# Charles Sanders Peirce

﻿
Charles Sanders Peirce
Charles Sanders Peirce

Charles Sanders Peirce
 Born September 10, 1839 Cambridge, Massachusetts Died April 19, 1914 (aged 74) Milford, Pennsylvania Nationality American Fields Logic, Mathematics, Statistics,[1][2] Philosophy, Metrology,[3] Chemistry, Experimental psychology[4] Economics,[5] Linguistics,[6] History of science Religious   stance Episcopal but unconventional
C. S. Peirce articles
General:    Charles Sanders Peirce
Charles Sanders Peirce bibliography
Philosophical:    Categories (Peirce)
Semiotic elements and
classes of signs (Peirce)

Pragmatic maximPragmaticism
SynechismTychism
Classification of the sciences (Peirce)
Biographical:    Juliette Peirce
Charles Santiago Sanders Peirce
Abbreviations
B:x Brent, Joseph (1998),
Charles Sanders Peirce:
A Life
, 2nd edition,[7] page x
CDPT Commens Dictionary
of Peirce's Terms
CP x.y Collected Papers
volume x, paragraph y
EP x:y The Essential Peirce
volume x, page y
W x:y Writings of Charles S. Peirce
volume x, page y

Charles Sanders Peirce ( /ˈpɜrs/ like "purse";[8] September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician, and scientist, born at 3 Phillips Place in Cambridge, Massachusetts. Peirce was educated as a chemist and employed as a scientist for 30 years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, and semiotics, and for his founding of pragmatism. In 1934, the philosopher Paul Weiss called Peirce "the most original and versatile of American philosophers and America's greatest logician".[9]

An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself a logician first and foremost. He made major contributions to logic, but logic for him encompassed much of that which is now called epistemology and philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder. As early as 1886 he saw that logical operations could be carried out by electrical switching circuits, the same idea as was used decades later to produce digital computers.[10]

## Life

Peirce's birthplace. Currently, Lesley University's Graduate School of Arts and Social Sciences

Charles Sanders Peirce was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of astronomy and mathematics at Harvard University, perhaps the first serious research mathematician in America. At 12 years of age, Charles read an older brother's copy of Richard Whately's Elements of Logic, then the leading English-language text on the subject. Thus began his lifelong fascination with logic and reasoning.[11] He went on to obtain the B.A. and M.A. from Harvard; in 1863 the Lawrence Scientific School awarded him a B.Sc. that was Harvard's first summa cum laude chemistry degree;[12] and otherwise his academic record was undistinguished. [13] At Harvard, he began lifelong friendships with Francis Ellingwood Abbot, Chauncey Wright, and William James. [14] 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 Harvard's employing Peirce in any capacity. [15]

Peirce suffered from his late teens onward from a nervous facial condition then known as "facial neuralgia", which would today be diagnosed as trigeminal neuralgia. Brent says that when in the throes of its pain "he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper".[16] Its consequences may have led to the social isolation which made his life's later years so tragic.

### Early employment

Between 1859 and 1891, Peirce was intermittently employed in various scientific capacities by the United States Coast Survey,[17] where he enjoyed his highly influential father's protection[18] until the latter's death in 1880. That employment exempted Peirce from having to take part in the Civil War; it would have been very awkward for him to do so, as the Boston Brahmin Peirces sympathized with the Confederacy.[19] At the Survey, he worked mainly in geodesy and gravimetry, refining the use of pendulums to determine small local variations in the strength of Earth's gravity.[17] He was elected a resident fellow of the American Academy of Arts and Sciences in January 1867.[20] The Survey sent him to Europe five times,[21] first in 1871, as part of a group sent to observe a solar eclipse; while there, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford,[22] British mathematicians and logicians whose turn of mind 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.[23] On April 20, 1877 he was elected a member of the National Academy of Sciences.[24] Also in 1877, he proposed measuring the meter as so many wavelengths of light of a certain frequency,[25] the kind of definition employed from 1960 to 1983.

