultimate actuality, its "subjective aim" or what Whitehead calls the
occasion's "superject." Once it has become fully actualized, the
occasion as superject becomes an objective datum for those occasions
which follow it, and the process begins again.
This same process of concrescence is described in its extensive
characters in part IV, where the mereological (formal relations of
part and whole) as well as topological (non-metrical relations of
neighborhood and connection) characteristics of extension are
developed. Unlike the subtle discussion of prehensions, Whitehead's
theory of extension reads very much like a text book on the logic of
spatial relations. Indeed, a great deal of contemporary work in
artificial intelligence and spatial reasoning identifies this section
of PR as foundational to this field of research, which often goes by
the intimidating title of "mereotopology."
The holistic character of prehension and the analytical nature of
extension invite the reader to interpret the former as a theory of
"internal relations" and the latter as a theory of "external
relations." Put simply, external relations treat the self-identity of
a thing as the first, analytically given fact, while internal
relations treat it as the final, synthetically developed result. But
Whitehead explicitly associates internal relations with extension, and
externality with that of prehension. This seeming paradox can be
resolved by noting that, even though prehension is the process of the
actual occasion's "internalizing" the rest of reality as it composes
its own self-identity, the achieved result (the superject) is the
atomic realization of that occasion in its ultimate externality to the
rest of the world. On the other hand, the mereological relations of
part and whole from which extension is built, are themselves so
intrinsically correlative to one another that each only meaningfully
expresses its own relational structures to the extent that it
completely internalizes the other.
Whitehead was never one to revisit a problem once he felt he had
addressed it adequately. With the publication of PR and the final
version of his theory of extension, Whitehead never returned to the
'problem of space' except on those limited occasions when his later
work required that he mention those earlier developments. Those later
works were effectively focused upon the 'problem of history' to the
exclusion of all else. The primary book on this topic is Adventures of
Ideas ("AI," 1933).
AI is a pithy and engaging book whose opening pages entice the reader
with clear and evidently non-technical language. But it is a book that
needs to be approached with care. Whitehead assumes, without
explanation, knowledge on the part of his readers of the metaphysical
scheme of PR, and resorts to the terminology of that book whenever the
argument requires it. Indeed, AI is the application of Whitehead's
process metaphysics to the "problem of history." Whitehead surveys
numerous cultural forms from a thoroughly relational perspective,
analyzing the ways in which these connections contribute both to the
rigidities of culture and the possibilities for novelty in various
"adventures" in the accumulation of meanings and values. Many of the
forces in this adventure of meaning are blind and senseless, thus
presenting the challenge of becoming more deliberate in our processes
of building and changing them.
In line with this, two other works bear mentioning: The Function of
Reason ("FR," 1929) and Modes of Thought ("MT," 1938). FR presents an
updated version of Aristotle's three classes of soul (the vegetative,
the animate, and the rational); only in Whitehead's case, the
classifications are, as the title states, functional rather than
facultative. Thus, for Whitehead, the function of reason is "promote
the art of life," which is a three-fold function of "(i) to live, (ii)
to live well, (iii) to live better" (FR 4, 8). Thus, reason for
Whitehead is intrinsically organic in both origin and purpose. But the
achievement of a truly reasonable life is a matter that involves more
than just the logical organization of propositional knowledge. It is a
matter of full and sensitive engagement with the entire lived world.
This is the topic of MT, Whitehead's final major publication. In
arguing for a multiplicity of modes of thought, Whitehead offered his
final great rebellion against the excessive focus on language that
dominated the philosophical thought of his day. In this work,
Whitehead also offered his final insight as to the purpose and
function of philosophy itself. "The use of philosophy," Whitehead
concluded, "is to maintain an active novelty of fundamental ideas
illuminating the social system. It reverses the slow descent of
accepted thought towards the inactive commonplace." In this respect,
"philosophy is akin to poetry" (MT 174).
