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Encyclopedia > Charles Peirce
Western Philosophy
19th/20th century philosophy
Name: Charles Sanders Peirce
Birth: September 10, 1839 (Cambridge, Massachusetts)
Death: April 19, 1914 (Milford, Pennsylvania)
School/tradition: Pragmaticism (Pragmatism)
Main interests: Metaphysics, Logic, Epistemology, Mathematics, Science

Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. Although educated as a chemist and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or semeiotic, that he is largely appreciated today. The philosopher Paul Weiss, writing in the Dictionary of American Biography for 1934, called Peirce "the most original and versatile of American philosophers and America's greatest logician" (Brent, 1). In the 18th century the philosophies of The Enlightenment would begin to have dramatic effect, and the landmark works of philosophers such as Immanuel Kant and Jean-Jacques Rousseau would have an electrifying effect on a new generation of thinkers. ... The 20th century brought with it upheavals that produced a series of conflicting developments within philosophy over the basis of knowledge and the validity of various absolutes. ... Download high resolution version (700x1072, 265 KB) Charles Sanders Peirce Credit: National Oceanic and Atmospheric Administration/Department of Commerce [1] Source http://www. ... September 10 is the 253rd day of the year (254th in leap years). ... 1839 (MDCCCXXXIX) was a common year starting on Tuesday (see link for calendar). ...   Settled: 1630 â€“ Incorporated: 1636 Zip Code(s): 02138, 02139, 02140, 02141, 02142 â€“ Area Code(s): 617 / 857 Official website: http://www. ... This article is about the U.S. State. ... April 19 is the 109th day of the year in the Gregorian calendar (110th in leap years). ... Year 1914 (MCMXIV) was a common year starting on Thursday (see link for calendar). ... The Milford Community House and Pike County Public Library Milford is a borough in Pike County, Pennsylvania, United States. ... Official language(s) None Capital Harrisburg Largest city Philadelphia Area  Ranked 33rd  - Total 46,055 sq mi (119,283 km²)  - Width 280 miles (455 km)  - Length 160 miles (255 km)  - % water 2. ... Pragmaticism was a term used by Charles Sanders Peirce for his philosophy, in order to distance himself from pragmatism of William James ... For themes emphasized by Charles Peirce, see Pragmaticism. ... Plato and Aristotle (right), by Raphael (Stanza della Segnatura, Rome). ... Logic, from Classical Greek λόγος logos (the word), is the study of patterns found in reasoning. ... This article does not cite its references or sources. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... Part of a scientific laboratory at the University of Cologne. ... IPA may refer to: The International Phonetic Alphabet or India Pale Ale ... September 10 is the 253rd day of the year (254th in leap years). ... 1839 (MDCCCXXXIX) was a common year starting on Tuesday (see link for calendar). ... April 19 is the 109th day of the year in the Gregorian calendar (110th in leap years). ... Year 1914 (MCMXIV) was a common year starting on Thursday (see link for calendar). ... Leonardo da Vinci is seen as an epitome of the Renaissance man or polymath A polymath (Greek polymathÄ“s, πολυμαθής, meaning knowing, understanding, or having learnt in quantity, compounded from πολυ- much, many, and the root μαθ-, meaning learning, understanding[1]) is a person well educated in a wide variety of subjects or... ... For other uses, see Philosophy (disambiguation). ...   Settled: 1630 â€“ Incorporated: 1636 Zip Code(s): 02138, 02139, 02140, 02141, 02142 â€“ Area Code(s): 617 / 857 Official website: http://www. ... Semeiotic is a term used by Charles Sanders Peirce to distinguish his theory of sign relations from other approaches to the same subject matter. ... Paul Weiss (19 May 1901 - 5 July 2002) was an American philosopher, known for his work in metaphysics and for his efforts to reverse age discrimination policies at American universities. ...