During the 1880s, Peirce's indifference to bureaucratic detail waxed while his Survey work's quality and timeliness waned. Peirce took years to write reports that he should have completed in months. Meanwhile, he wrote entries, ultimately thousands during 1883–1909, on philosophy, logic, science, and other subjects for the encyclopedic Century Dictionary.[26] 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.[27] In 1891, Peirce resigned from the Coast Survey at Superintendent Thomas Corwin Mendenhall's request.[28] He never again held regular employment.

### Johns Hopkins University

In 1879, Peirce was appointed Lecturer in logic at the new Johns Hopkins University, which was strong in a number of areas that interested him, such as philosophy (Royce and Dewey did 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). 1883 saw publication of his Studies in Logic by Members of the Johns Hopkins University containing works by himself and Allan Marquand, Christine Ladd, Benjamin Ives Gilman, and Oscar Howard Mitchell. They were among his graduate students.[29] This nontenured position proved to be the only academic appointment Peirce ever held.

Brent documents something Peirce never suspected, namely that 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.[30] Peirce's efforts may also have been hampered by a difficult personality; Brent conjectures as to further psychological difficulty.[31]

Peirce's personal life also handicapped him. His first wife, Harriet Melusina Fay ("Zina"), left him in 1875.[32] He soon took up with a woman, Juliette, whose maiden name, given variously as Froissy and Pourtalai[33] and nationality (she spoke French[34]) remain uncertain,[35] but his divorce from Zina became final only in 1883, whereupon he married Juliette.[36] That year, 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 in January 1884.[37] Over the years Peirce sought academic employment at various universities without success.[38] He had no children by either marriage.[39]

Cambridge, where Peirce was born and raised, New York City, where he often visited and sometimes lived, and Milford, where he spent the later years of his life with his second wife Juliette.
Juliette and Charles by the well at their home, "Arisbe", in 1907

### Poverty

In 1887 Peirce spent part of his inheritance from his parents to buy 2,000 acres (8 km2) of rural land near Milford, Pennsylvania, which never yielded an economic return.[40] There he had a 1854 farmhouse remodeled to his design.[41] The Peirces named the property "Arisbe". There they lived with a few interruptions for the rest of their lives,[42] Charles writing prolifically, much of it unpublished to this day (see Works). Living beyond their means soon led to grave financial and legal difficulties.[43] He spent much of his last two decades unable to afford heat in winter and subsisting on old bread 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.[44] Several people, including his brother James Mills Peirce[45] and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage.[46]

Peirce did some scientific and engineering consulting and wrote much for meager pay, mainly encyclopedic dictionary entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison, he became friendly). He did translations for the Smithsonian Institution, at its director Samuel Langley's instigation. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried inventing.[47] He began but did not complete a number of books.[48] In 1888, President Grover Cleveland appointed him to the Assay Commission.[49]

"Arisbe" in 2011

From 1890 on, he had a friend and admirer in Judge Francis C. Russell of Chicago,[50] who introduced Peirce to editor Paul Carus and owner Edward Hegeler of the pioneering American philosophy journal The Monist, which eventually published articles by Peirce,[51] at least 14. He wrote many texts in James Mark Baldwin's Dictionary of Philosophy and Psychology (1901–5); half of those credited to him appear to have been written actually by Christine Ladd-Franklin under his supervision.[52] He applied in 1902 to the newly formed Carnegie Institution for a grant to write a systematic book of his life's work. The 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.[53]

The one who did the most to help Peirce in these desperate times was his old friend William James, dedicating his Will to Believe (1897) to Peirce, and arranging for Peirce to be paid to give two series of lectures at or near Harvard (1898 and 1903).[54] Most important, each year from 1907 until James's death in 1910, James wrote to his friends in the Boston intelligentsia to request financial aid for Peirce; the fund continued even after James died. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him.[55] It has been believed that this was also why Peirce used "Santiago" ("St. James" in Spanish) as a middle name, but he appeared in print as early as 1890 as Charles Santiago Peirce. (See Charles Santiago Sanders Peirce for discussion and references).

