Stanford Encyclopedia of Philosophy
Charles Sanders Peirce
First published Fri Jun 22, 2001; substantive revision Wed Nov 12, 2014
Charles Sanders Peirce (1839–1914) was the founder of American pragmatism
(after about 1905 called by Peirce “pragmaticism” in order to differentiate
his views from those of William James, John Dewey, and others, which were
being labelled “pragmatism”), a theorist of logic, language,
communication, and the general theory of signs (which was often called by
Peirce “
semeiotic”), an extraordinarily prolific logician (mathematical and general),
and
a developer of an evolutionary, psycho-physically monistic metaphysical
system. Practicing geodesy and chemistry in order to earn a living, he
nevertheless considered scientific philosophy, and especially logic, to be his
true calling, his real vocation. In the course of his polymathic researches,
he wrote voluminously on an exceedingly wide range of topics, ranging from
mathematics, mathematical logic, physics, geodesy, spectroscopy, and
astronomy, on the one hand (that of mathematics and the physical sciences), to
psychology, anthropology, history, and economics, on the other (that of the
humanities and the social sciences).
* _1. Brief Biography_
(http://plato.stanford.edu/entries/peirce/#bio)
* _2. Difficulty of Access to Peirce's Writings_
(http://plato.stanford.edu/entries/peirce/#access)
* _3. Deduction, Induction, and Abduction_
(http://plato.stanford.edu/entries/peirce/#dia)
* _4. Pragmatism, Pragmaticism, and the Scientific Method_
(http://plato.stanford.edu/entries/peirce/#prag)
* _5. Anti-determinism, Tychism, and Evolutionism_
(http://plato.stanford.edu/entries/peirce/#anti)
* _6. Synechism, the Continuum, Infinites, and Infinitesimals_
(http://plato.stanford.edu/entries/peirce/#syn)
* _7. Probability, Verisimilitude, and Plausibility_
(http://plato.stanford.edu/entries/peirce/#prob)
* _8. Psycho-physical Monism and Anti-nominalism_
(http://plato.stanford.edu/entries/peirce/#psych)
* _9. Triadism and the Universal Categories_
(http://plato.stanford.edu/entries/peirce/#triad)
* _10. Mind and Semeiotic_
(http://plato.stanford.edu/entries/peirce/#mind)
* _11. Semeiotic and Logic_
(http://plato.stanford.edu/entries/peirce/#seme)
* _12. The Classification of the Sciences_
(http://plato.stanford.edu/entries/peirce/#class)
* _13. Logic_ (http://plato.stanford.edu/entries/peirce/#logic)
* _14. Peirce's Reduction Thesis_
(http://plato.stanford.edu/entries/peirce/#red)
* _15. Contemporary Practical Application of Peirce's Ideas_
(http://plato.stanford.edu/entries/peirce/#con)
* _16. Significant Students of Peirce_
(http://plato.stanford.edu/entries/peirce/#stud)
* _Bibliography_ (http://plato.stanford.edu/entries/peirce/#Bib)
* _Academic Tools_ (http://plato.stanford.edu/entries/peirce/#Aca)
* _Other Internet Resources_
(http://plato.stanford.edu/entries/peirce/#Oth)
* _Related Entries_ (http://plato.stanford.edu/entries/peirce/#Rel)
____________________________________
1. Brief Biography
Charles Sanders Peirce was born on September 10, 1839 in Cambridge,
Massachusetts, and he died on April 19, 1914 in Milford, Pennsylvania. His
writings extend from about 1857 until near his death, a period of approximately
57 years. His published works run to about 12,000 printed pages and his known
unpublished manuscripts run to about 80,000 handwritten pages. The topics
on which he wrote have an immense range, from mathematics and the physical
sciences at one extreme, to economics, psychology, and other social
sciences at the other extreme.
Peirce's father Benjamin Peirce was Professor of Mathematics at Harvard
University and was one of the founders of, and for a while a director of, the
U. S. Coast and Geodetic Survey as well as one of the founders of the
Smithsonian Institution. The department of mathematics at Harvard was
essentially built by Benjamin. From his father, Charles Sanders Peirce
received most
of the substance of his early education as well as a good deal of
intellectual encouragement and stimulation. Benjamin's didactic technique
mostly
took the form of setting interesting problems for his son and checking
Charles's solutions to them. In this challenging instructional atmosphere
Charles
acquired his lifelong habit of thinking through philosophical and
scientific problems entirely on his own. To this habit, perhaps, is to be
attributed
Charles Peirce's considerable originality.
Peirce graduated from Harvard in 1859 and received the bachelor of science
degree in chemistry in 1863, graduating summa cum laude. Except for his
remarkable marks in chemistry Peirce was a poor student, typically in the
bottom third of his class. Obviously, the standard curriculum bored him, so
that he mostly avoided doing seriously its required work. For thirty-two
years, from 1859 until the last day of 1891, he was employed by the U. S.
Coast
and Geodetic Survey, mainly surveying and carrying out geodetic
investigations. Some of this work Peirce undertook simply to finance his
diurnal
existence (and that of his first wife Melusina (Zina) Fay), while he devoted
the
main force of his thinking to abstract logic. Nevertheless, the geodetic
tasks involved making careful measurements of the intensity of the earth's
gravitational field by means of using swinging pendulums. The pendulums that
Peirce used were often of his own design. For over thirty years, then,
Peirce was involved in practical and theoretical problems associated with
making very accurate scientific measurements. This practical involvement in
physical science was crucial in his ultimately coming to reject scientific
determinism, as we shall see.
>From 1879 until 1884, Peirce maintained a second job teaching logic in the
Department of Mathematics at Johns Hopkins University. During that period
the Department of Mathematics was headed by the famous mathematician J. J.
Sylvester, whom Peirce had met earlier through his father Benjamin. This
teaching period also was characterized by Peirce's having several students who
made names for themselves in their own right. Among these were Oscar
Howard Mitchell, Allan Marquand, Benjamin Ives Gilman, Joseph Jastrow, Fabian
Franklin, Christine Ladd (later, after having married Fabian Franklin,
Christine Ladd-Franklin), Thorstein Veblen, and John Dewey. Brief commentary
will
be offered at the end of this essay on three of these figures: John Dewey,
Oscar Howard Mitchell, and Christine Ladd. It is sometimes said that
William James was also one of Peirce's students, but this claim is erroneous:
it
conflates the fact of James's being an old and a close friend of Peirce,
as well as being a fellow-member with Peirce in the so-called “Metaphysical
Club” in Cambridge, Massachusetts, with the non-fact of James's being a
student of Peirce at Johns Hopkins University along with John Dewey and
others.