Peirce was largely ignored during his lifetime, and the secondary literature was scant until after World War II. Much of his huge output is still unpublished. Although he wrote mostly in English, he published some popular articles in French as well. An innovator in fields such as mathematics, research methodology, the philosophy of science, epistemology, and metaphysics, he considered himself a logician first and foremost. While he made major contributions to formal logic, "logic" for him encompassed much of what is now called the philosophy of science and epistemology. He, in turn, saw logic as a branch of semiotics, of which he is a founder. In 1886, he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later to produce digital computers. Combatants Allied Powers: United Kingdom France Soviet Union United States Republic of China and others Axis Powers: Germany Italy Japan and others Commanders Winston Churchill Charles de Gaulle Joseph Stalin Franklin Roosevelt Chiang Kai-Shek Adolf Hitler Benito Mussolini Hideki Tojo Casualties Military dead: 17,000,000 Civilian dead: 33... The English language is a West Germanic language that originates in England. ... Philosophy of science studies the philosophical assumptions, foundations, and implications of science, including the formal sciences, natural sciences, and social sciences. ... This article does not cite its references or sources. ... Plato and Aristotle (right), by Raphael (Stanza della Segnatura, Rome). ... Logic, from Classical Greek λόγος logos (the word), is the study of patterns found in reasoning. ... Semiotics, or semiology, is the study of signs and symbols, both individually and grouped in sign systems. ...

Contents

Life

Brent (1998) is the only Peirce biography in English. 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. For others with a similar name, see Benjamin Pierce. ... A giant Hubble mosaic of the Crab Nebula, a supernova remnant. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... Harvard University (incorporated as The President and Fellows of Harvard College) , is a private university in Cambridge, Massachusetts. ... Richard Whately (February 1, 1787 - October 8, 1863), English logician and theological writer, archbishop of Dublin, was born in London. ... The Division of Engineering and Applied Sciences (DEAS) is a unit of the Faculty of Arts and Sciences at Harvard University responsible for research, as well as undergraduate and graduate education in applied mathematics, computer science, engineering, and technology. ... Chemistry (from Greek χημεία khemeia[1] meaning alchemy) is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms, such as gases, molecules, crystals, and metals. ... Francis Ellingwood Abbot, (Boston, November 6, 1836 – October 23, 1903) was a philosopher and theologian who sought to reconstruct theology in accord with scientific method. ... Chauncey Wright (September 10, 1830 - September 12, 1875), American philosopher and mathematician, was born at Northampton, Massachusetts. ... For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... Prof. ...


Peirce suffered all his life from what was then known as "facial neuralgia," a very painful nervous/facial condition. The Brent biography 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. Trigeminal neuralgia, or Tic Douloureux, is a neuropathic disorder of the trigeminal nerve that causes episodes of intense pain in the eyes, lips, nose, scalp, forehead, and jaw. ...


United States Coast Survey

Between 1859 and 1891, Charles was intermittently employed in various scientific capacities by the United States Coast Survey, where he enjoyed the protection of his highly influential father until the latter's death in 1880. This employment exempted Charles from having to take part in the Civil War. It would have been very awkward for him to do so, as the 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 the earth's gravity. The Survey sent him to Europe five times, the first in 1871, as part of a group dispatched to observe a solar eclipse. While in Europe, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford, British mathematicians and logicians whose 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). The National Geodetic Survey is the successor agency in the United States to the U.S. Coast and Geodetic Survey. ... Combatants United States of America (Union) Confederate States of America (Confederacy) Commanders Abraham Lincoln, Ulysses S. Grant Jefferson Davis, Robert E. Lee Strength 2,200,000 1,064,000 Casualties 110,000 killed in action, 360,000 total dead, 275,200 wounded 93,000 killed in action, 258,000 total... Motto: Deo Vindice (Latin: Under God, Our Vindicator) Anthem: God Save the South (unofficial) Dixie (traditional) The Bonnie Blue Flag (popular) Capital Montgomery, Alabama (until May 29, 1861) Richmond, Virginia (May 29, 1861–April 2, 1865) Danville, Virginia (from April 3, 1865) Language(s) English (de facto) Government Republic President... It has been suggested that geodetic system be merged into this article or section. ... Gravimetry is the measurement of a gravitational field. ... Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ... Gravity is a force of attraction that acts between bodies that have mass. ... Photo taken during the 1999 eclipse. ... Augustus De Morgan (June 27, 1806 – March 18, 1871) was an Indian-born British mathematician and logician. ... [William Stanley Jevons] William Stanley Jevons (September 1, 1835 - August 13, 1882), English economist and logician, was born in Liverpool. ... William Kingdon Clifford William Kingdon Clifford, FRS (May 4, 1845 - March 3, 1879) was an English mathematician who also wrote a fair bit on philosophy. ... For alternate meanings see star (disambiguation) Hundreds of stars are visible in this image taken by the Hubble Space Telescope of the Sagittarius Star Cloud in the Milky Way Galaxy. ... The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias), sometimes referred to simply as the Galaxy), is a barred spiral galaxy of the Local Group. ... President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ... The metre, or meter (symbol: m) is the SI base unit of length. ... The wavelength is the distance between repeating units of a wave pattern. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength[1]. The elementary particle that defines light is the photon. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ...


