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Charles Peirce


Charles Sanders Peirce (pronounced purse), (September 10, 1839 - April 19, 1914) was an American polymath, born in Cambridge, Massachusetts. Although educated as a chemist and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or semeiotic, that he is largely appreciated today. The philosopher Paul Weiss, writing in the Dictionary of American Biography for 1934, called Peirce "the most original and versatile of American philosophers and America's greatest logician"1

Peirce was largely ignored during his lifetime, and secondary literature on his works was scant until after World War II. Much of his huge output is still unpublished. An innovator in fields such as mathematics, research methodology, the philosophy of science, epistemology, and metaphysics, he considered himself a logician first and foremost. While he made major contributions to formal logic, "logic" for him encompassed much of what is now called the philosophy of science and epistemology. He, in turn, saw logic as a branch of semiotics, of which he is a founder. In 1886, he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later to produce digital computers.


The only Peirce biography in English is Joseph Brent's Charles Peirce, A Life, (1998). Charles Sanders Peirce was born September 10, 1839, the son of Sarah Hunt Mills and Benjamin Peirce, a professor of astronomy and mathematics at Harvard University, who was perhaps the first serious research mathematician in America. When he was 12 years old, Charles read an older brother's copy of Richard Whately's Elements of Logic, then the leading English language text on the subject, and acquired a lifelong fascination with logic and reasoning. He went on to obtain a BA and MA from Harvard, and in 1863 Harvard's Lawrence Scientific School awarded him its first M.Sc. in chemistry. This last degree was awarded summa cum laude; otherwise his academic record was undistinguished. At Harvard, he began lifelong friendships with Francis Ellingwood Abbot, Chauncey Wright, and William James. One of his Harvard instructors, Charles William Eliot, formed an unfavorable opinion of Peirce. This opinion proved fateful, because Eliot, while President of Harvard 1869-1909-a period encompassing nearly all of Peirce's working life-repeatedly vetoed having Peirce employed in any capacity at Harvard.

United States Coast Survey

Between 1859 and 1891, Charles was intermittently employed in various scientific capacities by the United States Coast Survey, where he enjoyed the protection of his highly influential father until the latter's death in 1880. This employment exempted Charles from having to take part in the Civil War. It would have been very awkward for him to do so, as the wealthy Boston Peirce family sympathized with the Confederacy. At the Survey, he worked mainly in geodesy and in gravimetry, refining the use of pendulums to determine small local variations in the strength of the earth's gravity. The Survey sent him to Europe five times, the first in 1871, as part of a group dispatched to observe a solar eclipse. While in Europe, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford, British mathematicians and logicians whose interests resembled his own. From 1869 to 1872, he was employed as an Assistant in Harvard's astronomical observatory, doing important work on determining the brightness of stars and the shape of the Milky Way.2 In 1878, he was the first to define the meter as so many wavelengths of light of a certain frequency, the definition employed until 19833.

During the 1880s, Peirce's became increasingly indifferent to bureaucratic detail, and the quality and timeliness of his Survey work suffered. Peirce took years to write reports that he should have completed in a few months. Meanwhile, he wrote hundreds of logic, philosophy, and science entries for the Century Dictionary. In 1885, an investigation by the Allison Commission exonerated Peirce, but led to the dismissal of Superintendent Julius Hilgard and several other Coast Survey employees for misuse of public funds. In 1891, Peirce resigned from the Coast Survey, at the request of Superintendent Thomas Corwin Mendenhall. He never again held regular employment.

Johns Hopkins University

In 1879, Peirce was appointed Lecturer in logic at the new Johns Hopkins University in Baltimore. That university was strong in a number of areas that interested him, such as philosophy; (Royce and Dewey earned their PhDs at Hopkins), psychology (taught by G. Stanley Hall and studied by Joseph Jastrow, who coauthored a landmark empirical study with Peirce), and mathematics (taught by J. J. Sylvester, who came to admire Peirce's work on mathematics and logic). This untenured position proved to be the only academic appointment Peirce ever held.

Brent, his biographer, documents something Peirce never suspected; his efforts to obtain academic employment, grants, and scientific respectability were repeatedly frustrated by the covert opposition of a major American scientist of the day, Simon Newcomb. A difficult personality may have contributed to Peirce's difficulty in finding academic employment. Brent conjectures that Peirce may have been manic-depressive, claiming that Peirce experienced eight nervous breakdowns between 1876 and 1911. Brent also believes that Peirce tried to alleviate his symptoms with ether, morphine, and cocaine.