Peirce's teaching job at Johns Hopkins was suddenly terminated for reasons
that are apparently connected with the fact that Peirce's second wife
(Juliette Annette Froissy, a.k.a. Juliette Annette Pourtalai) was a Gypsy,
moreover a Gypsy with whom Peirce had more or less openly cohabited before
marriage and before his divorce from his first wife Zina. (In fact Peirce
obtained his divorce from Zina only two days before marrying Juliette.) The
Johns
Hopkins position was Peirce's only academic employment, and after losing
it Peirce worked thereafter only for the U. S. Coast and Geodetic Survey
(and constructing entries for the Century Dictionary) and writing book reviews
for the Nation. The government employment came to an end the last day of
1891, ultimately because of funding objections to pure research (and perhaps
also to Peirce's extravagant spending and to his procrastination in
finishing his required reports) that were generated in an
ever-practical-minded
Congress. Thereafter, Peirce often lived on the edge of penury, eking out a
living doing intellectual odd-jobs (such as translating or writing
occasional pieces) and carrying out consulting work (mainly in chemical
engineering
and analysis). For the remainder of his life, except for money inherited
from his mother and aunt, Peirce was often in dire financial straits;
sometimes he managed to survive only because of the overt or covert charity of
relatives or friends, for example that of his old friend William James.
In his youth Peirce was amazingly precocious, and he began to study logic
seriously at an extraordinarily early age. According to noted Peirce scholar
Max Fisch in his“Introduction” to Volume 1 of The Writings of Charles S.
Peirce: A Chronological Edition, p. xviii, Peirce's introduction to and
first immersion in the study of logic came in 1851 within a week or two of his
turning 12 years of age. Remembering the occasion in 1910, in his “Note on
the Doctrine of Chances,” in Collected Papers of Charles S. Peirce, Volume
II, Section 408 (hereinafter such Collected Papers references will be
cited as CP, 2.408), Peirce himself remembered the crucial event as having
occurred in 1852, when he was 13 years old. Regardless of his exact age, at the
time of the event Charles encountered and then over a period of at most a
few days studied and absorbed a standard textbook of the time on logic by
Bishop Richard Whately. Having become fascinated by logic, he began to think
of all issues as problems in logic. During his freshman year at college
(Harvard), in 1855, when he was 16 years old, he and a friend began private
study of philosophy in general, starting with Schiller's Letters on the
Aesthetic Education of Man and continuing with Kant's Critique of Pure
Reason.
Schiller's distinction among the three basic human drives of Stofftrieb,
Formtrieb, and Speiltrieb Peirce never forgot or renounced, and it became
the basis for Peirce's distinction between the man of practical affairs, the
man of scientific activity, and the man of aesthetic practice. By Kant
Peirce was initially more or less repelled. After three years of intense study
of Kant, Peirce concluded that Kant's system was vitiated by what he called
its “puerile logic,” and about the age of 19 he formed the fixed
intention of devoting his life to the study of and to research in logic. It
was,
however, impossible at that time, as indeed Peirce's father Benjamin informed
him, to earn a living as a research logician; and Peirce described himself
at the time of his graduation from Harvard in 1859, just short of his 20th
birthday, as wondering “what I would do in life.” Within two years,
however, he had more or less resolved his problem. During those two years he
had
worked as an Aid on the Coast Survey, in Maine and Louisiana, then had
returned to Cambridge and had studied natural history and natural philosophy
at
Harvard. He said of himself that in 1861 he “No longer wondered what I
would do in life but defined my object.” It is evident that his adoption of
the profession of chemistry and his practice of geodesy allowed Charles both
to support himself (and before long also his first wife Zina) and to
continue to engage in researches on logic. From the early 1860's until his
death
in 1914 his output in logic was voluminous and varied. One of his logical
systems became the basis for Ernst Schroeder's great three-volume treatise
on logic, the Vorlesungen ueber die Algebra der Logik.
Peirce, then, had early and deep disagreements with Kant's position about
logic, and he never altered his view that Kant's view of logic was
superficial: “… he [i.e. Kant] never touches this last doctrine [i.e. logic]
without betraying marks of hasty, superficial study” (Collected Papers of
Charles
Sanders Peirce, Volume 2, Section 3; hereafter such Collected Papers
references will be cited as as CP, 2.3). Even worse, Peirce held, was the
Logik
of Hegel: Kant's fault “… is a hundredfold more true of Hegel's Logik …
. That work cannot justly be regarded as anything more than a sketch” (CP,
2.32).
Nevertheless, Peirce continued to respect and read the first Critique
throughout his life. For a fuller discussion of Peirce's own views about how
his work related to that of Kant, Hegel, and Schelling, see the supplementary
document:
_Peirce's View of the Relationship Between His Own Work and German
Idealism_
(http://plato.stanford.edu/entries/peirce/self-contextualization.html)
2. Difficulty of Access to Peirce's Writings
Peirce's extensive publications are scattered among various publication
media, and have been difficult to collect. Shortly after his death in 1914,
his widow Juliette sold his unpublished manuscripts to the Department of
Philosophy at Harvard University. Initially they were under the care of Josiah
Royce, but after Royce's death in 1916, and especially after the end of the
First World War, the papers were poorly cared for. Many of them were
misplaced, lost, given away, scrambled, and the like. Carolyn Eisele, one of
several genuine heroes in the great effort to locate and assemble Peirce's
writings, discovered a lost trunk full of Peirce's papers and manuscripts only
in the mid-1950s; the trunk had been secreted, apparently for decades, in
an unlit, obscure part of the basement in Harvard's Widener Library.
In the 1930's volumes of The Collected Papers of Charles Sanders Peirce
began to appear, with Charles Hartshorne, Paul Weiss, and Arthur Burks as
their editors. For almost three decades these volumes, and various collections
of entries culled from them were the only generally available source for
Peirce's thoughts. Unfortunately, many of the entries in the Collected
Papers are not integral pieces of Peirce's own design, but rather stretches of
writing that were cobbled together by the editors at their own discretion
(sometimes one might almost say “whim”) from different Peircean sources.