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. 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. Thomas Corwin Mendenhall (October 4, 1841 – March 23, 1924) was an autodidact US physicist and meteorologist. ...


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 untenured position proved to be the only academic appointment Peirce ever held. The Johns Hopkins University, founded in 1876, is a private institution of higher learning located in Baltimore, Maryland, United States. ... Royce da 59 is a Detroit born rapper who is often afiliated with Eminem & D-12. ... John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ... Granville Stanley Hall (February 1, 1844, Ashfield, Massachusetts - April 24, 1924) was a psychologist and educationalist who pioneered American psychology. ... Joseph Jastrow, Ph. ... James Joseph Sylvester James Joseph Sylvester (September 3, 1814 - March 15, 1897) was an English mathematician and lawyer. ...


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 that Peirce may have been manic-depressive, claiming that Peirce experienced eight nervous breakdowns between 1876 and 1911. Brent also believes that Peirce tried to alleviate his symptoms with ether, morphine, and cocaine. Simon Newcomb. ... Bipolar disorder was once known as manic-depression. ...


Peirce's personal life also proved a grave handicap. His first wife, Harriet Melusina Fay, left him in 1875. He soon took up with a woman 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 did not marry her until his divorce with Harriet became final in 1883. 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 a number of 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. Clark University, in Worcester, Massachusetts, in the United States, is a private teaching and research institution founded in 1887 by the industrialist Jonas Clark. ... The University of Wisconsin–Madison (also known as UW–Madison, Madison, University of Wisconsin, or UW) is a public research university located in Madison, Wisconsin. ... The University of Michigan, Ann Arbor (UM or U of M) is a coeducational public research university in the U.S. state of Michigan. ... Cornell redirects here. ... The Leland Stanford Junior University, commonly known as Stanford University (or simply Stanford), is a private university located approximately 37 miles (60 kilometers) southeast of San Francisco and approximately 20 miles northwest of San José in an unincorporated part of Santa Clara County. ... The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ...


Poverty

In 1887 Peirce spent part of his inheritance from his parents to purchase 2,000 rural acres near Milford, Pennsylvania, land which never yielded an economic return. On that land, he built a large house which he named "Arisbe" and where he spent the rest of his life, writing prolifically, much of it unpublished to this day. His insistence on living beyond his means soon led to grave financial and legal difficulties. Peirce spent much of the last two decades of his life so destitute that he could not afford heat in winter, and his only food was old bread kindly donated by the local baker. Unable to afford new stationery, he wrote on the verso side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while. Several people, including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage. 1887 (MDCCCLXXXVII) is a common year starting on Saturday (click on link for calendar) of the Gregorian calendar or a common year starting on Monday of the Julian calendar. ... The Milford Community House and Pike County Public Library Milford is a borough in Pike County, Pennsylvania, United States. ... Nickname: Big Apple, Gotham, NYC Location in the state of New York Coordinates: Country United States State New York Boroughs The Bronx Brooklyn Manhattan Queens Staten Island Settled 1613  - Mayor Michael Bloomberg (R) Area    - City 1,214. ... Gifford Pinchot Gifford Bryce Pinchot test (August 11, 1865 – October 4, 1946) was the first Chief of the United States Forest Service (1905–1910) and the Republican Governor of Pennsylvania (1923–1927, 1931–1935). ...