Peirce's personal life also proved a grave handicap. His first wife, Harriet Melusina Fay, from the prominent Cambridge family of Reverend Charles Fay, whom he married in October 1863, had left him in 1875. Peirce soon began living openly with a woman whose maiden name and nationality remain uncertain to this day (the best guess is that her name was Juliette Froissy Pourtalès and that she was French), but did not marry her until his divorce with Harriet became final in 1883. That year, Simon Newcomb pointed out to a Johns Hopkins trustee that Peirce, while a Hopkins employee, had lived and traveled with a woman to whom he was not married. The ensuing scandal led to his dismissal. Just why Peirce's later applications for academic employment at Clark University, University of Wisconsin, University of Michigan, Cornell University, Stanford University, and the University of Chicago were all unsuccessful can no longer be determined. Presumably, his having lived with Juliette for a number of years while still legally married to Harriet led him to be deemed morally unfit for academic employment anywhere in the United States. Peirce had no children by either marriage.


In 1887, Peirce spent part of his inheritance from his parents to purchase 2000 rural acres near Milford, Pennsylvania, land which never yielded an economic return. On that land, he built a large house which he named "Arisbe," where he spent the rest of his life, writing prolifically. Much of his writing remains unpublished to this day. His insistence on living beyond his means soon led to serious financial and legal difficulties. Peirce spent much of the last two decades of his life so destitute that he could not afford heat in winter, and his only food was old bread kindly donated by the local baker. Unable to afford new stationery, he wrote on the verso side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while. Several people, including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage.

Peirce did some scientific and engineering consulting and wrote a good deal for meager pay, primarily dictionary and encyclopedia entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison he became friendly). He did translations for the Smithsonian Institution, at the instigation of its director, Samuel Langley. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried his hand at inventing, and began but did not complete a number of books. In 1888, President Grover Cleveland appointed him to the Assay Commission. From 1890 onwards, he had a friend and admirer in Judge Francis C. Russell of Chicago, who introduced Peirce to Paul Carus and Edward Hegeler, the editor and owner, respectively, of the pioneering American philosophy journal The Monist, which eventually published a number of his articles. He applied to the newly formed Carnegie Institution for a grant to write a book summarizing his life's work. This application was doomed; his nemesis Newcomb served on the Institution's executive committee, and its President had been the President of Johns Hopkins at the time of Peirce's dismissal.

The one who did the most to help Peirce in these desperate times was his old friend William James, who dedicated his book of essays The Will to Believe (1896) to Peirce, and who arranged for Peirce to be paid to give four series of lectures at or near Harvard. Most important, each year from 1898 until his death in 1910, James would write to his friends in the Boston academic circles, asking that they make a financial contribution to help support Peirce. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him, and by adding "Santiago," "Saint James" in Spanish, to his full name4.

Peirce died destitute in Milford, Pennsylvania, on April 19, 1914, 20 years before his widow.


Bertrand Russell once said about Peirce, "Beyond doubt… he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (Yet his Principia Mathematica does not mention Peirce.) A. N. Whitehead, while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and process metaphysics, see the chapter by Lowe in Moore and Robin, 1964.) Karl Popper viewed Peirce as "one of the greatest philosophers of all times." Nevertheless, Peirce's accomplishments were not immediately recognized. His imposing contemporaries William James and Josiah Royce admired him, and Cassius Jackson Keyser at Columbia University and C. K. Ogden wrote about Peirce with respect, but he received little pubic recognition.

The first scholar to give Peirce his considered professional attention was Royce's student Morris Raphael Cohen, the editor of a 1923 anthology of Peirce's writings titled Chance, Love, and Logic, and the author of the first bibliography of Peirce's scattered writings. John Dewey had had Peirce as an instructor at Johns Hopkins, and from 1916 onwards, Dewey's writings repeatedly mention Peirce with deference. His 1938 Logic: The Theory of Inquiry reflects Peirce's theories. The publication of the first six volumes of the Collected Papers (1931-1935), the most important event to date in Peirce studies and one Cohen made possible by raising the needed funds, did not lead to an immediate outpouring of secondary studies. The editors of those volumes, Charles Hartshorne and Paul Weiss, did not become Peirce specialists. Early landmarks of the secondary literature include the monographs by Buchler (1939), Feibleman (1946), and Goudge (1950), the 1941 Ph.D. thesis by Arthur Burks (who went on to edit volumes 7 and 8 of the Collected Papers), and the edited volume Wiener and Young (1952). The Charles S. Peirce Society was founded in 1946; its Transactions, an academic journal specializing in Peirce, pragmatism, and American philosophy, has appeared since 1965.