Often a single entry will consist of patches of writing from very different
periods of Peirce's intellectual life, and these patches might even be in
tension or outright contradiction with each other. Such entries in the
Collected Papers make very difficult reading if one tries to regard them as
consistent, sustained passages of argument. They also tend to give the reader a
false picture of Peirce as unsystematic, desultory, and unable to complete a
train of thought. In general, even though Peirce is often obscure and even
at his best is seldom easy to read, the Collected Papers make Peirce's
thinking look much more obscure than it really is.
The only sensible and intelligent way to publish the works of someone like
Peirce, who wrote voluminously and over such a long period of time (57
years), is to arrange the publication chronologically and to employ extremely
careful editing. In such a fashion, the entire set of Peircean works can be
presented, as Peirce conceived them and in their natural temporal setting
and order. Finally, beginning in 1976 with the organizational conception of
Max H. Fisch and the help of Edward Moore, the Peirce Dition Project (PEP)
was created at Indiana University-Purdue University at Indianapolis
(UIPUI). Then, under the PEP, in the 1980s, there began to appear a
meticulously
edited chronological edition of carefully selected works of Peirce: this is
the Writings of Charles S. Peirce: a Chronological Edition, edited by The
Peirce Edition Project of the Indiana University-Purdue University at
Indianapolis. Although the Chronological Edition has been fettered from time
to
time by lack of proper funding, the Chronological Edition has succeeded in
covering extremely well in its first seven published volumes the major
writings from 1857 to 1892. (At the present time, October 2014, Volume 7 is
still awaiting publication, even though Volume 8, covering writings from 1890
to 1892 already has been published. Volume 7 is to be an edition of Peirce's
definitions for the Century Dictionary. It is to be edited by the Peirce
Edition Project in conjunction with the University of Quebec at Montreal
(UQAM)), under the supervision of Professor Francois Latraverse.) The
impressive achievement of the PEP is finally making it possible to assess the
real
Peirce, instead of the chopped-up and then re-pasted-together picture of
previously available of Peirce. In particular the Chronological Edition has
made it possible to see the development of Peirce's thinking from its
earliest stages to its later developments. Questions long vexed in Peirce
scholarship are finally beginning to be debated usefully by Peirce scholars:
whether there is genuine systematic unity in Peirce's thought, whether his
ideas
changed or remained the same over time, in what particulars his thought
did change and why, when exactly certain notions were first conceived by
Peirce, whether there were definite “periods” in Peirce's intellectual
development, and what exactly Peirce meant by some of his more obscure notions
such as his universal categories (on which see below). Continued funding for
the Peirce Edition Project is obviously a crucial priority in the ongoing
effort to bring to public light the thoughts of this extremely important
American philosopher.
In addition to the Chronological Edition of the Peirce Edition Project,
other venues for editing and publishing Peirce's work are regularly found,
and there are several excellent editions of particular lectures,
lecture-series, chains of correspondence, and the like. Just four such editions
will be
mentioned here. First, there is the edition of Peirce's Cambridge
Conferences Lectures of 1898, edited by Kenneth Laine Ketner and with a forward
by
Hilary Putnam, entitled Reasoning and the Logic of Things. Second, there is
the edition of Peirce's Harvard Lectures on Pragmatism of 1903, edited by
Patricia Ann Turrisi, entitled Pragmatism as a Principle and Method of
Right Thinking. Third, there is the four-volume edition of Peirce's
mathematical writings edited by Carolyn Eisele, entitled The New Elements of
Mathematics by Charles S. Peirce. Fourth, there is the two-part edition of
Peirce's
writings on the history and logic of science edited by Carolyn Eisele,
entitled Historical Perspectives on Peirce's Logic of Science: A History of
Science.
3. Deduction, Induction, and Abduction
Prior to about 1865, thinkers on logic commonly had divided arguments into
two subclasses: the class of deductive arguments (a.k.a. necessary
inferences) and the class of inductive arguments (a.k.a. probable inferences).
About this time, Peirce began to hold that there were two utterly distinct
classes of probable inferences, which he referred to as inductive inferences
and abductive inferences (which he also called hypotheses and retroductive
inferences). Peirce reached this conclusion by entertaining what would happen
if one were to interchange propositions in the syllogism AAA-1 (Barbara):
All Ms are Ps; all Ss are Ms; therefore, all Ss are Ps. This valid
syllogism Peirce accepted as representative of deduction. But he also seemed
typically to regard it in connection with a problem of drawing conclusions on
the basis of taking samples. For let us regard being an M as being a member
of a population of some sort, say being a ball of the population of balls in
some particular urn. Let us regard P as being some property a member of
this population can have, say being red. And, finally, let us regard being an
S as being a member of a random sample taken from this population. Then
our syllogism in Barbara becomes: All balls in this urn are red; all balls in
this particular random sample are taken from this urn; therefore, all
balls in this particular random sample are red. Peirce regarded the major
premise here as being the Rule, the minor premise as being the particular
Case,
and the conclusion as being the Result of the argument. The argument is a
piece of deduction. In this example the argument is also an argument from
population to random sample that is also a necessary inference.
But now let us see what happens if we form a new argument by interchanging
the conclusion (the Result) with the major premise (the Rule). The
resultant argument becomes: All Ss are Ps (Result); all Ss are Ms (Case);
therefore, all Ms are Ps (Rule). This is the invalid syllogism AAA-3. But let
us
now construe it as pertaining to drawing conclusions on the basis of taking
samples. The argument then becomes: All balls in this particular random
sample are red; all balls in this particular random sample are taken from this
urn; therefore, all balls in this urn are red. What we have here is an
argument from sample to population. This sort of argument is what Peirce
understood to be the core meaning of induction. That is to say, for Peirce,
induction in the most basic sense is argument from random sample to
population.
It should be clear that inductive inference is not necessary inference: it
might well turn out that the claims stated in the premises are true even
though the claim made in the conclusion is false.