Peirce died destitute in Milford, Pennsylvania, twenty years before his widow.

## Reception

Bertrand Russell (1959) wrote,[56] "Beyond doubt [...] he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (Russell's Principia Mathematica does not mention Peirce; Peirce's work was not widely known till later.)[57] 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 Lowe 1964.[23]) Karl Popper viewed Peirce as "one of the greatest philosophers of all times".[58] Yet Peirce's achievements were not immediately recognized. His imposing contemporaries William James and Josiah Royce[59] admired him, and Cassius Jackson Keyser at Columbia and C. K. Ogden wrote about Peirce with respect, but to no immediate effect.

The first scholar to give Peirce his considered professional attention was Royce's student Morris Raphael Cohen, the editor of an anthology of Peirce's writings titled Chance, Love, and Logic (1923) and the author of the first bibliography of Peirce's scattered writings.[60] John Dewey studied under Peirce at Johns Hopkins[29] and, from 1916 onwards, Dewey's writings repeatedly mention Peirce with deference. His 1938 Logic: The Theory of Inquiry is much influenced by Peirce.[61] The publication of the first six volumes of the Collected Papers (1931–35), the most important event to date in Peirce studies and one that Cohen made possible by raising the needed funds[62] did not prompt an 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 W. Burks (who went on to edit volumes 7 and 8), and the studies edited by Wiener and Young (1952). The Charles S. Peirce Society was founded in 1946. Its Transactions, an academic quarterly 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. So began her 40 years of research on Peirce the 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)[63] includes many of his relevant articles, including a wide-ranging survey (Fisch 1986: 422–48) of the impact of Peirce's thought through 1983.

Peirce has gained a significant international following, marked by university research centers devoted to Peirce studies and pragmatism in Brazil (CeneP/CIEP), Finland (HPRC, including Commens), Germany (Wirth's group, Hoffman's and Otte's group, and Deuser's and Härle's group[64]), France (L'I.R.S.C.E.), Spain (GEP), and Italy (CSP). His writings have been translated into several languages, including German, French, Finnish, Spanish, and Swedish. Since 1950, there have been French, Italian, Spanish, British, and Brazilian 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, U.S. Peirce scholars have clustered at Indiana University - Purdue University Indianapolis, home of the Peirce Edition Project (PEP), and the Pennsylvania State University.

Currently, considerable interest is being taken in Peirce's ideas by researchers wholly outside the arena of academic philosophy. The interest comes from industry, business, technology, intelligence organizations, and the military; and it has resulted in the existence of a substantial number of agencies, institutes, businesses, and laboratories in which ongoing research into and development of Peircean concepts are being vigorously undertaken.
—Robert Burch, 2001, updated 2010[17]

## Works

Peirce's reputation rests largely on a number of academic papers published in American scientific and scholarly journals such as Proceedings of the American Academy of Arts and Sciences, the Journal of Speculative Philosophy, The Monist, Popular Science Monthly, the American Journal of Mathematics, Memoirs of the National Academy of Sciences, The Nation, and others. See Articles by Peirce, published in his lifetime for an extensive list with links to them online. The only full-length book (neither extract nor pamphlet) that Peirce authored and saw published in his lifetime[65] was Photometric Researches (1878), a 181-page 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. Besides lectures during his years (1879–1884) as Lecturer in Logic at Johns Hopkins, he gave at least nine series of lectures, many now published; see Lectures by Peirce.