Peirce did some scientific and engineering consulting and wrote a good deal for meager pay, primarily dictionary and encyclopedia entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison he became friendly). He did translations for the Smithsonian Institution, at the instigation of its director, Samuel Langley. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried his hand at inventing, and began but did not complete a number of books. In 1888, President Grover Cleveland appointed him to the Assay Commission. From 1890 onwards, he had a friend and admirer in Judge Francis C. Russell of Chicago, who introduced Peirce to Paul Carus and Edward Hegeler, the editor and owner, respectively, of the pioneering American philosophy journal The Monist, which eventually published a number of his articles. He applied to the newly formed Carnegie Institution for a grant to write a book summarizing his life's work. 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 Nation logo The Nation is a weekly left-liberal periodical devoted to politics and culture. ... Wendell Phillips Garrison (1840-1907) was an American editor and author, born at Cambridgeport, Mass. ... The Smithsonian Institution Building or Castle on the National Mall serves as the Institutions headquarters. ... Samuel Pierpont Langley (August 22, 1834 in Roxbury, Massachusetts near Boston, – February 27, 1906, Aiken, South Carolina) was an American astronomer, physicist, inventor, aeronautics pioneer and aircraft engineer. ... Stephen Grover Cleveland (March 18, 1837 – June 24, 1908) was the 22nd (1885–1889) and 24th (1893–1897) President of the United States, and the only President to serve two non-consecutive terms. ... Paul Carus (1852‑1919). ... The Open Court Publishing Company is a publisher with offices in Chicago and La Salle, Illinois. ... The Open Court Publishing Company is a publisher with offices in Chicago and La Salle, Illinois. ... The Carnegie Institution of Washington (CIW) is a foundation established by Andrew Carnegie in 1902 to support scientific research. ... Look up nemesis in Wiktionary, the free dictionary. ...


The one who did the most to help Peirce in these desperate times was his old friend William James, who dedicated his Will to Believe to Peirce, and who arranged for Peirce to be paid to give four series of lectures at or near Harvard. Most important, each year from 1898 until his death in 1910, James would write to his friends in the Boston intelligentsia, asking that they make a financial contribution to help support Peirce. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him, and by adding Santiago, "Saint James' in Spanish, to his full name (Brent, 315–16, 374). For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ...


Peirce died destitute in Milford, Pennsylvania, twenty years before his widow. The Milford Community House and Pike County Public Library Milford is a borough in Pike County, Pennsylvania, United States. ...


Reception

Bertrand Russell opined, "Beyond doubt [...] he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (Yet his Principia Mathematica does not mention Peirce.) A. N. Whitehead, while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and process metaphysics, see the chapter by Lowe in Moore and Robin, 1964.) Karl Popper viewed Peirce as "one of the greatest philosophers of all times". Nevertheless, Peirce's accomplishments were not immediately recognized. His imposing contemporaries William James and Josiah Royce admired him, and Cassius Jackson Keyser at Columbia and C. K. Ogden wrote about Peirce with respect, but to no immediate effect. Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ... Alfred North Whitehead Alfred North Whitehead (February 15, 1861 _ December 30, 1947) was a British philosopher and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. ... Conventional Platonic metaphysics posits the real world of metaphysical reality as being timeless. ... Sir Karl Raimund Popper, CH, MA, Ph. ... For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... Josiah Royce (November 20, 1855, Grass Valley, California. ... This article needs to be wikified. ... Charles Kay Ogden (June 1, 1889 - March 21, 1957) is a linguist and writer most prominently known as the author of a constructed language called Basic English. ...


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 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. Morris Raphael Cohen (July 25, 1880 - January 28, 1947) was a Jewish philosopher, lawyer and legal scholar who united pragmatism with logical positivism and linguistic analysis. ... John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ... Charles Hartshorne (June 5, 1897 – October 9, 2000) was a prominent philosopher who concentrated primarily on the philosophy of religion and metaphysics. ... Paul Weiss (19 May 1901 - 5 July 2002) was an American philosopher, known for his work in metaphysics and for his efforts to reverse age discrimination policies at American universities. ...


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. The history of ideas is a field of research in history that deals with the expression, preservation, and change of human ideas over time. ...


Peirce has come to enjoy a significant international following. There are university research centers devoted to Peirce studies and pragmatism in Brazil, Finland, Germany, and Spain. His writings have been translated into several languages, including German, French, Finnish, and Swedish. Since 1950, there have been French, Italian, and British Peirceans of note. For many years, the North American philosophy department most devoted to Peirce was the University of Toronto's, thanks in good part to the leadership of Thomas Goudge and David Savan. In recent years, American Peirce scholars have clustered at Indiana University - Purdue University Indianapolis, the home of the Peirce Edition Project, and the Pennsylvania State University. For themes emphasized by Charles Peirce, see Pragmaticism. ... The University of Toronto (U of T) is a coeducational public research university in Toronto, Ontario. ... → Indiana University School of Medicine → Purdue University Indianapolis Extension Center → Indiana University School of Law Indianapolis → Indiana University School of Dentistry Type of institution Public Endowment $389. ... The Pennsylvania State University (commonly known as Penn State) is a state-related, land-grant 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 2001/2005.)