Let us now go further and see what happens if, from the deduction AAA-1, we
form a new argument by interchanging the conclusion (the Result) with the
minor premise (the Case). The resultant argument becomes: All Ms are Ps
(Rule); all Ss are Ps (Result); therefore, all Ss are Ms (Case). This is the
invalid syllogism AAA-2. But let us now regard it as pertaining to drawing
conclusions on the basis of taking samples. The argument then becomes: All
balls in this urn are red; all balls in this particular random sample are
red; therefore, all balls in this particular random sample are taken from
this urn. What we have here is nothing at all like an argument from
population to sample or an argument from sample to population: rather, it is a
form
of probable argument entirely different from both deduction and induction.
It has the air of conjecture or “educated guess” about it. This new type
of argument Peirce called hypothesis (also, retroduction, and also,
abduction). It should be clear that abduction is never necessary inference
There is no need to consider the variant of AAA-1 that is obtained by
interchanging the Rule and the Case in AAA-1. The resultant argument is of the
form AAA-4, which is exactly the same argument as AAA-1 with interchanged
premises. So it is simply deduction over again.
Peirce's thinking about deduction, induction, and abduction can be seen
also from examples he gives of arguments that are similar to the syllogisms he
discusses, but retain the universal affirmative judgment only for the
Case, using a definite percentage between 0% and 100% for both the Rule and
the
Result.
Corresponding to AAA-1 (deduction) we have the following argument: X% of
Ms are Ps (Rule); all Ss are Ms (Case); therefore, X% of Ss are Ps
(Result). Construing this argument, as we did before, as applying to drawing
balls
from urns, the argument becomes: X% of the balls in this urn are red; all
the balls in this random sample are taken from this urn; therefore, X% of
the balls in this random sample are red. Peirce still regards this argument
as being a deduction, even though it is not—as the argument AAA-1 is—a
necesary inference. He calls such an argument a “statistical deduction” or a “
probabilistic deduction proper.”
Corresponding to AAA-3 (induction) we have the following argument: X% of
Ss are Ps (Result); all Ss are Ms (Case); therefore, X% of Ms are Ps
(Rule). Construing this argument as applying to drawing balls from urns, the
argument becomes: X% of the balls in this random sample are red; all the balls
in this random sample are taken from this urn; therefore, X% of the balls
in this urn are red. Here we still have an argument whose essence is the
logical transition from a random sample to the population from which the
sample is taken. The inference is made by virtue of what Hans Reichenbach
called
“the straight rule”: the proportion of a trait found in the sample is
attributed also to the population.
Corresponding to AAA-2 (abduction) we have the following argument: X% of
Ms are Ps (Rule); X% of Ss are Ps (Result); therefore, all Ss are Ms (Case).
Construing this argument as applying to drawing balls from urns, the
argument becomes: X% of the balls in this urn are red; X% of the balls in
this
random sample are red; therefore, all the balls in this random sample are
taken from this urn. Again here we have the character of an educated guess
or inference to a plausible explanation.
Over many years Peirce modified his views on the three types of arguments,
sometimes changing his views but mostly extending them by expanding his
commentary upon the original trichotomy. Occasionally he swerved between one
view and another concerning which larger class of arguments a particular
instance or sub-type of argument belonged to. For example, he seemed to have
some hesitation about whether arguments from analogy should be construed as
inductions (arguments from a sample of the properties of things to a
population of the properties of things) or abductions (conjectures made on the
basis of sufficient similarity, which notion might not easily be analyzed in
terms of sets of properties).
The most important extension Peirce made of his earliest views on what
deduction, induction, and abduction involved was to integrate the three
argument forms into his view of the systematic procedure for seeking truth
that he
called the “scientific method.” As so integrated, deduction, induction,
and abduction are not simply argument forms any more: they are three phases
of the methodology of science, as Peirce conceived this methodology. In
fact, in Peirce's most mature philosophy he virtually (perhaps totally and
literally) equates the trichotomy with the three phases he discerns in the
scientific method. Scientific method begins with abduction or hypothesis:
because of some perhaps surprising or puzzling phenomenon, a conjecture or
hypothesis is made about what actually is going on. This hypothesis should be
such as to explain the surprising phenomenon, such as to render the
phenomenon more or less a matter of course if the hypothesis should be true.
Scientific method then proceeds to the stage of deduction: by means of
necessary
inferences, conclusions are drawn from the provisionally-adopted hypothesis
about the obtaining of phenomena other than the surprising one that
originally gave rise to the hypothesis. Conclusions are reached, that is to
say,
about other phenomena that must obtain if the hypothesis should actually be
true. These other phenomena must be such that experimental tests can be
performed whose results tell us whether the further phenomena do obtain or do
not obtain. Finally, scientific method proceeds to the stage of induction:
experiments are actually carried out in order to test the
provisionally-adopted hypothesis by ascertaining whether the deduced results do
or do not
obtain. At this point scientific method enters one or the other of two “
feedback loops.” If the deduced consequences do obtain, then we loop back to
the deduction stage, deducing still further consequences of our hypothesis and
experimentally testing for them again. But, if the deduced consequences do
not obtain, then we loop back to the abduction stage and come up with some
new hypothesis that explains both our original surprising phenomenon and
any new phenomena we have uncovered in the course of testing our first, and
now failed, hypothesis. Then we pass on to the deduction stage, as before.
The entire procedure of hypothesis-testing, and not merely that part of it
that consists of arguing from sample to population, is called induction in
Peirce's later philosophy.
An important part of Peirce's full conception of scientific method is what
he called the “economics (or: economy) of research.” The idea is that,
because research is difficult, research labor-time is valuable and should not
be wasted. Both in the creation of hypotheses to be tested and in the
experiments chosen to test these hypotheses, we should act so as to get the
very
most cognitive bang for the buck, so to say. The object is to proceed at
every stage so as to maximize the reduction in indeterminacy of our beliefs.
Peirce had an elaborate, mathematical theory of some aspects of the
economy of research, and he published several complex papers on this topic.
The
following section of the present article contains further information on
Peirce's notion of the economy of research.
4. Pragmatism, Pragmaticism, and the Scientific Method
Probably Peirce's best-known works are the first two articles in a series
of six that originally were collectively entitled Illustrations of the Logic
of Science and published in Popular Science Monthly from November 1877
through August 1878. The first is entitled “The Fixation of Belief” and the
second is entitled “How to Make Our Ideas Clear.” In the first of these
papers Peirce defended, in a manner consistent with not accepting naive
realism, the superiority of the scientific method over other methods of
overcoming doubt and “fixing belief.” In the second of these papers Peirce
defended
a “pragmatic” notion of clear concepts.