Harvard University bought from Peirce's widow soon after his death the papers found in his study, but did not microfilm them until 1964. Only after Richard Robin (1967)[66] catalogued this Nachlass did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totaling over 100,000 pages.[67] Most of it remains unpublished, except on microfilm. For more on the vicissitudes of Peirce's papers, see Houser (1989).[68]

The first published anthology of Peirce's articles was the one-volume Chance, Love and Logic: Philosophical Essays, edited by Morris Raphael Cohen, 1923, still in print. Other one-volume anthologies were published in 1940, 1957, 1958, 1972, 1994, and 2009, most still in print. The main posthumous editions[69] of Peirce's works in their long trek to light, often multi-volume, and some still in print, have included:

1931–58: Collected Papers of Charles Sanders Peirce (CP), 8 volumes, includes many published works, along with a selection of previously unpublished work and a smattering of his correspondence. This long-time standard edition drawn from Peirce's work from the 1860s to 1913 remains the most comprehensive survey of his prolific output from 1893 to 1913. It is organized thematically, but texts (including lecture series) are often split up across volumes, while texts from various stages in Peirce's development are often combined, requiring frequent visits to editors' notes.[70] Edited (1–6) by Charles Hartshorne and Paul Weiss and (7–8) by Arthur Burks, in print from Harvard and online via InteLex.

1975–87: Charles Sanders Peirce: Contributions to The Nation, 4 volumes, includes Peirce's more than 300 reviews and articles published 1869–1908 in The Nation. Edited by Kenneth Laine Ketner and James Edward Cook, out of print except online via InteLex.

1976: The New Elements of Mathematics by Charles S. Peirce, 4 volumes in 5, included many previously unpublished Peirce manuscripts on mathematical subjects, along with Peirce's important published mathematical articles. Edited by Carolyn Eisele, out of print.

1977: Semiotic and Significs: The Correspondence between C. S. Peirce and Victoria Lady Welby (2nd edition 2001), included Peirce's entire correspondence (1903–1912) with Victoria, Lady Welby. Peirce's other published correspondence is largely limited to the 14 letters included in volume 8 of the Collected Papers, and the 20-odd pre-1890 items included so far in the Writings. Edited by Charles S. Hardwick with James Cook, out of print.

1981–now: Writings of Charles S. Peirce, A Chronological Edition (W), Volumes 1–6 & 8, of a projected 30. 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 (PEP), whose mission is to prepare a more complete critical chronological edition. Only seven volumes have appeared to date, but they cover the period from 1859–1892, when Peirce carried out much of his best-known work. W 8 was published in November 2009; and work continues on W 7, 9, and 11. In print from Indiana U. and (1–6) online via InteLex.

1985: Historical Perspectives on Peirce's Logic of Science: A History of Science, 2 volumes. Auspitz has said,[71] "The extent of Peirce's immersion in the science of his day is evident in his reviews in the Nation [...] and in his papers, grant applications, and publishers' prospectuses in the history and practice of science", referring latterly to Historical Perspectives. Edited by Carolyn Eisele, out of print.

1992: Reasoning and the Logic of Things collects in one place Peirce's 1898 series of lectures invited by William James. Edited by Kenneth Laine Ketner, with commentary by Hilary Putnam, in print from Harvard.

1992–98: The Essential Peirce (EP), 2 volumes, is an important recent sampler of Peirce's philosophical writings. Edited (1) by Nathan Hauser and Christian Kloesel and (2) by PEP editors, in print from Indiana U.

1997: Pragmatism as a Principle and Method of Right Thinking collects Peirce's 1903 Harvard "Lectures on Pragmatism" in a study edition, including drafts, of Peirce's lecture manuscripts, which had been previously published in abridged form; the lectures now also appear in EP 2. Edited by Patricia Ann Turisi, in print from SUNY.

2010: Philosophy of Mathematics: Selected Writings collects important writings by Peirce on the subject, many not previously in print. Edited by Matthew E. Moore, in print from Indiana U.

## Mathematics

The Peirce quincuncial projection of a sphere keeps angles true except at several isolated points and results in less distortion of area than in other projections.

Peirce's most important work in pure mathematics was in logical and foundational areas. He also worked on linear algebra, matrices, various geometries, topology and Listing numbers, Bell numbers, graphs, the four-color problem, and the nature of continuity.

