Charles Sanders Peirce

Charles Sanders Peirce
Charles Sanders Peirce
Born	10 September 1839(1839-09-10) Cambridge, Massachusetts
Died	19 April 1914 (aged 74)
Nationality	American
Fields	Chemistry Philosophy Mathematics
Religious stance	Episcopal but unconventional

Charles Sanders Peirce (pronounced /ˈpɜrs/ purse^[1]) (September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician, and scientist, born in Cambridge, Massachusetts. Peirce was educated as a chemist and employed as a scientist for 30 years. It is largely his contributions to logic, mathematics, philosophy, and semiotics (and his founding of pragmatism) that are appreciated today. In 1934, the philosopher Paul Weiss called Peirce "the most original and versatile of American philosophers and America's greatest logician".^[2]

An innovator in mathematics, statistics, research methodology, philosophy of science, epistemology, and metaphysics, 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, in turn, 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, an idea used decades later to produce digital computers.

Life

Charles Peirce's birthplace near Harvard Yard.

Charles Sanders Peirce was the son of Sarah Hunt Mills and Benjamin Peirce, 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. He went on to obtain the BA and MA from Harvard, and in 1863 the 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 Harvard employ Peirce in any capacity.

Peirce suffered from his late teens through the rest of his life from what was then known as "facial neuralgia", a very painful nervous/facial condition. The biography by Joseph Brent^[3] 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." His condition would today be diagnosed as trigeminal neuralgia. Its consequences may have led to the social isolation which made the later years of his life so tragic.

United States Coast Survey

Between 1859 and 1891, Peirce 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 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. 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 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 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. (On Peirce the astronomer, see Lenzen's chapter in Moore and Robin, 1964.) In 1876 he was elected a member of the National Academy of Sciences. In 1878, he was the first to define the meter as so many wavelengths of light of a certain frequency, the definition employed until 1983 (Taylor 2001: 5)^[4].

During the 1880s, Peirce's indifference to bureaucratic detail waxed while the quality and timeliness of his Survey work waned. Peirce took years to write reports that he should have completed in mere months. Meanwhile, he wrote hundreds of logic, philosophy, and science entries for the Century Dictionary.^[5] 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. That university 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). 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. Peirce's ability to find academic employment may also have been frustrated by a difficult personality. Brent conjectures about various psychological and other difficulties.

Peirce's personal life also handicapped him. His first wife, Harriet Melusina Fay, left him in 1875. He soon took up with a woman, Juliette, whose maiden name and nationality remain uncertain to this day (the best guess is that her name was Juliette Froissy and that she was French), but his divorce from Harriet became final only in 1883, after which he married Juliette. 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. Just why Peirce's later applications for academic employment at Clark University, University of Wisconsin–Madison, 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 years while still legally married to Harriet led him to be deemed morally unfit for academic employment anywhere in the USA. Peirce had no children by either marriage.

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, land which never yielded an economic return. There he built a large house which he named "Arisbe" where he spent the rest of his life, writing prolifically, much of it unpublished to this day. His living beyond his means soon led to grave financial and legal difficulties. Peirce 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. 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, mainly 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 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. He 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 the owner, respectively, of the pioneering American philosophy journal The Monist, which eventually published 14 or so articles by Peirce. He applied to the newly formed Carnegie Institution for a grant to write a book summarizing 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.

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 four series of lectures at or near Harvard (1898, 1903, 1907). Most important, each year from 1898 until his death in 1910, James wrote to his friends in the Boston intelligentsia, asking that they contribute financially to help support Peirce. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him.^[6]

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

Reception

Bertrand Russell opined (1959:276), "Beyond doubt [...] he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (His Principia Mathematica does not mention Peirce, but Peirce's work was not widely known until after this was written.) 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".^[7] Nevertheless, Peirce's accomplishments were not immediately recognized. His imposing contemporaries William James and Josiah Royce 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 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 is Peircean through and through. The publication of the first six volumes of the Collected Papers (1931–35), 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 W. 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. Thus 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) reprints many of the relevant articles, including a wide-ranging survey (Fisch 1986: 422-48) 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,^[8] Finland,^[9] Germany,^[10] France^[11], Spain^[12], and Italy^[13]. His writings have been translated into several languages, including German, French, Finnish, Spanish, and Swedish. Since 1950, there have been French, Italian, Spanish 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. (Burch 2001/2006^[14].)

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. The only full-length book (neither extract nor pamphlet) that Peirce authored and saw published in his lifetime 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 eight 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)^[15] catalogued this Nachlass did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totaling over 100,000 pages.^[16] Most of it remains unpublished, except on microfilm. For more on the vicissitudes of Peirce's papers, see Houser (1989)^[17].

List of major articles and lectures

See Charles Sanders Peirce bibliography for extensive list of his works, along with links to many of them readable online.