In 1949, while doing unrelated archival work, the historian of mathematics Carolyn Eisele (1902-2000) chanced on an autograph letter by Peirce. She began forty years of research on Peirce as a mathematician and scientist, culminating in Eisele (1976, 1979, 1985). Beginning around 1960, the philosopher and historian of ideas Max Fisch (1900-1995) emerged as an authority on Peirce; Fisch (1986) reprinted many of the relevant articles, including a wide-ranging survey (Fisch 1986: 422-448) of the impact of Peirce's thought through 1983.

Peirce has come to enjoy a significant international following. There are university research centers devoted to Peirce studies and pragmatism in Brazil, Finland, Germany, and Spain. Since 1950, there have been French, Italian, and British Peirceans of note. For many years, the North American philosophy department most devoted to Peirce was the University of Toronto's, thanks in good part to the leadership of Thomas Goudge and David Savan. In recent years, American Peirce scholars have clustered at Indiana University - Purdue University Indianapolis, the home of the Peirce Edition Project, and the Pennsylvania State University.

Robert Burch has commented on Peirce's current influence as follows:

Currently, considerable interest is being taken in Peirce's ideas from outside the arena of academic philosophy. The interest comes from industry, business, technology, and the military; and it has resulted in the existence of a number of agencies, institutes, and laboratories in which ongoing research into and development of Peircean concepts is being undertaken.5.


Peirce's reputation is largely based on a number of academic papers published in American scholarly and scientific journals. These papers, along with a selection of Peirce's previously unpublished work and a smattering of his correspondence, fill the eight volumes of the Collected Papers of Charles Sanders Peirce, published between 1931 and 19586. An important recent sampler of Peirce's philosophical writings is the two volume The Essential Peirce7 .

The only book Peirce published in his lifetime was Photometric Researches (1878), a monograph on the applications of spectrographic methods to astronomy. While at Johns Hopkins, he edited Studies in Logic (1883), containing chapters by himself and his graduate students. He was a frequent book reviewer and contributor to The Nation,reprinted in Ketner and Cook (1975-1987).

In 2001 Peirce's entire correspondence with Lady Victoria Welby was published.8 Peirce's other published correspondence is largely limited to 14 letters included in volume 8 of the Collected Papers, and about 20 pre-1890 items included in the Writings.

Harvard University acquired the papers found in Peirce's study soon after his death, but did not microfilm them until 1964. Only after Richard Robin (1967) catalogued this Nachlass did it become clear that Peirce had left approximately 1,650 unpublished manuscripts, totalling 80,000 pages. Carolyn Eisele9 published some of this work, but most of it remains unpublished.10.

The limited coverage, and defective editing and organization, of the Collected Papers led Max Fisch and others in the 1970s to found the Peirce Edition Project, whose mission is to prepare a more complete critical chronological edition, known as the Writings. Only six out of a planned 31 volumes have appeared to date, but they cover the period from 1859-1890, when Peirce carried out much of his best-known work.

On a New List of Categories (1867)

On May 14, 1867, Peirce presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences, which published it the following year. Among other things, this paper outlined a theory of three universal categories that Peirce continued to apply throughout philosophy and elsewhere for the rest of his life. Peirce scholars generally regard the "New List" as his blueprint for a pragmatic philosophy.

Logic of Relatives (1870)

By 1870, the drive that Peirce exhibited to understand the character of knowledge, starting with our partly innate and partly inured models of the world and working up to the conduct of our scientific inquiries into it, which had led him to inquire into the three-roled relationship of objects, signs, and impressions of the mind, now brought him to a point where he needed a theory of relations more powerful than that provided by the available logical formalisms. His first concerted effort to supply this gap was rolled out in his 60-page paper "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic,"11published in Memoirs of the American Academy of Arts and Sciences in 1870 and also separately as an extraction. The logic of relatives, short for the logic of relative terms, is the study of relations in their logical, philosophical, or semiotic aspects, as distinguished from-though closely coordinated with-their more properly formal, mathematical, or objective aspects. The consideration of relative terms has its roots in antiquity, but it entered a radically new phase of development with Peirce's 1870 paper, which is one of the wellsprings of contemporary systems of logic.

Illustrations of the Logic of Science (1877-1878)

Published in Popular Science Monthly Vols. 12-13 (see entries at the Charles Sanders Peirce bibliography, this series of articles is foundational for Peirce's pragmatism as a method of inquiry, especially "The Fixation of Belief" (1877) and "How to Make Our Ideas Clear" (1878).

Logic of Relatives (1883)

"Logic of Relatives (1883)," more precisely, "Note B. The Logic of Relatives," is the title of a 17-page addendum to the chapter entitled "A Theory of Probable Inference" that C.S. Peirce contributed to the volume Studies in Logic by Members of the Johns Hopkins University, 188312. This volume, edited by Peirce, collected works of his students at Johns Hopkins. As a body, these works broke new ground in several different directions of logical exploration at once.