3. Influence and Legacy
Evaluating Whitehead's influence is a difficult matter. While
Whitehead's influence has never been great, in the opening years of
the 21st century it appears to be growing in a broad range of
otherwise divergent disciplines. Fulfilling his own vision of the use
of philosophy, Whitehead's ideas are a rich trove of alternative
approaches to traditional problems. His thoroughgoing relational and
process orientation offers numerous opportunities to reimagine the
ways in which the world is connected and how those connections
manifest themselves.
The most prominent area of ongoing Whiteheadian influence is within
process theology. While Whitehead's explicit philosophical treatments
of God seldom went beyond that of an ideal principle of maximal
coherence, many others have developed these ideas further. Writers
such as Charles Hartshorne and John Cobb have speculated on, and
argued for, a much more robust, ontological conception of God. Nothing
in Whitehead's own writings require such developments, but neither are
they in any way precluded. The God of process theology tends to be far
more personal and much more of a co-participant in the creative
process of the universe than that which one often finds in orthodox
religions.
Within philosophy itself, Whitehead's influence has been smaller and
much more diffuse. Yet those influences are likely to crop up in what
seem, on the surface at least, to be improbable places. The literature
here is too vast to enumerate, but it includes researches from all of
the major philosophical schools including pragmatism, analytical, and
continental thought. The topics engaged include ontology,
phenomenology, personalism, philosophical anthropology, ethics,
political theory, economics, etc.
There are also a variety of ways in which Whitehead's work continues
to influence scientific research. This influence is, again, typically
found only in the work of widely scattered individuals. However, one
area where this is not the case is Whitehead's theory of extension.
Whitehead's work on the logical basis of geometry is widely cited as
foundational in the study of mereotopology, which in turn is of
fundamental importance in the study of spatial reasoning, especially
in the context of artificial intelligence.
There is also a growing interest in Whitehead's work within physics,
where it is proving to be a valuable source of ideas to help
re-conceive the nature of physical relations. This is particularly
true of such bizarre phenomena as quantum entanglement, which seems to
violate orthodox notions of mechanistic interaction. There is a
renewed interest in Whitehead's arguments regarding relativity,
particularly because of their potential tie-in with other bimetric
theories of space and gravity. Other areas of interest include
biology, where Whitehead's holistic relationalism again offers
alternative models of explanation.
4. References and Further Reading
Those of Whitehead's primary texts which have been mentioned in the
article are listed below in chronological order. More technical works
have been "starred" with an asterisk. Original publication dates are
given, as well as more recent printings. Of these more recent
printings, those done by Dover Publications have been favored because
they retain the pagination of the original imprints. On the other
hand, the volume of the secondary literature on Whitehead is truly
astounding, and a comprehensive list would go far beyond the limits of
this article. So while the secondary works listed below can hardly be
viewed as definitive, they do offer a useful starting place. The
secondary sources are divided into two groups, those that are
relatively more accessible and those that are relatively more
technical.
a. Primary Sources
* *A Treatise on Universal Algebra (Cambridge: Cambridge
University Press, 1898.)
* *The Axioms of Projective Geometry (Cambridge: Cambridge
University Press, 1906.)
* *The Axioms of Descriptive Geometry, (Cambridge: Cambridge
University Press, 1907. Mineaola: Dover Phoenix Editions, 2005.)
o The two Axioms books are models of expository clarity, yet
they are still books on formal mathematics. Hence, they have been
reluctantly "starred."
* *Principia Mathematica, volumes I – III, with Bertrand Russell
(Cambridge: Cambridge University Press, 1910 – 1913.)
* An Introduction to Mathematics (London: Home University Library
of Modern Knowledge, 1911. Oxford: Oxford University Press, 1958.)
* *An Enquiry into the Principles of Natural Knowledge (Cambridge:
Cambridge University Press, 1919.)