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, and 1994, most still in print. The main posthumous editions 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 work in Peirce studies is organized thematically, but texts from different times are often stitched together, making for contradictory pieces, requiring frequent visits to editors' notes, and obscuring Peirce's development. Edited (1–6) by Charles Hartshorne and Paul Weiss and (7–8) by Arthur Burks, in print from Harvard and on InteLex CD-ROM.

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 on InteLex CD-ROM.

1976: The New Elements of Mathematics by Charles S. Peirce (NEM), 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), 6 volumes 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 six volumes have appeared to date, but they cover the period from 1859–1890, when Peirce carried out much of his best-known work. W 8's publication is planned for spring 2010; and work continues on W 7, 9, and 11. In print from Indiana University.

1985: Historical Perspectives on Peirce's Logic of Science: A History of Science, 2 volumes. Auspitz has said^[18], "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 University.

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.

Mathematics

Peirce regarded mathematics as prior not only to special sciences (of nature and mind) but also to philosophy, and as broadly divided into mathematics (1) of logic, (2) of discrete series, and (3) of pseudo-continuous series (as he called them, including the real numbers) and continuous series. He was active not only in various "pure" areas, but also in probability and statistics.

Mathematics of logic

Peirce made a number of striking discoveries in foundational mathematics, nearly all of which came to be appreciated only long after his death. He:

• Discovered in 1880^[19] how that which is now called Boolean algebra could be expressed by means of a single binary operation, either NAND or its dual, NOR. (See also De Morgan's Laws). This discovery anticipated Sheffer by 33 years.
• In Peirce (1881)^[20] set out the now-classic axiomatization of natural number arithmetic, a few years before Dedekind and Peano did so. In the same paper Peirce introduced the first purely cardinal definition of a finite set^[21], by the property now called that of being "Dedekind-finite".
• Discovered, independently of Dedekind, an important formal definition of an infinite set, namely, as a set that can be put into a one-to-one correspondence with one of its proper subsets.
• In Peirce (1885), set out what can be read as the first (primitive) axiomatic set theory, anticipating Zermelo by about two decades.

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."^[22] 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 actual mathematics of relations now taken for granted was "borrowed" from Peirce, not always with all due credit (Anellis 1995^[23]). Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relational algebra. These theoretical resources gradually worked their way into applications, in large part instigated by the work of Edgar F. Codd, who happened to be a doctoral student of the Peirce editor and scholar Arthur W. Burks, on the relational model or the relational paradigm for implementing and using databases.

In the four-volume work The New Elements of Mathematics by Charles S. Peirce (1976), mathematician and Peirce scholar Carolyn Eisele published a large number of Peirce's previously unpublished manuscripts on mathematical subjects, including the drafts for an introductory textbook, allusively titled The New Elements of Mathematics, that presented mathematics from a decidedly novel, if not revolutionary, standpoint.

In 1902 Peirce applied to the newly established Carnegie Institution for aid "in accomplishing certain scientific work", presenting an "explanation of what work is proposed" plus an "appendix containing a fuller statement". These parts of the letter, along with excerpts from earlier drafts, can be found in NEM 4 (Eisele 1976). The appendix is organized as a "List of Proposed Memoirs on Logic", and No. 12 among the 36 proposals is titled "On the Definition of Logic", the earlier draft of which is quoted in full in #Logic_as_formal_semiotic, below.

On Peirce and his contemporaries Ernst Schröder and Gottlob Frege, Hilary Putnam (1982)^[24] wrote that he found through research that, though Frege had priority by four years, it was Peirce and his student Oscar Howard Mitchell who effectively discovered the quantifier for the mathematical world. The main evidence for Putnam's claims is "On the Algebra of Logic: A Contribution to the Philosophy of Notation"^[25] (1885), published in the premier American mathematical journal of the day. Peano and Ernst Schröder, among others, cited this article and used or adapted Peirce's notations, which are a typographical variant of those currently used. Peirce apparently was ignorant of Frege's work, despite their rival achievements in logic, philosophy of language, and the foundations of mathematics.

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,^[26] 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 John F. Sowa's conceptual graphs and of Sun-Joo Shin's diagrammatic reasoning.

A philosophy of logic, grounded in his categories and semiotic, can be extracted from Peirce's writings. This philosophy, as well as Peirce's logical work more generally, is exposited and defended in Hilary Putnam (1982); the Introduction in Houser et al. (1997)^[27]; and Dipert's chapter in Misak (2004)^[28]. Jean Van Heijenoort (1967)^[29], Jaakko Hintikka in his chapter in Brunning and Forster (1997), and Geraldine Brady (2000)^[30] 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)^[23].

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;
• Arthur Prior, whose Formal Logic and chapter in Moore and Robin (1964) praised and studied Peirce's logical work.

Logical graphs

Logic of information

.... The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &tc. — which make up the comprehension of man. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead. (C.S. Peirce, "The Logic of Science, or, Induction and Hypothesis" (1866), W 1:467.)