Logic of Relatives (1897)

Published in The Monist vol. VII, (2): 161-217.

The Simplest Mathematics (1902)

"The Simplest Mathematics" is the title of a paper by Peirce, intended as Chapter 3 of his unfinished magnum opus The Minute Logic. The paper is dated January-February 1902 but was not published until the appearance of his Collected Papers, Volume 4. in 1933. Peirce introduces the subject of the paper as "certain extremely simple branches of mathematics which, owing to their utility in logic, have to be treated in considerable detail, although to the mathematician they are hardly worth consideration"13.

"Kaina Stoicheia" (1904)

"Kaina Stoicheia" (Καινα στοιχεια) or "New Elements" is the title of several manuscript drafts of a document that Peirce wrote circa 1904, intended as a preface to a book on the foundations of mathematics. It presents a consummate integration of his ideas on the interrelations of logic, mathematics, and semeiotic, or the theory of signs14.


In order to understand Peirce's philosophical work, it is important to remember that Peirce was a working scientist for 30 years, and was a professional philosopher only during the five years he lectured at Johns Hopkins. He learned philosophy mainly by reading a few pages of Kant's Critique of Pure Reason, in the original German, every day while a Harvard undergraduate. His writings bear on a wide array of disciplines, including astronomy, metrology, geodesy, mathematics, logic, philosophy, the history and philosophy of science, linguistics, economics, and psychology. This work has become the subject of renewed interest and approval, resulting in a revival inspired not only by his anticipations of recent scientific developments, but also by his demonstration of how philosophy can be applied effectively to human problems.

Peirce's writings repeatedly refer to a system of three categories, named "Firstness", "Secondness", and "Thirdness", devised early in his career in reaction to his reading of Aristotle, Kant, and Hegel. He later initiated the philosophical tendency known as pragmatism, a variant of which his life-long friend William James made popular. Peirce believed that any truth is provisional, and that the truth of any proposition cannot be certain but only probable. The name he gave to this state of affairs was "fallibilism." This fallibilism and pragmatism may be seen as taking roles in his work similar to those of skepticism and positivism, respectively, in the work of others.

Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:

Do not block the way of inquiry.
Although it is better to be methodical in our investigations, and to consider the economics of research, yet there is no positive sin against logic in trying any theory which may come into our heads, so long as it is adopted in such a sense as to permit the investigation to go on unimpeded and undiscouraged. On the other hand, to set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning, as it is also the one to which metaphysicians have in all ages shown themselves the most addicted.15


Peirce's recipe for pragmatic thinking, labeled pragmatism and also known as pragmaticism, is recapitulated in several versions of the so-called pragmatic maxim. Here is one of his more emphatic statements of it:

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.16

William James, among others, regarded two of Peirce's papers, "The Fixation of Belief" (1877) and "How to Make Our Ideas Clear" (1878) as being the origin of pragmatism. Peirce conceived pragmatism to be a method for clarifying the meaning of difficult ideas through the application of the pragmatic maxim. He differed from William James and the early John Dewey, in some of their tangential enthusiasms, by being decidedly more rationalistic and realistic.

Peirce's pragmatism may be understood as a method of sorting out conceptual confusions by linking the meaning of concepts to their operational or practical consequences. This understanding of pragmatism bears no resemblance to "vulgar" pragmatism, in which the search for truth is driven by a ruthless and Machiavellian regard for mercenary or political advantage. Rather, Peirce sought an objective method of verification to test the truth of putative knowledge. His pragmatism was a method of experimentational mental reflection, arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances, a method which allowed the generation of explanatory hypotheses, and which was conducive to the employment and improvement of verification. This pragmatism went beyond the usual foundational alternatives or rationalism (deduction from self-evident truths), and empiricism (inductive reasoning|induction from experiential phenomena).

His approach is often confused with empiricism, but is distinguished from it by the following three dimensions:

  • An active process of theory generation, with no prior assurance of truth;
  • Subsequent application of the contingent theory, aimed toward developing its logical and practical consequences;
  • Evaluation of the provisional theory's utility for the anticipation of future experience, in the senses of prediction and control.

Peirce's pragmatism was the first time the scientific method was proposed as an epistemology for philosophical questions. A theory that proves itself more successful in predicting and controlling our world than its rivals, is said to be nearer the truth. This is an operational notion of truth employed by scientists. Unlike the other pragmatists, Peirce never explicitly advanced a theory of truth. His scattered comments about truth proved influential to several epistemic truth theorists, and served as a useful foil for deflationary and correspondence theories of truth.