Perhaps the single most important fact to keep in mind in trying to
understand Peirce's philosophy concerning clarity and the proper method of
fixing
belief is that all his life Peirce was a practicing physical scientist:
already mentioned is the fact that he worked as a physical scientist for 32
years in his job with the United States Coast and Geodetic Survey. As Peirce
understood the topics of philosophy and logic, philosophy and logic were
themselves also sciences, although not physical sciences. Moreover, he
understood philosophy to be the philosophy of science, and he understood logic
to be the logic of science (where the word “science” has a sense that is
best captured by the German word Wissenschaft).
It is in this light that his specifications of the nature of pragmatism are
to be understood. It is also in this light that his later calling of his
views “pragmaticism,” in order to distinguish his own scientific philosophy
from other conceptions and theories that were trafficked under the title “
pragmatism,” is to be understood. When he said that the whole meaning of a
(clear) conception consists in the entire set of its practical
consequences, he had in mind that a meaningful conception must have some sort
of
experiential “cash value,” must somehow be capable of being related to some
sort
of collection of possible empirical observations under specifiable
conditions. Peirce insisted that the entire meaning of a meaningful conception
consisted in the totality of such specifications of possible observations. For
example, Peirce tended to spell out the meaning of dispositional
properties such as “hard” or “heavy” by using the same sort of counterfactual
constructions as, say, Karl Hempel would use. Peirce was not a simple
operationalist in his philosophy of science; nor was he a simple
verificationist in
his epistemology: he believed in the reality of abstractions, and in many
ways his thinking about universals resembles that of the medieval realists
in metaphysics. Nevertheless, despite his metaphysical leanings, Peirce's
views bear a strong family resemblance to operationalism and verificationism.
In regard to physical concepts in particular, his views are quite close to
those of, say, Einstein, who held that the whole meaning of a physical
concept is determined by an exact method of measuring it.
The previous point must be tempered with the fact that Peirce increasingly
became a philosopher with broad and deep sympathies for both transcendental
idealism and absolute idealism. His Kantian affinities are simpler and
easier to understand than his Hegelian leanings. Having rejected a great deal
in Kant, Peirce nevertheless shared with Charles Renouvier the view that
Kant's (quasi-)concept of the Ding an sich can play no role whatsoever in
philosophy or in science other than the role that Kant ultimately assigned to
it, viz. the role of a Grenzbegriff: a boundary-concept, or, perhaps a bit
more accurately, a limiting concept. A supposed “reality” that is “outside”
of every logical possibility of empirical or logical interaction with “it”
can play no direct role in the sciences. Science can deal only with
phenomena, that is to say, only with what can “appear” somehow in experience.
All scientific concepts must somehow be traceable back to phenomenological
roots. Thus, even when Peirce calls himself a “realist” or is called by
others a “realist,” it must be kept in mind that Peirce was always a realist
of the Kantian “empirical” sort and not a Kantian “transcendental realist.”
His realism is similar to what Hilary Putnam has called “internal realism.
” (As was said, Peirce was also a realist in quite another sense of he
word: he was a realist or an anti-nominalist in the medieval sense.)
Peirce's Hegelianism, to which he increasingly admitted as he approached
his most mature philosophy, is more difficult to understand than his
Kantianism, partly because it is everywhere intimately tied to his entire late
theory of signs (semeiotic) and sign use (semeiosis), as well as to his
evolutionism and to his rather puzzling doctrine of mind. There are at least
four
major components of his Hegelian idealism. First, for Peirce the world of
appearances, which he calls “the phaneron,” is a world consisting entirely
of signs. Signs are qualities, relations, features, items, events, states,
regularities, habits, laws, and so on that have meanings, significances, or
interpretations. Second, a sign is one term in a threesome of terms that
are indissolubly connected with each other by a crucial triadic relation
that Peirce calls “the sign relation.” The sign itself (also called the
representamen) is the term in the sign relation that is ordinarily said to
represent or mean something. The other two terms in this relation are called
the
object and the interpretant. The object is what would ordinarily would be
said to be the “thing” meant or signified or represented by the sign, what
the sign is a sign of. The interpretant of a sign is said by Peirce to be
that to which the sign represents the object. What exactly Peirce means by
the interpretant is difficult to pin down. It is something like a mind, a
mental act, a mental state, or a feature or quality of mind; at all events
the interpretant is something ineliminably mental. Third, the interpretant
of a sign, by virtue of the very definition Peirce gives of the
sign-relation, must itself be a sign, and a sign moreover of the very same
object that
is (or: was) represented by the (original) sign. In effect, then, the
interpretant is a second signifier of the object, only one that now has an
overtly mental status. But, merely in being a sign of the original object,
this
second sign must itself have (Peirce uses the word “determine”) an
interpretant, which then in turn is a new, third sign of the object, and again
is
one with an overtly mental status. And so on. Thus, if there is any sign at
all of any object, then there is an infinite sequence of signs of that
same object. So, everything in the phaneron, because it is a sign, begins an
infinite sequence of mental interpretants of an object.
But now, there is a fourth component of Peirce's idealism: Peirce makes
everything in the phaneron evolutionary. The whole system evolves. Three
figures from the history of culture loomed exceedingly large in the
intellectual
development of Peirce and in the cultural atmosphere of the period in
which Peirce was most active: Hegel in philosophy, Lyell in geology, and
Darwin
(along with Alfred Russel Wallace) in biology. These thinkers, of course,
all have a single theme in common: evolution. Hegel described an evolution
of ideas, Lyell an evolution of geological structures, and Darwin an
evolution of biological species and varieties. Peirce absorbed it all.
Peirce's
entire thinking, early on and later, is permeated with the evolutionary
idea, which he extended generally, that is to say, beyond the confines of any
particular subject matter. For Peirce, the entire universe and everything in
it is an evolutionary product. Indeed, he conceived that even the most
firmly entrenched of nature's habits (for example, even those habits that are
typically called “natural laws”) have themselves evolved, and accordingly
can and should be subjects of philosophical and scientific inquiry. One can
sensibly seek, in Peirce's view, evolutionary explanations of the
existence of particular natural laws. For Peirce, then, the entire phaneron
(the
world of appearances), as well as all the ongoing processes of its
interpretation through mental significations, has evolved and is evolving.