Geometry and continuity

Peirce produced a quincuncial projection of a sphere which kept angles true and resulted in less distortion of area than did other projections.

Continuity and synechism are important, even crucial, in Peirce's philosophy. He worked long on the mathematics of continua and noted both that, in an 1882 paper, he anticipated Dedekind and that, unknowingly at the time, he was largely anticipated by Cantor; he held for many years that the real numbers constituted a pseudocontinuum and that a true continuum of instants was not a "multitude" (as he called it) or Cantorian aleph, that it had, within any lapse of time, room enough for any multitude howsoever great, and that it was the real subject matter of that which we now call topology.^[31] In 1908 he gave up on that particular conception of continua.^[32]

Probability and statistics

Peirce held that science achieves statistical probabilities, not certainties, and that chance, a veering from law, is very real. He assigned probability to an argument’s conclusion rather than to a proposition, event, etc., as such. 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.^[33] Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability. Peirce (sometimes with Jastrow) investigated the probability judgments of experimental subjects, pioneering decision analysis.

Peirce was one of the founders of statistics. He formulated modern statistics in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). With a repeated measures design, he introduced blinded, controlled randomized experiments (before Fisher). He invented optimal design for experiments on gravity, in which he "corrected the means". He used logistic regression, correlation, and smoothing. Peirce extended the work on outliers by Benjamin Peirce, his father. He introduced terms "confidence" and "likelihood" (before Neyman and Fisher). (See the historical books of Stephen Stigler.)

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, in Fisch, Moore, and Robin 1964, 486).

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 astronomy, metrology, geodesy, mathematics, logic, philosophy, the history and philosophy of science, statistics, linguistics, economics, and psychology. 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 a pervasive three-category system, fallibilism, critical common-sensism ("dismiss make-believes" such as the absolutely incognizable and the foundational hyperbolic doubt), logic as formal semiotic, philosophical pragmatism, which he founded, Scholastic realism, theism, objective idealism, and belief in the reality of continuity and of chance, mechanical necessity, and evolutionary love. In his work, fallibilism and pragmatism may be seen as playing roles somewhat similar to those of skepticism and positivism, respectively, in others' work. However, for Peirce, fallibilism is a basis for belief in the reality of chance and continuity, and pragmatism fortifies belief in the reality of the general.

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 seek novel phenomena or resort to special experiences or experiments in order to settle its questions.^[34] 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 which Peirce developed in reaction to his reading of Aristotle, Kant, and Hegel, categories which Peirce would apply throughout philosophy and elsewhere for the rest of his life. Most students of Peirce will readily agree about their prevalence throughout 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 which one finds formed by the three grades of clearness in "How To Make Our Ideas Clear" (1878 foundational paper for 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.

 *Note: An interpretant is an interpretation in the sense of the product of an interpretive process or the content of an interpretation.

Esthetics and ethics

Peirce did not write extensively in esthetics and ethics, but held that, together with logic in the broad sense, those studies constituted the normative sciences. He defined esthetics as the study of good and bad; and characterized the good as "the admirable". He held that, as the study of good and bad, esthetics is the study of the ends governing all conduct and comes ahead of other normative studies.^[38]

Peirce reserved the spelling "aesthetics" for the study of artistic beauty.

Philosophy: Logic, or semiotic

Logic as philosophical

Peirce regarded logic per se as a division of philosophy, as a normative science after esthetics and ethics, as more basic than metaphysics^[39], and as "the art of devising methods of research"^[40]. More generally, as inference, "logic is rooted in the social principle", since inference depends on a standpoint that, in a sense, is unlimited^[41]. Peirce called (with no sense of deprecation) "mathematics of logic" much of the kind of thing which, in current research and applications, is called simply "logic". He was productive in both (philosophical) logic and logic's mathematics, which were connected deeply in his work and thought.

Peirce argued that logic is formal semiotic^[42], the formal study of signs in the broadest sense, not only signs that are artificial, linguistic, or symbolic, but also signs that are semblances or indexical such as reactions. Peirce held that "all this universe is perfused with signs, if it is not composed exclusively of signs"^[43], along with their representational and inferential relations. He argued that, since all thought takes time, all thought is in signs^[44] and sign processes ("semiosis") such as the inquiry process. He divided logic into: (1) speculative grammar, or stechiology, on how signs can represent and signify and, in relation to that, what kinds of signs there are, how they combine, and how some embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative rhetoric, or methodeutic, the philosophical theory of inquiry, including pragmatism.