Pragmatism is regarded as a distinctively American philosophy. As advocated by James, John Dewey, Ferdinand Canning Scott Schiller, George Herbert Mead, and others, it has proved durable and popular. But Peirce did not seize on this fact to enhance his reputation. While it is sometimes stated that James' and other philosophers' use of the word pragmatism so dismayed Peirce that he renamed his own variant pragmaticism, this was not the main reason (Haack, 55). This is revealed by the context in which Peirce introduced the latter term:

But at present, the word pragmatism begins to be met with occasionally in the literary journals, where it gets abused in the merciless way that words have to expect when they fall into literary clutches.… So then, the writer, finding his bantling "pragmatism" so promoted, feels that it is time to kiss his child good-by and relinquish it to its higher destiny; while to serve the precise purpose of expressing the original definition, he begs to announce the birth of the word "pragmaticism," which is ugly enough to be safe from kidnappers.17.

In a 1908 article 39 he expressed areas of agreement and disagreement with his fellow pragmatists. Peirce remained joined with them about:

the reality of generals and habits, to be understood, as are hypostatic abstractions, in terms of potential concrete effects even if unactualized;
the falsity of necessitarianism;
the character of consciousness as only "visceral or other external sensation."

and differed with their:

"angry hatred of strict logic";
view that "truth is mutable";
view that infinity is unreal; and
"confusion of active willing (willing to control thought, to doubt, and to weigh reasons) with willing not to exert the will (willing to believe)."

Peirce's pragmatism, in its core senses as a method and theory of definitions and the clearness of ideas, is a department within his theory of method of inquiry18, which he variously called Methodeutic and Philosophical or Speculative Rhetoric. He applied his pragmatism as a method throughout his work.

Formal Logic

Peirce was very conscious of the limitations of language, and of the attempt to define human thought in terms of logical steps. He acknowledged that the intuitive mind understands reality in ways that have not yet been defined, and sought to harness intuitive thought so that it could be applied scientifically to yield new insights in research and investigation.

How often do we think of the thing in algebra? When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose, coincide with the laws of multiplication in the object. Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it? It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use-whether reflected on or not-by association immediately regulate the action of the mind; and these may be regarded as laws of the symbol itself which it cannot as a symbol transgress.19

Logic as Formal Semiotic

On the Definition of Logic. Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word "formal" in the definition is also defined.20

Though Frege is credited with being the first to invent “formal logic,” Hilary Putnam points out that Peirce and his students discovered it in the effective sense that they developed it independently and made it widely known. The main evidence for Putnam's claims is Peirce (1885), published in the premier American mathematical journal of the day. Giuseppe Peano, Ernst Schröder, among others, cited this article. Peirce was apparently ignorant of Frege's work, despite their rival achievements in logic, philosophy of language, and the foundations of mathematics. 2122 23

Peirce's other major discoveries in formal logic include:

  • Distinguishing (Peirce, 1885) between first-order and second-order quantification.
  • Seeing that Boolean calculations could be carried out by means of electrical switches (W5:421-24), anticipating Claude Shannon by more than 50 years.
  • Devising the existential graphs, a diagrammatic notation for the predicate calculus. These graphs form the basis of the conceptual graphs of John F. Sowa, and of Sun-Joo Shin's diagrammatic reasoning.

A philosophy of logic, grounded in his categories and semeiotic, can be extracted from Peirce's writings. This philosophy, as well as Peirce's logical work more generally, is exposited and defended in 24 25 , and 26 Jean Van Heijenoort (1967)27, Jaakko Hintikka 28in his chapter in Brunning and Forster (1997), and Geraldine Brady (2000)29 divide those who study formal (and natural) languages into two camps: the model-theorists / semanticists, and the proof theorists / universalists. Hintikka and Brady view Peirce as a pioneer model theorist. On how the young Bertrand Russell, especially his Principles of Mathematics and Principia Mathematica, did not do Peirce justice, see Anellis (1995).

Peirce's work on formal logic had admirers other than Ernst Schröder; the philosophical algebraist William Kingdon Clifford and the logician William Ernest Johnson, both British; the Polish school of logic and foundational mathematics, including Alfred Tarski; and Arthur Prior, whose Formal Logic and chapter in Moore and Robin (1964) praised and studied Peirce's logical work.


It may be added that algebra was formerly called Cossic, in English, or the Rule of Cos; and the first algebra published in England was called "The Whetstone of Wit," because the author supposed that the word cos was the Latin word so spelled, which means a whetstone. But in fact, <>