He worked on applied mathematics in economics, engineering, and map projections (such as the Peirce quincuncial projection), and was especially active in probability and statistics.[72]

Discoveries

Peirce made a number of striking discoveries in formal logic and foundational mathematics, nearly all of which came to be appreciated only long after he died:

In 1860[73] he suggested a cardinal arithmetic for infinite numbers, years before any work by Georg Cantor (who completed his dissertation in 1867) and without access to Bernard Bolzano's 1851 (posthumous) Paradoxien des Unendlichen.

The Peirce arrow,
symbol for "(neither)...nor...", also called the Quine dagger.

In 1880–81[74] he showed how Boolean algebra could be done via a repeated sufficient single binary operation (logical NOR), anticipating Henry M. Sheffer by 33 years. (See also De Morgan's Laws).

In 1881[75] he set out the axiomatization of natural number arithmetic, a few years before Richard Dedekind and Giuseppe Peano. In the same paper Peirce gave, years before Dedekind, the first purely cardinal definition of a finite set in the sense now known as "Dedekind-finite", and implied by the same stroke an important formal definition of an infinite set (Dedekind-infinite), as a set that can be put into a one-to-one correspondence with one of its proper subsets.

In 1885[76] he distinguished between first-order and second-order quantification.[77][78] In the same paper he set out what can be read as the first (primitive) axiomatic set theory, anticipating Zermelo by about two decades (Brady 2000,[79] pp. 132–3).

In 1886 he saw that Boolean calculations could be carried out via electrical switches,[10] anticipating Claude Shannon by more than 50 years.

Existential graphs: Alpha graphs

By the later 1890s[80] he was devising existential graphs, a diagrammatic notation for the predicate calculus. Based on them are John F. Sowa's conceptual graphs and Sun-Joo Shin's diagrammatic reasoning.

The New Elements of Mathematics

Peirce wrote drafts for an introductory textbook, with the working title The New Elements of Mathematics, that presented mathematics from an original standpoint. Those drafts and many other of his previously unpublished mathematical manuscripts finally appeared[72] in The New Elements of Mathematics by Charles S. Peirce (1976), edited by mathematician Carolyn Eisele.

Nature of mathematics

Peirce agreed with Auguste Comte in regarding mathematics as more basic than philosophy and the special sciences (of nature and mind). Peirce classified mathematics into three subareas: (1) mathematics of logic, (2) discrete series, and (3) pseudo-continua (as he called them, including the real numbers) and continua. Influenced by his father Benjamin, Peirce argued that mathematics studies purely hypothetical objects and is not just the science of quantity but is more broadly the science which draws necessary conclusions; that mathematics aids logic, not vice versa; and that logic itself is part of philosophy and is the science about drawing conclusions necessary and otherwise.[81]

### Mathematics of logic

Mathematical logic and foundations, some noted articles
• On an Improvement in Boole's Calculus of Logic (1867)
• Description of a Notation for the Logic of Relatives (1870)
• On the Algebra of Logic (1880)
• A Boolean Algebra with One Constant (1880 MS)
• On the Logic of Number (1881)
• Note B: The Logic of Relatives (1883)
• On the Algebra of Logic: A Contribution to the
Philosophy of Notation (1884/1885)
• The Logic of Relatives (1897)
• The Simplest Mathematics (1902 MS)
• Prolegomena To an Apology For Pragmaticism (1906,
on existential graphs)

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had just recently awakened from its Cinderella slumbers. Much of the mathematics of relations now taken for granted was "borrowed" from Peirce, not always with all due credit; on that and on how the young Bertrand Russell, especially his Principles of Mathematics and Principia Mathematica, did not do Peirce justice, see Anellis (1995).[57] In 1918 the logician C. I. Lewis wrote, "The contributions of C.S. Peirce to symbolic logic are more numerous and varied than those of any other writer — at least in the nineteenth century."[82] Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relational algebra.