Presuppositions of logic

In his "F.R.L." [First Rule of Logic] (1899), he states that the first, and "in one sense, this sole", rule of reason is that, in order to learn, one needs to desire to learn and desire it without resting satisfied with that which one is inclined to think.^[39] So, the first rule is, to wonder. Peirce proceeds to a critical theme in the shaping of theories, not to mention associated practices:

...there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:

Peirce adds, that method and economy are best in research but no outright sin inheres in trying any theory in the sense that the investigation via its trial adoption can proceed unimpeded and undiscouraged, and that "the one unpardonable offence" is a philosophical barricade against truth's advance, an offense to which "metaphysicians in all ages have shown themselves the most addicted". Peirce in many writings holds that logic precedes metaphysics (ontological, religious, and physical).^[45]

Peirce goes on to list four common barriers to inquiry: (1) Assertion of absolute certainty; (2) maintaining that something is absolutely unknowable; (3) maintaining that something is absolutely inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena. To refuse absolute certainty is the heart of fallibilism, which Peirce unfolds into refusals to set up any of the listed barriers. Peirce elsewhere argues (1897) that logic's presupposition of fallibilism leads at length to the view that chance and continuity are very real (tychism and synechism).^[46]

One might have thought that, as a whole, the topic belongs within theory of inquiry ("Methodeutic" or "Philosophical or Speculative Rhetoric"), his third department of logic; but the First Rule of Logic pertains to the mind's presuppositions in undertaking reason and logic, presuppositions, for instance, that there are truth and real things independent of what you or I think of them.^[47] He describes such ideas as, collectively, hopes which, in particular cases, one is unable seriously to doubt.^[48] Peirce's view that there is no way to conceive of the absolutely incognizable leads to his rejecting the conception (usually ascribed to Kant) of the unknowable thing-in-itself. Peirce's view that it is idle or counterproductive to start philosophy from paper doubts, make-believe doubts, leads to his rejection of Cartesian foundationalism^[49] and, along with his rejection of the unknowable thing-in-itself, to what he called critical common-sensism ("dismiss make-believes"), which he regarded as a prerequisite for Pragmatism.^[50]

Logic as formal semiotic

Peirce's semiotic is philosophical logic studied in terms of signs and sign processes. Often using examples from common experience, Peirce defines and discusses things like assertions and interpretations in terms of philosophical logic rather than of psychology, linguistics, or social studies. In a formal vein, Peirce says:

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. (Peirce, "Carnegie Application", NEM 4:54).

Peirce called his general study of signs semiotic or semeiotic. Both terms are current in both singular and plural forms.^[51] Peirce began writing on semiotic in the 1860s, around the time that he devised his system of three categories. From the beginning he based his semiotic on the understanding of a triadic sign relation. His 1907 definition of semiosis is "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs".^[52]

Dynamics of inquiry

Every mind which passes from doubt to belief must have ideas which follow after one another in time. Every mind which reasons must have ideas which not only follow after others but are caused by them. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. (Peirce, "On Time and Thought", W 3:68–69.)

Throughout the 1860s, the young but rapidly maturing Peirce was busy establishing a conceptual base camp and a technical supply line for a lifetime's intellectual adventures. In the long view, among best titles for the story, it all seems to relate to the dynamics of inquiry. This broad subject area has a part given by nature and a part ruled by nurture. On first approach, one can see a question of articulation and a question of explanation:

• What is needed to articulate the workings of the active form of representation that is known as conscious experience?

• What is needed to account for the workings of the reflective discipline of inquiry that is known as science?

Pursuit of these questions finds them entangled together and finally incomprehensible apart from each other, but for exposition's sake it is convenient to organize a study of Peirce's assault on the summa by following first the trails of thought that led him to develop a theory of signs ('semiotic'), and tracking next the ways of thinking that led him to develop within it a theory of inquiry, one that would be up to the task of saying 'how science works'.

Opportune points of departure for exploring the dynamics of representation, such as led to Peirce's theories of inference and information, inquiry and signs, are those that he took for his own springboards. Perhaps the most significant influences radiate from points on parallel lines of inquiry in Aristotle's work, points where the intellectual forerunner focused on many of the same issues and even came to strikingly similar conclusions, at least about the best ways to begin. To keep on course to a firmer basis for understanding Peirce, it serves to consider the following loci in Aristotle:

• The basic terminology of psychology, in On the Soul.

• The founding description of sign relations, in On Interpretation;

• The differentiation of the genus of reasoning into three species of inference that are commonly translated into English as abduction, deduction, and induction, in the Prior Analytics.

In addition to the three elementary modes of inference, that Peirce would assay to be irreducible, Aristotle analyzed several kinds of compound inference, most importantly the kind known as 'reasoning by analogy' or 'reasoning from example', employing for the latter description the Greek word 'paradeigma', from which we get our word 'paradigm'.

Inquiry is a form of reasoning process; it institutes a specially conducted manner of thinking. Philosophers of the school that is commonly called 'pragmatic' hold with Peirce that "all thought is in signs",^[44] where 'sign' is the word for the broadest conceivable variety of indices, semblances, signals, symbols, formulas, texts, and so on up the line, that might be imagined. Even intellectual concepts and mental ideas are held to be a special class of signs, corresponding to internal states of the thinking agent that both issue in and result from the interpretation of external signs.