* The Concept of Nature (Cambridge: Cambridge University Press,
1920. Mineola: Dover, May 2004.)
* *The Principle of Relativity with Applications to Physical
Science (Cambridge: Cambridge University Press, 1922. Mineola: Dover
Phoenix Editions, 2004.)
* Science and the Modern World (New York: The Macmillan Company,
1925. New York: The Free Press, 1967.)
* Religion in the Making (New York: The Macmillan Company, 1926.
New York: Fordham University Press, 1996.)
o This later edition is particularly useful because of the
detailed glossary of terms at the end of the text.
* Symbolism, Its Meaning and Effect (New York: The Macmillan
Company, 1927. New York: Fordham University Press, 1985.)
* The Aims of Education (New York: The Macmillan Company, 1929.
New York: The Free Press, 1967.)
* **Process and Reality (New York: The Macmillan Company 1929. New
York: The Free Press, 1978.)
o Easily one of the most difficult books in the entire
Western philosophical canon, this volume earns two asterisks.
* The Function of Reason (Princeton: Princeton University Press,
1929. Boston: Beacon Press, 1962.)
* *Adventures of Ideas (New York: The Macmillan Company, 1933. New
York: The Free Press, 1985.)
* Modes of Thought (New York: The Macmillan Company, 1938. New
York: The Free Press, 1968.)
* Essays in Science and Philosophy (New York: Philosophical
Library Inc., 1948.)
b. Secondary Sources
(Relatively more accessible secondary texts:)
* Eastman, Timothy E. and Keeton, Hank (editors): Physics and
Whitehead: Quantum, Process, and Experience (Albany: State University
of New York Press, January 2004.)
o This is an important recent survey of some of the ways in
which Whitehead's thought is being employed in contemporary physics.
* Kraus, Elizabeth M.: The Metaphysics of Experience (New York:
Fordham University Press, April 1979.)
o This book is a particularly useful companion to PR because
of the care with which Kraus has flow-charted the relational
structures of Whitehead's argument.
* Lowe, Victor: Alfred North Whitehead: The Man and his Work,
volumes I and II (Baltimore: The Johns Hopkins Press, 1985 & 1990.)
o These volumes are the definitive biography of Whitehead.
* Mesle, C. Robert & Cobb, John B.: Process Theology: A Basic
Introduction (Atlanta: Chalice Press, September 1994.)
o This is a solid and very readable survey of contemporary
process theology.
* Schilpp, Paul Arthur, editor: The Philosophy of Alfred North
Whitehead, "The Library of Living Philosophers," (LaSalle: Open Court
Publishing Company, 1951.)
o This book is a collection of essays on Whitehead's work by
his contemporaries.
(Relatively more technical secondary texts:)
* Casati, Roberto and Varzi, Achille C.: Parts and Places: The
Structures of Spatial Representation (Cambridge, MA: The MIT Press,
1999.)
o This text is a college level introduction to
mereotopology, and includes an extensive bibliography on the subject
and its history.
* Ford, Lewis: Emergence of Whitehead's Metaphysics, 1925-1929
(Albany: SUNY Press, 1985.)
o This book is an examination of the historical development
of Whitehead's metaphysical ideas.
* Hall, David L.: The Civilization of Experience, A Whitehedian
Theory of Culture (New York: Fordham University Press, New 1973.)
o Hall's work attempts, among other things, to derive an
ethical theory from Whitehead's metaphysics.
* Jones, Judith A. Intensity: An Essay in Whiteheadian Ontology
(Nashville: Vanderbilt University Press, 1998.)
o This work is widely considered to be one of the most
important pieces of secondary literature on Whitehead.
* Nobo, Jorge Luis.: Whitehead's Metaphysics of Extension and
Solidarity (Albany: SUNY Press, 1986.)
* Palter, William: Whitehead's Philosophy of Science (Chicago:
University of Chicago Press, June 1960.)
o This work is widely viewed as the definitive text on
Whitehead's theory of science and nature.
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