Works

Peirce's reputation rests largely on a number of academic papers published in American scholarly and scientific journals. These papers, along with a selection of Peirce's previously unpublished work and a smattering of his correspondence, fill the eight volumes of the Collected Papers of Charles Sanders Peirce, published between 1931 and 1958. An important recent sampler of Peirce's philosophical writings is the two volume The Essential Peirce (Houser and Kloesel (eds.) 1992, Peirce Edition Project (eds.) 1998). Year 1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ... Year 1958 (MCMLVIII) was a common year starting on Wednesday of the Gregorian calendar. ...


The only book Peirce published in his lifetime was Photometric Researches (1878), a monograph on the applications of spectrographic methods to astronomy. While at Johns Hopkins, he edited Studies in Logic (1883), containing chapters by himself and his graduate students. He was a frequent book reviewer and contributor to The Nation, work reprinted in Ketner and Cook (1975–87). The Nation logo The Nation is a weekly left-liberal periodical devoted to politics and culture. ...


Hardwick (2001) published Peirce's entire correspondence 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 in the Writings. Victoria, Lady Welby (1837–1912), also styled the Hon. ...


Harvard University acquired the papers found in Peirce's study soon after his death, but did not microfilm them until 1964. Only after Richard Robin (1967) catalogued this Nachlass did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totalling 80,000 pages. Eisele (1976, 1985) published some of this work, but most of it remains unpublished. For more on the vicissitudes of Peirce's papers, see (Houser 1989). Harvard University (incorporated as The President and Fellows of Harvard College) , is a private university in Cambridge, Massachusetts. ...


The limited coverage, and defective editing and organization, of the Collected Papers led Max Fisch and others in the 1970s to found the Peirce Edition Project, whose mission is to prepare a more complete critical chronological edition, known as the Writings. Only 6 out of a planned 31 volumes have appeared to date, but they cover the period from 1859–1890, when Peirce carried out much of his best-known work.


On a New List of Categories (1867)

On a New List of Categories is a paper by Charles Sanders Peirce, presented to the American Academy of Arts and Sciences on 14 May 1867 and published in its Proceedings the following year, that proposes to revise the fundamental metaphysical categories of philosophy, as previously given by Aristotle, Kant...

Logic of Relatives (1870)

By 1870, the drive that Peirce exhibited to understand the character of knowledge, starting with our partly innate and partly inured models of the world and working up to the conduct of our scientific inquiries into it, having led him to inquire into the three-roled relationship of objects, signs, and impressions of the mind, now brought him to the pass of needing more power in a theory of relations than the available logical formalisms were up to providing. His first concerted effort to supply the gap was rolled out in his paper "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic". But the nameplate "LOR of 1870" will do for ease of identification. Logic of Relatives (1870), more precisely, Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Booles Calculus of Logic, is the title of a 60 page memoir that Charles Sanders Peirce published in the Memoirs of the American Academy of Arts...


Logic of Relatives (1883)

Logic of Relatives (1883), more precisely, Note B. The Logic of Relatives, is the title of a 17 page addendum to the chapter entitled A Theory of Probable Inference that C.S. Peirce contributed to the volume, Studies in Logic by Members of the Johns Hopkins University, published by Little...

Logic of Relatives (1897)

The Simplest Mathematics (1902)

The Simplest Mathematics is the title of a paper by Charles Sanders Peirce, intended as Chapter 3 of his unfinished magnum opus, the Minute Logic. The paper is dated January–February 1902 but was not published until the appearance of his Collected Papers, Volume 4 in 1933. ...

Kaina Stoicheia (1904)

Main article: Kaina Stoicheia

Kaina Stoicheia (Καινα στοιχεια) or New Elements is the title of several manuscript drafts of a document that Charles Sanders Peirce wrote circa 1904, intended as a preface to a book on the foundations of mathematics. ...

Peirce's 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 Peircian studies. (Max Fisch, in (Moore and Robin 1964), 486).