The subsumption of inquiry within reasoning in general and the inclusion of thinking within the class of sign processes let us approach the subject of inquiry from two different perspectives:

• The syllogistic approach treats inquiry as a species of logical process, and is limited to those of its aspects that can be related to the most basic laws of inference.

• The sign-theoretic approach views inquiry as a genus of semiosis, an activity taking place within the more general setting of sign relations and sign processes.

Signs

Sign relation

Anything is a sign — not absolutely as itself, but instead in some relation or other. The sign relation is the key. It defines three roles encompassing (1) the sign, (2) the sign's subject matter, called its object, and (3) the sign's meaning or ramification as formed into a kind of effect called its interpretant (a further sign, for example a translation). It is an irreducible triadic relation, according to Peirce. The roles are distinct even when the things that fill those roles are not.

Extension × intension = information. The triadic relation requires an understanding of relation as such. Two traditional approaches, necessary though insufficient, are the way of extension (a sign's objects, also called breadth or denotation) and the way of intension (a sign's meaning, also called depth, comprehension, signification, or nowadays connotation). Peirce adds a third, the way of information, including change of information, in order to integrate the other two approaches into a unified whole. For example, because of the equation above, if the total amount of information stays the same, then the more that a term signifies or 'intends' about things, the fewer become the things to which it 'extends' or applies.^[53]

Determination. A sign depends on its object in such a way as to represent its object — the object determines the sign. A physically causal sense of this stands out especially when a sign consists in an indicative reaction. The interpretant depends likewise on both the sign and the object — the object determines the sign to determine the interpretant. But this determination is not a succession of dyadic events, like a row of toppling dominoes; sign determination is triadic. For example, an interpretant does not merely represent something which represented an object; instead an interpretant represents something as a sign representing an object. It is an informational kind of determination, a rendering of something more determinately representative.^[54] It is not strictly deterministic, and varies in measure, like an influence. Peirce defines sign, object, and interpretant by their (triadic) mode of determination, not by the idea of representation, since that is part of what is being defined.^[55]

Semiotic elements

Peirce held there are exactly three basic elements in semiosis (sign action):

1. A sign (or representamen^[56]) represents, in the broadest possible sense of "represents". It is something interpretable as saying something about something. It is not necessarily symbolic, linguistic, or artificial.
2. An object (or semiotic object) is a subject matter of a sign and an interpretant. It can be anything discussable or thinkable, a thing, event, relationship, quality, law, argument, etc., and can even be fictional, for instance Hamlet.^[57] All of those are special or partial objects. The object most accurately is the universe of discourse to which the partial or special object belongs.^[58] For instance, a perturbation of Pluto's orbit is a sign about Pluto but ultimately not only about Pluto.
3. An interpretant (or interpretant sign) is the sign's more or less clarified meaning or ramification, a kind of form or idea of the difference which the sign's being true or undeceptive would make. (Peirce's sign theory concerns meaning in the broadest sense, including logical implication, not just the meanings of words as properly clarified by a dictionary.) The interpretant is a sign (a) of the object and (b) of the interpretant's "predecessor" (the interpreted sign) as being a sign of the same object. The interpretant is an interpretation in the sense of a product of an interpretive process or a content in which an interpretive relation culminates, though this product or content may itself be an act, a state of agitation, a conduct, etc. As Peirce sometimes put it (he defined sign at least 76 times^[59]), the sign stands for the object to the interpretant.

Some of the understanding needed by the mind depends on familiarity with the object. In order to know what a given sign denotes, the mind needs some experience of that sign's object collaterally to that sign or sign system, and in that context Peirce speaks of collateral experience, collateral observation, collateral acquaintance, all in much the same terms.^[60]

The object determines (not in the deterministic sense, but in a sense of "specializes," bestimmt^[54]) the sign to determine another sign — the interpretant — to be related to the object as the sign is related to the object, hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself, and is definitive of sign, object, and interpretant in general.^[59]

Classes of signs

Among Peirce's many sign typologies, three stand out, interlocked. They depend respectively on (I) the sign itself, (II) the sign's relation to its denoted object, and (III) the sign's relation to its object and to its interpretant. Additionally, each of the three typologies is a three-way division, a trichotomy, via Peirce's three phenomenological categories. One typology classifies the sign by the sign's own category. A second classifies the sign by the category of the sign's way of denoting its object. The third classifies the sign by the category which the sign's interpretant attributes to the sign's way of denoting the object.

I. Qualisign, sinsign, legisign (also called tone, token, type, and also called potisign, actisign, famisign): This typology emphasizes the sign itself in terms of the phenomenological category which it embodies—the qualisign is a quality, a possibility, a "First"; the sinsign is a reaction or resistance, a singular object, an actual event or fact, a "Second"; and the legisign is a habit, a rule, a representational relation, a "Third".

II. Icon, index, symbol: This typology, the best known one, emphasizes the different ways in which the sign refers to its object—the icon (also called semblance or likeness) by a quality of its own, the index by real connection to its object, and the symbol by a habit or rule for its interpretant.