Now, no one familiar with Hegel can escape the obvious comparison: we have
in Peirce an essentially idealist theory that is similar to the idealism
that Hegel puts forward in the Phaenomenologie des Geistes. Furthermore, both
Hegel and Peirce make the whole evolutionary interpretation of the
evolving phaneron to be a process that is said to be logical, the “action” of
logic itself. Of course there are differences between the two philosophers.
For example, what exactly Hegel's logic is has been shrouded in mystery for
every Hegelian after Hegel himself (and some philosophers, for example
Popper, would say for every Hegelian including Hegel). By contrast Peirce's
logic is reasonably clear, and he takes great pains to work it out in
intricate
detail; basically Peirce's logic is the whole logical apparatus of the
physical and social sciences.
One implication of the unending nature of the interpretation of appearances
through infinite sequences of signs is that Peirce cannot be any type of
epistemological foundationalist or believer in absolute or apodeictic
knowledge. He must be, and is, an anti-foundationalist and a fallibilist. From
his earliest to his latest writings Peirce opposed and attacked all forms of
epistemological foundationalism and in particular all forms of Cartesianism
and a priorism. Philosophy must begin wherever it happens to be at the
moment, he thought, and not at some supposed ideal foundation, especially not
in some world of “private references.” The only important thing in
thinking scientifically to apply the scientific method itself. This method he
held
to be essentially public and reproducible in its activities, as well as
self-correcting in the following sense: No matter where different researchers
may begin, as long as they follow the scientific method, their results
will eventually converge toward the same outcome. (The pragmatic, or
pragmaticistic, conception of meaning implies that two theories with exactly
the
same empirical content must have, despite superficial appearances, the same
meaning.) This ideal point of convergence is what Peirce means by “the truth,”
and “reality” is simply what is meant by “the truth.” That these
Peircean notions of reality and truth are inherently idealist rather than
naively
realist in character should require no special pleading.
Connected with Peirce's anti-foundationalism is his insistence on the
fallibility of particular achievements in science. Although the scientific
method will eventually converge to something as a limit, nevertheless at any
temporal point in the process of scientific inquiry we are only at a
provisional stage of it and cannot ascertain how far off we may be from the
limit to
which we are somehow converging. This insistence on the fallibilism of
human inquiry is connected with several other important themes of Peirce's
philosophy. His evolutionism has already been discussed: fallibilism is
obviously connected with the fact that science is not shooting at a fixed
target
but rather one that is always moving. What Peirce calls his “tychism,”
which is his anti-deterministic insistence that there is objective chance in
the world, is also intimately connected to his fallibilism. (Tychism will be
discussed below.) Despite Peirce's insistence on fallibilism, he is far
from being an epistemological pessimist or sceptic: indeed, he is quite the
opposite. He tends to hold that every genuine question (that is, every
question whose possible answers have empirical content) can be answered in
principle, or at least should not be assumed to be unanswerable. For this
reason, one his most important dicta, which he called his first principle of
reason, is “Do not block the way of inquiry!”
For Peirce, as we saw, the scientific method involves three phases or
stages: abduction (making conjectures or creating hypotheses), deduction
(inferring what should be the case if the hypotheses are the case), and
induction
(the testing of hypotheses). The process of going through the stages should
also be carried out with concern for the economy of research. Peirce's
understanding of scientific method, then, is not very different from the
standard idea of scientific method (which, indeed, perhaps itself derived
historically from the ideas of William Whewell and Peirce) as being the method
of
constructing hypotheses, deriving consequences from these hypotheses, and
then experimentally testing these hypotheses (guided always by the
economics of research). Also, as was said above, Peirce increasingly came to
understand his three types of logical inference as being phases or stages of
the
scientific method. For example, as Peirce came to extend and generalize his
notion of abduction, abduction became defined as inference to and
provisional acceptance of an explanatory hypothesis for the purpose of testing
it.
Abduction is not always inference to the best explanation, but it is always
inference to some explanation or at least to something that clarifies or
makes routine some information that has previously been “surprising,” in
the sense that we would not have routinely expected it, given our
then-current state of knowledge. Deduction came to mean for Peirce the drawing
of
conclusions as to what observable phenomena should be expected if the
hypothesis is correct. Induction came for him to mean the entire process of
experimentation and interpretation performed in the service of hypothesis
testing.
A few further comments are perhaps in order in connection with Peirce's
idea of the economy (or: the economics) of research. Concern for the economy
of research is a crucial and ineliminable part of Peirce's idea of the
scientific method. He understood that science is essentially a human and
social
enterprise and that it always operates in some given historical, social,
and economic context. In such a context some problems are crucial and
paramount and must be attended-to immediately, while other problems are
trivial or
frivolous or at least can be put off until later. He understood that in
the real context of science some experiments may be vitally important while
others may be insignificant. Peirce also understood that the economic
resources of the scientist (time, money, ability to exert effort, etc.) are
always scarce, even though all the while the “great ocean of truth,” which
lies
undiscovered before us, is infinite. All resources for carrying out
research, such as personnel, person-hours, and apparatus, are quite costly;
accordingly, it is wasteful, indeed irrational, to squander them. Peirce
proposed, therefore, that careful consideration be paid to the problem of how
to
obtain the biggest epistemological “bang for the buck.” In effect, the
economics of research is a cost/benefit analysis in connection with states of
knowledge. Although this idea has been insufficiently explored by Peirce
scholars, Peirce himself regarded it as central to the scientific method and
to the idea of rational behavior. It is connected with what he called “
speculative rhetoric” or “methodeutic” (which will be discussed below).