Relational logic gained applications. In mathematics, it influenced the abstract analysis of E. H. Moore and the lattice theory of Garrett Birkhoff. In computer science, the relational model for databases was developed with Peircean ideas in work of Edgar F. Codd, who was a doctoral student[83] of Arthur W. Burks, a Peirce scholar. In economics, relational logic was used by Frank P. Ramsey, John von Neumann, and Paul Samuelson to study preferences and utility and by Kenneth J. Arrow in Social Choice and Individual Values, following Arrow's association with Tarski at City College of New York.

On Peirce and his contemporaries Ernst Schröder and Gottlob Frege, Hilary Putnam (1982)[77] documented that Frege's work on the logic of quantifiers had little influence on his contemporaries, although it was published four years before the work of Peirce and his student Oscar Howard Mitchell. Putnam found that mathematicians and logicians learned about the logic of quantifiers through the independent work of Peirce and Mitchell, particularly through Peirce's "On the Algebra of Logic: A Contribution to the Philosophy of Notation"[76] (1885), published in the premier American mathematical journal of the day, and cited by Peano and Schröder, among others, who ignored Frege. They also adopted and modified Peirce's notations, typographical variants of those now used. Peirce apparently was ignorant of Frege's work, despite their overlapping achievements in logic, philosophy of language, and the foundations of mathematics.

• Philosophical algebraist William Kingdon Clifford[84] and logician William Ernest Johnson, both British;
• The Polish school of logic and foundational mathematics, including Alfred Tarski;
• Arthur Prior, who praised and studied Peirce's logical work in a 1964 paper[23] and in Formal Logic (saying on page 4 that Peirce "perhaps had a keener eye for essentials than any other logician before or since.").

Jean Van Heijenoort (1967),[85] Jaakko Hintikka (1997),[86] and Geraldine Brady (2000)[79] 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.

A philosophy of logic, grounded in his categories and semiotic, can be extracted from Peirce's writings and, along with Peirce's logical work more generally, is exposited and defended in Hilary Putnam (1982);[77] the Introduction in Nathan Houser et al. (1997);[87] and Randall Dipert's chapter in Cheryl Misak (2004).[88]

### Continua

Continuity and synechism are central in Peirce's philosophy. He embraced infinitesimals and worked long on the mathematics of continua. He long held that the real numbers constitute a pseudo-continuum;[89] that a true continuum is the real subject matter of analysis situs (topology); and that a true continuum of instants exceeds—and within any lapse of time has room for—any Aleph number (any infinite multitude as he called it) of instants.[90]

In 1908 Peirce wrote that he found that a true continuum might have or lack such room. Jérôme Havenel (2008): "It is on May 26, 1908, that Peirce finally gave up his idea that in every continuum there is room for whatever collection of any multitude. From now on, there are different kinds of continua, which have different properties."[91]

### Probability and statistics

Peirce held that science achieves statistical probabilities, not certainties, and that spontaneity (absolute chance) is real (see Tychism on his view). Most of his statistical writings promote the frequency interpretation of probability (objective ratios of cases), and many of his writings express skepticism about (and criticize the use of) probability when such models are not based on objective randomization.[92] Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability before Karl Popper.[93][94] Peirce (sometimes with Joseph Jastrow) investigated the probability judgments of experimental subjects, "perhaps the very first" elicitation and estimation of subjective probabilities in experimental psychology and (what came to be called) Bayesian statistics.[2]

Peirce was one of the founders of statistics. He formulated modern statistics in "Illustrations of the Logic of Science" (1877–8) and "A Theory of Probable Inference" (1883). With a repeated measures design, he introduced blinded, controlled randomized experiments in 1884 (Hacking 1990:205)[1] (before Ronald A. Fisher).[2] He invented optimal design for experiments on gravity, in which he "corrected the means". He used correlation and smoothing. Peirce extended the work on outliers by Benjamin Peirce, his father.[2] He introduced terms "confidence" and "likelihood" (before Jerzy Neyman and Fisher). (See Stephen Stigler's historical books and Ian Hacking 1990[1]).