III. Rheme, dicisign, argument (also called sumisign, dicisign, suadisign, also seme, pheme, delome, and regarded as very broadened versions of the traditional term, proposition, argument): This typology emphasizes that which the interpretant represents to be the sign's way of referring to its object—the rheme, for example a term, is a sign interpreted to represent its object in respect of quality; the dicisign, for example a proposition, is a sign interpreted to represent its object in respect of fact; and the argument is a sign interpreted to represent its object in respect of habit or law. This is the culminating typology of the three, where the sign is understood as a structural element of inference.

Every sign falls under one class or another within (I) and within (II) and within (III). Thus each of the three typologies is a three-valued parameter for every sign. The three parameters are not independent of each other; many co-classifications aren't found, for reasons pertaining to the lack of either habit-taking or singular reaction in a quality, and the lack of habit-taking in a singular reaction. The result is not 27 but instead ten classes of signs fully specified at this level of analysis.

Modes of inference

Borrowing a brace of concepts from Aristotle, Peirce examined three basic modes of reasoning that play roles in inquiry, processes currently known as abductive, deductive, and inductive inference. Peirce also called abduction "retroduction" and, earliest of all, "hypothesis". He characterized it as guessing and as inference to the best explanation. Peirce sometimes expounded the modes of inference by transformations of the classical Barbara (AAA) syllogism, for example in "Deduction, Induction, and Hypothesis" (1878, see CP 2:623). He does this by rearranging the rule (which serves as deduction's major premiss), the case (deduction's minor premiss), and the result (deduction's conclusion):

Peirce went on in 1883 in "A Theory of Probable Inference" (Studies in Logic) to equate hypothetical inference with the induction of characters of objects. Eventually dissatisfied, by 1900 he was distinguishing them again and taking the syllogistic forms as not quite basic. In 1903 he presented the following logical form for abductive inference:^[61]

The surprising fact, C, is observed;

But if A were true, C would be a matter of course,

Hence, there is reason to suspect that A is true.

Note that the logical form does not also cover induction, since induction does not depend on surprise and does not introduce a new idea in its conclusion. Abduction seeks a hypothesis to account for facts; induction seeks facts to test a hypothesis. Peirce now regarded abduction as plainly preparatory to further study and inference. In his methodeutic or theory of inquiry (see below), Peirce regards the three modes as clarified by their coordination in essential roles in inquiry and science, with abduction generating a possible hypothesis to account for a surprising phenomenon, deduction clarifying the relevant necessary predictive consequences of the hypothesis, and induction testing the sum of the predictions against the sum of the data to show something actually in operation.^[62]

Pragmatism

Peirce's recipe for pragmatic thinking, called both pragmatism and pragmaticism, is recapitulated in several versions of the so-called pragmatic maxim. Here is one of his more emphatic reiterations 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.^[63]

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

Peirce's pragmatism is a method of sorting out conceptual confusions by equating the meaning of any concept with the conceivable operational or practical consequences of whatever it is which the concept portrays. This pragmatism bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavellian search for mercenary or political advantage. Rather, Peirce's pragmatic maxim is the heart of his pragmatism as a method of experimentational mental reflection^[64] arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances—a method hospitable to the generation of explanatory hypotheses, and conducive to the employment and improvement of verification^[65] to test the truth of putative knowledge. As such a method, pragmatism leads beyond the usual duo of foundational alternatives, namely:

• Deduction from self-evident truths, or rationalism;

• Induction from experiential phenomena, or empiricism.

His approach is distinct from foundationalism, empiricist or otherwise, as well as from coherentism, by the following three dimensions:

• 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, and that in dual senses of the word: prediction and control. Peirce's identification of these three dimensions serves to flesh out an approach to inquiry far more solid than the standard image of simple inductive generalization as describing a pattern observed in phenomena. 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 than its rivals in predicting and controlling our world is said to be nearer the truth. This is an operational notion of truth employed by scientists. Peirce held, that the scientific method is the best for theoretical questions but not always better than tradition, instinct, etc., for time-sensitive practical questions, but will in the long run produce the most secure results on which action can ultimately be based.

In "How to Make Our Ideas Clear", Peirce discusses three grades of clearness of conception:

1. Clearness of the familiar conception.

2. Clearness as of a definition's parts, the clearness in virtue of which logicians call a concept or definition "distinct".

3. Clearness in virtue of clearness of conceivable consequences of the object as conceived of. Here he introduced that which he later called the Pragmatic Maxim.

By way of example of how to clarify conceptions, he addresses truth and the real as questions of the presuppositions of reasoning in general. In clearness's second grade, he defines truth as a sign's correspondence to its object, and the real as the object of such correspondence, such that truth and the real are independent of that which you or I or any definite community of researchers think. Then in clearness's third grade (the pragmatic grade), he defines the truth as that which would be reached, sooner or later but still inevitably, by research adequately prolonged, such that the real does depend on that final opinion—a dependence to which he appeals in theoretical arguments elsewhere, for instance for the long-term validity of the rule of induction.^[66] Peirce argues that even to argue against the independence and discoverability of truth and the real is to presuppose that there is, about that very question under argument, a truth with just such independence and discoverability.