5. Anti-determinism, Tychism, and Evolutionism
Against powerful currents of determinism that derived from the
Enlightenment philosophy of the eighteenth century, Peirce urged that there
was not the
slightest scientific evidence for determinism and that in fact there was
considerable scientific evidence against it. Always by the words “science”
and “scientific” Peirce understood reference to actual practice by
scientists in the laboratory and the field, and not reference to entries in
scientific textbooks. In attacking determinism, therefore, Peirce appealed to
the
evidence of the actual phenomena in laboratories and fields. Here, what is
obtained as the actual observations (e.g. measurements) does not fit
neatly into some one point or simple function. If we take, for example, a
thousand measurements of some physical quantity, even a simple one such as
length
or thickness, no matter how carefully we may do so, we will not obtain the
same result a thousand times. Rather, what we get is a distribution
(often, but not always and certainly not necessarily, something akin to a
normal
or Gaussian distribution) of hundreds of different results. Again, if we
measure the value of some variable that we assume to depend on some given
parameter, and if we let the parameter vary while we take successive
measurements, the result in general will not be a smooth function (for
example, a
straight line or an ellipse); rather, it will typically be a “jagged”
result, to which we can at best fit a smooth function by using some clever
method
(for example, fitting a regression line by the method of least-squares).
Naively, we might imagine that the variation and relative inexactness of our
measurements will become less pronounced and obtrusive the more refined
and microscopic are our measurement tools and procedures. Peirce, the
practicing scientist, knew better. What actually happens, if anything, is that
our
variations get relatively greater the finer is our instrumentation and the
more delicate our procedures. (Obviously, Peirce would not have been the
least surprised by the results obtained from measurements at the quantum
level.)
What the directly measured facts of scientific practice seem to tell us,
then, is that, although the universe displays varying degrees of habit (that
is to say, of partial, varying, approximate, and statistical regularity),
the universe does not display deterministic law. It does not directly show
anything like total, exact, non-statistical regularity. Moreover, the
habits that nature does display always appear in varying degrees of
entrenchment
or “congealing.” At one end of the spectrum, we have the nearly law-like
behavior of larger physical objects like boulders and planets; but at the
other end of the spectrum, we see in human processes of imagination and
thought an almost pure freedom and spontaneity; and in the quantum world of
the
very small we see the results of almost pure chance.
The immediate, “raw” result, then, of scientific observation through
measurement is that not everything is exactly fixed by exact law (even if
everything should be constrained to some degree by habit). In his earliest
thinking about the significance of this fact, Peirce opined that natural law
pervaded the world but that certain facets of reality were just outside the
reach or grasp of law. In his later thinking, however, Peirce came to
understand this fact as meaning that reality in its entirety was lawless and
that
pure spontaneity had an objective status in the phaneron. Peirce called his
doctrine that chance has an objective status in the universe “tychism,” a
word taken from the Greek word for “chance” or “luck” or “what the gods
happen to choose to lay on one.” Tychism is a fundamental doctrinal part of
Peirce's mature view, and reference to his tychism provides an added reason
for Peirce's insisting on the irreducible fallibilism of inquiry. For
nature is not a static world of unswerving law but rather a dynamic and dicey
world of evolved and continually evolving habits that directly exhibit
considerable spontaneity. (Peirce would have embraced quantum indeterminacy.)
One possible path along which nature evolves and acquires its habits was
explored by Peirce using statistical analysis in situations of experimental
trials in which the probabilities of outcomes in later trials are not
independent of actual outcomes in earlier trials, situations of so-called “
non-Bernoullian trials.” Peirce showed that, if we posit a certain primal habit
in nature, viz. the tendency however slight to take on habits however tiny,
then the result in the long run is often a high degree of regularity and
great macroscopic exactness. For this reason, Peirce suggested that in the
remote past nature was considerably more spontaneous than it has now become,
and that in general and as a whole all the habits that nature has come to
exhibit have evolved. Just as ideas, geological formations, and biological
species have evolved, natural habit has evolved.
In this evolutionary notion of nature and natural law we have an added
support of Peirce's insistence on the inherent fallibilism of scientific
inquiry. Nature may simply change, even in its most entrenched fundamentals.
Thus, even if scientists were at one point in time to have conceptions and
hypotheses about nature that survived every attempt to falsify them, this fact
alone would not ensure that at some later point in time these same
conceptions and hypotheses would remain accurate or even pertinent.
An especially intriguing and curious twist in Peirce's evolutionism is that
in Peirce's view evolution involves what he calls its “agapeism.” Peirce
speaks of evolutionary love. According to Peirce, the most fundamental
engine of the evolutionary process is not struggle, strife, greed, or
competition. Rather it is nurturing love, in which an entity is prepared to
sacrifice its own perfection for the sake of the wellbeing of its neighbor.
This
doctrine had a social significance for Peirce, who apparently had the
intention of arguing against the morally repugnant but extremely popular
socio-economic Darwinism of the late nineteenth century. The doctrine also had
for
Peirce a cosmic significance, which Peirce associated with the doctrine of
the Gospel of John and with the mystical ideas of Swedenborg and Henry
James. In Part IV of the third of Peirce's six papers in Popular Science
Monthly, entitled “The Doctrine of Chances,” Peirce even argued that simply
being
logical presupposes the ethics of self-sacrifice: “He who would not
sacrifice his own soul to save the whole world, is, as it seems to me,
illogical
in all his inferences, collectively.” To social Darwinism, and to the
related sort of thinking that constituted for Herbert Spencer and others a
supposed justification for the more rapacious practices of unbridled
capitalism,
Peirce referred in disgust as “The Gospel of Greed.”
6. Synechism, the Continuum, Infinites, and Infinitesimals
Along with Richard Dedekind and Georg Cantor, Peirce was one of the first
scientific thinkers to argue in favor of the existence of actually infinite
collections, and to maintain that the paradoxes that Bernard Bolzano had
associated with the idea of infinite collections were not really
contradictions at all. His criterion of the difference between finite and
infinite
collections was that the so-called “syllogism of transposed quantity,” which
had been introduced by Augustus de Morgan, constituted a deductively valid
argument only when applied to finite sets; as applied to infinite sets it
was invalid. The syllogism of transposed quantity runs as follows. We have a
binary relation R defined on a set S, such that the following two premises
are true of the relation (where the quantifications are taken over the set
S). First, for all x there is a y such that Rxy. Second, for all x, y, z,
Rxz and Ryz implies that x = y. The conclusion (of the syllogism of
transposed quantity) is that for all x there exists a y such that Ryx. One of
Peirce's favorite examples helps elucidate the idea, even if it perhaps be not
perfectly politically correct: Every Texan kills some Texan; no Texan is
killed by more than one Texan; therefore every Texan is killed by some
Texan. The argument's conclusion follows validly only if the set of Texans is
finite.
