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.
Table of Contents (Clicking on the links below will take you to those parts of this article)
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.)
(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.) (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.) (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.) (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.) (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.) (These volumes are the definitive biography of Whitehead.)
Mesle, C. Robert & Cobb, John B.: Process Theology: A Basic
Introduction (Atlanta: Chalice Press, September 1994.) (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.) (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.) (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.) (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.)
(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.) (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.) (This work is widely viewed
as the definitive text on Whitehead’s theory of science and
nature.)