Peirce's pragmatism, as method and theory of definitions and the clearness of ideas, is a department within his theory of inquiry,^[67] which he variously called "Methodeutic" and "Philosophical or Speculative Rhetoric". He applied his pragmatism as a method throughout his work.

Theory of inquiry

In The Fixation of Belief (1877), Peirce outlined four methods of inquiry and settling belief: (1) the method of tenacity (sticking with that which one is inclined to think), (2) the method of authority, (3) the method of congruity or the a priori or the dilettante or "what is agreeable to reason" (which leads to argumentation which gets finally nowhere), and (4) the method of science, whereby inquiry actually tests itself and criticizes, corrects, and improves itself. Peirce held that, in practical affairs, slow and stumbling ratiocination is often dangerously inferior to instinct, sentiment, and tradition, and that the scientific method is best suited to theoretical research,^[68] which in turn should not be bound to the other methods and practical ends; yet what recommends scientific method above others finally is that it is deliberately designed to arrive, eventually, at the most secure beliefs, upon which the most successful actions can eventually be based.

Peirce extracted the pragmatic model or theory of inquiry from its raw materials in classical logic and refined it in parallel with the early development of symbolic logic to address problems about the nature of scientific reasoning.

Abduction, deduction, and induction do not make complete sense in isolation from each other but comprise a cycle understandable as a whole insofar as they collaborate toward the end of inquiry. In the pragmatic way of thinking in terms of conceivable consequences, every thing has a purpose, and a thing's purpose is the first thing that we should try to note about it. Inquiry's purpose is to reduce doubt and lead to a state of belief, which a person in that state will usually call 'knowledge' or 'certainty'. The three kinds of inference function systematically to reduce the uncertainties and difficulties that occasioned the inquiry, and thus, to the extent that inquiry succeeds, lead to an increase in the knowledge or skills, in other words an augmentation in the competence or performance of the agent or community engaged in the inquiry.

For instance, abduction's purpose is to guess toward best or most-simplifying explanations, which deduction can explicate and which induction can evaluate. This adds mild but meaningful constraints of plausibility, practical testability, and so on, to the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality. Likewise, each of the other types of inference realizes its purpose only in accord with its proper role in the whole cycle of inquiry. No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its principal components.

The ensuing question, 'What sort of constraint, exactly, does pragmatic thinking of the end of inquiry place on our guesses?', is generally recognized as the problem of 'giving a rule to abduction'. Peirce's overall answer was the pragmatic maxim. In 1903 Peirce called the question of pragmatism "the question of the logic of abduction".^[69]

Peirce characterized the scientific method as follows:^[70]

1. Abduction (or retroduction). Guessing, generation of explanatory hypothesis. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises in the effort to resolve the wonder of surprising observations in the given realm or realms. All explanatory content of theories is reached by way of abduction, the most insecure among modes of inference. One can hope to discover only that which time would reveal sooner or later anyway, so, to expedite this, the economics of research demands and even governs abduction^[71], whose modicum of success depends on one's being somehow attuned to nature, by dispositions learned and, some of them, likely inborn. Abduction has general inductive justification in that it works often enough and that nothing else works^[72], at least not quickly enough when science is already properly rather slow, the work of indefinitely many generations. Given that abduction relies on inborn or developed instinct attuned to nature and is driven by the need to economize the inquiry process, its explanatory hypotheses should be optimally simple in the sense of "natural" (for which Peirce cites Galileo and which Peirce distinguishes from "logically simple"). Given that abduction is insecure guesswork, it should have consequences with conceivable practical bearing leading at least to mental tests, and, in science, lending themselves to scientific testing.

2. Deduction. Analysis of hypothesis and deduction of its consequences in order to test the hypothesis. Two stages:

i. Explication. Logical analysis of the hypothesis in order to render it as distinct as possible.

ii. Demonstration (or deductive argumentation). Deduction of hypothesis's consequence. Corollarial or, if needed, Theorematic.

3. Induction. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real "is only the object of the final opinion to which sufficient investigation would lead".^[66] In other words, if there were something to which an inductive process involving ongoing tests or observations would never lead, then that thing would not be real. Three stages:

i. Classification. Classing objects of experience under general ideas.

ii. Probation (or direct Inductive Argumentation): Crude (the enumeration of instances) or Gradual (new estimate of proportion of truth in the hypothesis after each test). Gradual Induction is Qualitative or Quantitative; if Quantitative, then dependent on measurements, or on statistics, or on countings.

iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result".^[70]

Philosophy: Metaphysics

Peirce divided metaphysics into (1) ontology or general metaphysics, (2) religious metaphysics, and (3) physical metaphysics.