If by Rxy in the syllogism of transposed quantity we take f(x) = y, where
the function is defined on and has values in the set S, then the second
premise of the syllogism of transposed quantity says that f is a one-one
function. The conclusion says that every member of S is the image under f of
some member of S. Thus the syllogism of transposed quantity says that no
one-one function can map the set S to a proper subset of itself. This
assertion
holds, of course, only if S is a finite set. So, as it turns out, Peirce's
definition of the difference between finite and infinite sets is virtually
equivalent to the standard one, which is found in Section 5 of Richard
Dedekind's Was Sind und Was Sollen die Zahlen?, to the effect that an infinite
set is one that can be placed into a one-to-one correspondence with a
proper subset of itself. Peirce claimed on various occasions to have reached
his
definition of the difference between finite and infinite collections at
least six years before Dedekind reached his own definition.
Peirce held that the continuity of space, time, ideation, feeling, and
perception is an irreducible deliverance of science, and that an adequate
conception of such continua is an extremely important part of all the sciences.
The doctrine of the continuity of nature he called “synechism,” a word
deriving from the Greek preposition that means “(together) with.” In
mid-1892, somewhat under the influence of reading Cantor's works, Peirce
defined a
(linear) continuum to be a linearly-ordered infinite set C such that (1)
for any two distinct members of C there exists a third member of C that is
strictly between these; and (2) every countably infinite subset of C that
has an upper (lower) bound in C has a least upper bound (greatest lower
bound) in C. The first property he called “Kanticity” and the second “
Aristotelicity.” (Today we would likely call these properties “density” and “
closedness,” respectively.) The second condition has the corollary that a
continuum contains all its limit points, and sometimes Peirce used this
property
in conjunction with “Kanticity” to define a continuum.
Toward the end of the nineteenth century, however, Peirce began to hold
that Kanticity and Aristotelicity, even when conjoined, were insufficient to
define adequately the notion of a continuum. He maintained that he had
framed an updated conception of continua by somewhat loosening his attachment
to
Cantor's ideas. He began to write in ways that, at least at first glance,
seem close to falling into Cantor's Paradox; Peirce, however, tried to
avoid outright contradiction by means of embracing some sort of non-standard
idea about the identity of points on a line. For example, in Lecture 3 of his
Cambridge Conferences Lectures of 1898, published as Reasoning and the
Logic of Things, Peirce says that if a line is cut into two portions, the
point at which the cut takes place actually becomes two points. What Peirce's
new approach is, in mathematical detail, and whether or not it contains
hidden but real contradictions, is a problem that has not yet been solved by
researchers into Peirce's logic and mathematics.
Connected with his new conception of the continuum is Peirce's increasingly
frequent and sometimes pugnacious defenses of the doctrine of the reality
of infinitesimal quantities. The doctrine was not newly taken up by Peirce
late in the nineteenth century; indeed, he had held the doctrine for some
time, and it had been the doctrine of his father Benjamin. He considered it
superior to the newer doctrine of limits for providing a foundation for the
differential and integral calculus. What was new was that Peirce began to
see the doctrine of infinitesimals as the key to his updated doctrine of
the continuum. Thus, adding to his long-standing defense of infinitely large
magnitudes (Peirce often used the word “multitudes.”), Peirce began
vigorously to defend infinitely small magnitudes, infinitesimal magnitudes.
Many
examples of such defenses can be found. Carolyn Eisele collected a number
of such examples in her edited work The New Elements of Mathematics by
Charles S. Peirce. See, for example, Volume 2, pages 169–170, where Peirce
says “
My personal opinion is that there is positive evidence of the real
existence of infinitesimals; and that the admission of them would considerably
simplify the introduction to the calculus.” See also Volume 3, Part 1, pages
121–124, 125–127, 128–131, and 742–750. By the end of the nineteenth
century Peirce's view about infinitesimals was so rare and remarkable that
Josiah Royce remarked, in a footnote of his “Supplementary Essay” for The
World
and the Individual, First Series, that outside of Italy Peirce was
virtually the only mathematical philosopher who believed in infinitesimals.
(See
footnote 2, page 562 of this work by Royce.)
Not only did Peirce defend infinitesimals. He furthermore claimed that he
had proved the consistency of introducing infinitesimals into the system of
real numbers in such a way as to form a new system in which there were
infinitely many entities that were not equal to zero and yet were all smaller
than any real number r that is not equal to zero, no matter how small r
might be. To use modern terminology, Peirce was claiming to have shown the
existence of ordered fields that were non-Archimedean. It was these
non-Archimedean fields that Peirce now wanted to call genuine continua.
Additionally,
Peirce wanted to use his notion infinitesimal quantities and his revised
concept of the continuum in order to justify the traditional pre-Gaussian
definitions and underpinnings of the differential calculus.
Peirce also made a number of remarks that suggest, in connection with the
foregoing enterprise, that he had a novel conception of the topology of
points in a continuum. All these remarks he connected with his previous
defenses of infinite sets. For these reasons some Peirce scholars, and in
particular the great Peirce scholar Carolyn Eisele, have suggested that his
ideas
were an anticipation of Abraham Robinson's non-standard analysis of 1964.
Whether this actually be so or not, however, is at the present time far from
clear. Peirce certainly says many things that are quite suggestive of the
construction of non-standard models of the theory of ordered fields by means
of using equivalence classes of countably infinite Cartesian Products of
the standard real numbers and then applying Loś's Theorem. However, no
commentator up to now has provided anything even remotely resembling a careful
and detailed exposition of Peirce's thinking in this area. Unfortunately,
most of Peirce's published writing and public talks on this topic were
designed for audiences that were extremely unsophisticated mathematically (a
fact
that he lamented). For that reason most of what Peirce said on the topic
is picturesque and intriguing, but extremely obscure. The entire analysis of
Peirce's notion of an infinitesimal, as well as the exact bearing this
notion has on his concept of a real continuum and on his idea of the topology
of the points of a continuum, still awaits meticulous mathematical
discussion.
--
--
Centroids: The Center of the Radical Centrist Community
<[email protected]>
Google Group: http://groups.google.com/group/RadicalCentrism
Radical Centrism website and blog: http://RadicalCentrism.org
---
You received this message because you are subscribed to the Google Groups
"Centroids: The Center of the Radical Centrist Community" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
For more options, visit https://groups.google.com/d/optout.