## Philosophy

It is not sufficiently recognized that Peirce's career was that of a scientist, not a philosopher; and that during his lifetime he was known and valued chiefly as a scientist, only secondarily as a logician, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fact becomes a standing premise of Peircean studies.
—Max Fisch 1964, p. 486.[23]

Peirce was a working scientist for 30 years, and arguably was a professional philosopher only during the five years he lectured at Johns Hopkins. He learned philosophy mainly by reading, each day, a few pages of Kant's Critique of Pure Reason, in the original German, while a Harvard undergraduate. His writings bear on a wide array of disciplines, including mathematics, logic, philosophy, statistics, astronomy,[23] metrology,[3] geodesy, experimental psychology,[4] economics,[5] linguistics,[6] and the history and philosophy of science. This work has enjoyed renewed interest and approval, 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 philosophy includes (see below in related sections) a pervasive three-category system, belief that truth is immutable and is both independent from actual opinion (fallibilism) and discoverable (no radical skepticism), logic as formal semiotic on signs, on arguments, and on inquiry's ways—including philosophical pragmatism (which he founded), critical common-sensism, and scientific method—and, in metaphysics: Scholastic realism, belief in God, freedom, and at least an attenuated immortality, objective idealism, and belief in the reality of continuity and of absolute chance, mechanical necessity, and creative love. In his work, fallibilism and pragmatism may seem to work somewhat like skepticism and positivism, respectively, in others' work. However, for Peirce, fallibilism is balanced by an anti-skepticism and is a basis for belief in the reality of absolute chance and of continuity,[95] and pragmatism commits one to anti-nominalist belief in the reality of the general (CP 5.453–7).

For Peirce, First Philosophy, which he also called cenoscopy, is less basic than mathematics and more basic than the special sciences (of nature and mind). It studies positive phenomena in general, phenomena available to any person at any waking moment, and does not settle questions by resorting to special experiences.[96] He divided such philosophy into (1) phenomenology (which he also called phaneroscopy or categorics), (2) normative sciences (esthetics, ethics, and logic), and (3) metaphysics; his views on them are discussed in order below.

### Theory of categories

On May 14, 1867, the 27-year-old 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. The paper outlined a theory of predication, involving three universal categories that Peirce developed in response to reading Aristotle, Kant, and Hegel, categories that Peirce applied throughout philosophy and elsewhere for the rest of his life. Most students of Peirce will readily agree on their prevalence in his philosophical work. Peirce scholars generally regard the "New List" as foundational or breaking the ground for Peirce's "architectonic", his blueprint for a pragmatic philosophy. In the categories one will discern, concentrated, the pattern that one finds formed by the three grades of clearness in "How To Make Our Ideas Clear" (1878 paper foundational to pragmatism), and in numerous other trichotomies in his work.

"On a New List of Categories" is cast as a Kantian deduction; it is short but dense and difficult to summarize. The following table is compiled from that and later works.[97] In 1893, Peirce restated most of it for a more general audience.[98]

Peirce's Categories (technical name: the cenopythagorean categories)[99]
Name: Typical characterizaton: As universe of experience: As quantity: Technical definition: Valence, "adicity":
Firstness.[100] Quality of feeling. Ideas, chance, possibility. Vagueness, "some". Reference to a ground (a ground is a pure abstraction of a quality).[101] Essentially monadic (the quale, in the sense of the such,[102] which has the quality).
Secondness.[103] Reaction, resistance, (dyadic) relation. Brute facts, actuality. Singularity, discreteness, “this”. Reference to a correlate (by its relate). Essentially dyadic (the relate and the correlate).
Thirdness.[104] Representation, mediation. Habits, laws, necessity. Generality, continuity, "all". Reference to an interpretant*. Essentially triadic (sign, object, interpretant*).

*Note: An interpretant is an interpretation (human or otherwise) in the sense of the product of an interpretive process.

### Esthetics and ethics

Peirce did not write extensively in esthetics and ethics,[105] but came by 1902 to hold that esthetics, ethics, and logic, in that order, comprise the normative sciences.[106] He defined esthetics as the study of good and bad, and thus of the ends governing all conduct.[107]