Ontology. Peirce was a Scholastic Realist, declaring for the reality of generals as early as 1868^[73]. Regarding modalities (possibility, necessity, etc.), he came in later years to regard himself as having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote:

I formerly defined the possible as that which in a given state of information (real or feigned) we do not know not to be true. But this definition today seems to me only a twisted phrase which, by means of two negatives, conceals an anacoluthon. We know in advance of experience that certain things are not true, because we see they are impossible.

Peirce retained, as useful for some purposes, the definitions in terms of information states, but insisted that the pragmaticist is committed to a strong modal realism by conceiving of objects in terms of predictive general conditional propositions about how they would behave under certain circumstances.^[74]

Religious Metaphysics. Peirce believed in God, and characterized such belief as founded in an instinct explorable in musing over the worlds of ideas, brute facts, and evolving norms — and it is a belief in God not as an actual or existent being (in Peirce's sense of those words), but all the same as a real being.^[75] In "A Neglected Argument for the Reality of God" (1908),^[70] Peirce sketches, for God's reality, an argument to a hypothesis of God as the Necessary Being, a hypothesis which he describes in terms of how it would tend to develop and become compelling in musement and inquiry by a normal person who is led, by the hypothesis, to consider as being purposed the features of the worlds of ideas, brute facts, and evolving norms, such that the thought of such purposefulness will "stand or fall with the hypothesis"; meanwhile, according to Peirce, the hypothesis, in supposing an "infinitely incomprehensible" being, starts off at odds with its own nature as a purportively true conception, and so, no matter how much the hypothesis grows, it both (A) inevitably regards itself as partly true, partly vague, and as continuing to define itself without limit, and (B) inevitably has God appearing likewise vague but growing, though God as the Necessary Being is not vague or growing; but the hypothesis will hold it to be more false to say the opposite, that God is purposeless.

Physical Metaphysics. Peirce held the view, which he called objective idealism, that "matter is effete mind, inveterate habits becoming physical laws".^[76] Peirce asserted the reality of (1) chance (his tychist view), (2) mechanical necessity (anancist view), and (3) that which he called the law of love (agapist view). They embody his categories Firstness, Secondness, and Thirdness, respectively. He held that fortuitous variation (which he also called "sporting"), mechanical necessity, and creative love are the three modes of evolution (modes called "tychasm", "anancasm", and "agapasm"^[77]) of the universe and its parts. He found his conception of agapasm embodied in Lamarckian evolution; the overall idea in any case is that of evolution tending toward an end or goal, and it could also be the evolution of a mind or a society; it is the kind of evolution which manifests workings of mind in some general sense. He said that overall he was a synechist, holding with reality of continuity.^[78]

Science of review

Peirce outlined two fields, "Cenoscopy" and "Science of Review", both of which could be called "philosophy" and both of which included philosophy about science. Peirce distinguished First Philosophy as "Cenoscopy," placed it after mathematics and before special sciences (physical, chemical, biological, psychological, social) among the Sciences of Discovery, and he included within it the general study of inquiry and scientific method. Cenoscopic philosophy concerns positive phenomena in general, does not rely on findings from special sciences, and is the kind discussed earlier in this article. Peirce distinguished Ultimate Philosophy as "Science of Review" or "Synthetic Philosophy", placed it between Science of Discovery and Practical Science, and characterized it as "...arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science". His examples of Science of Review included Humboldt's Cosmos, Comte's Philosophie positive, and Spencer's Synthetic Philosophy.^[79]

Peirce placed, within Science of Review, the work and theory of classifying the sciences (including mathematics and philosophy). His classifications, on which he worked for many years, draw on argument and wide knowledge, and are of interest both as a map for navigating his philosophy and as an accomplished polymath's survey of research in his time.

See also

Contemporaries associated with Peirce

Abbreviations

• CDPT = Commens Dictionary of Peirce's Terms.
• CP x.y = Collected Papers of Charles Sanders Peirce, volume x, paragraph y.
• EP x:y = The Essential Peirce: Selected Philosophical Writings, volume x, page y.
• NEM x:y = The New Elements of Mathematics by Charles S. Peirce, volume x, page y.
• W x:y = Writings of Charles S. Peirce: A Chronological Edition, volume x, page y.

For more information on editions, see #Works above.

Notes

External links

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Charles Sanders Peirce bibliography has numerous links throughout to Peirce materials readable online, including:

• Biographical and overview articles at Arisbe, the Peirce Edition Project, the Stanford Encyclopedia of Philosophy, the Internet Encyclopedia of Philosophy, and elsewhere.
• Dozens of individual works by Peirce readable online.
• Online collections of Peirce's writings and of Peirce-related articles, also online bibliographies and Peirce's definitions in the Baldwin dictionary.

An earlier version of this article, by Jaime Nubiola, was posted at Nupedia.