Peirce's lifelong work in science bears on a wide array of disciplines, including astronomy, metrology, geodesy, mathematics, logic, philosophy, the history and philosophy of science, linguistics, economics, and psychology. This work has become the subject of renewed interest and approval, 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. A giant Hubble mosaic of the Crab Nebula, a supernova remnant. ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... Logic, from Classical Greek λόγος logos (the word), is the study of patterns found in reasoning. ... For other uses, see Philosophy (disambiguation). ... The history and philosophy of science (HPS) is an academic discipline that encompasses the philosophy of science and the history of science. ... Linguistics is the scientific study of language. ... Face-to-face trading interactions on the New York Stock Exchange trading floor Look up economics in Wiktionary, the free dictionary. ... Psychology is an academic and applied discipline involving the scientific study of mental processes and behavior. ...


Peirce's writings repeatedly refer to a system of three categories, named Firstness, Secondness, and Thirdness, devised early in his career in reaction to his reading of Aristotle, Kant, and Hegel. He later emphasized the principle of logic that he called the maxim of pragmatism, on which his lifelong friend William James based a popular philosophical movement known as pragmatism. Peirce believed that any truth is provisional, and that the truth of any proposition cannot be certain but only probable. The philosophical recognition of this fact he called fallibilism. In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply According to the Aristotelian tradition, a being is anything that can be said to be in the various senses of this word. ... Aristotle (Greek: AristotélÄ“s) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... Georg Wilhelm Friedrich Hegel (August 27, 1770 - November 14, 1831) was a German philosopher born in Stuttgart, Württemberg, in present-day southwest Germany. ... The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce. ... For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... For themes emphasized by Charles Peirce, see Pragmaticism. ... Fallibilism refers to the philosophical doctrine that absolute certainty about knowledge is impossible; or at least that all claims to knowledge could, in principle, be mistaken. ...


Pragmatism

William James, among others, regarded two of Peirce's papers, "The Fixation of Belief" (1877) and "How to Make Our Ideas Clear" (1878), as being the origin of pragmatism. Peirce conceived pragmatism to be a method for clarifying the meaning of difficult ideas through the application of a maxim of logic that he called the pragmatic maxim. Here is one of Peirce's more emphatic statements of this principle: For themes emphasized by Charles Peirce, see Pragmaticism. ... Pragmaticism was a term used by Charles Sanders Peirce for his philosophy, in order to distance himself from pragmatism of William James ... The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce (1839-1914). ... For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ...

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. (CP 5.438.)

Peirce's pragmatism may be understood as a method for resolving conceptual confusions by linking the meanings of one's conception of an object to one's conception of the operational or practical consequences of the object (not of the conception) in case the object is as one conceived of it. "Then, your conception of those effects is the whole of your conception of the object." (Peirce does not hold the ethically challenging view that one's conception of the practical effect of the conception of the object is the whole of one's conception of the object.) The concepts of belief, knowledge, and truth were some of the difficult ideas that Peirce sought to clarify by means of the pragmatic maxim. Doing this required a theory of inquiry that moderated the conventional dualism of foundational alternatives, namely:

His approach is distinguished from either coherentism or foundationalism by virtue of the following three dimensions: Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... In epistemology and in its broadest sense, rationalism is any view appealing to reason as a source of knowledge or justification (Lacey, 286). ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. ... In philosophy generally, empiricism is a theory of knowledge emphasizing the role of experience. ... Coherentism - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... ...

  1. Active process of theory generation, with no prior assurance of truth.
  2. Subsequent application of the tentative theory, aimed toward developing its logical and practical consequences.
  3. Evaluation of the provisional theory's utility for the anticipation of future experience, and that in dual senses of the word, namely, prediction and control.

Peirce's appreciation of these three dimensions serves to flesh out a physiognomy of inquiry far more solid than the flatter image of inductive generalization simpliciter, which is merely the relabeling of phenomenological patterns. Peirce's pragmatism was the first time the scientific method was proposed as an epistemology for philosophical questions. Anticipation can refer to: Anticipation (album), a 1971 album by Carly Simon. ... A prediction or forecast is a statement or claim that a particular event will occur in the future. ... Look up Control in Wiktionary, the free dictionary. ... Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. ... This article does not cite its references or sources. ...


As advocated by James, John Dewey, Ferdinand Canning Scott Schiller, George Herbert Mead, and others, pragmatism has proved durable and popular. But Peirce did not seize on this fact to enhance his reputation. Instead, what James and others called pragmatism so dismayed Peirce that he renamed his own variant pragmaticism, joking that it was "ugly enough to be safe from kidnappers" (CP 5.414), that is, no one would ever appropriate a neologism so ugly. John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ... British Philosopher, 1864 to 1937. ... George Herbert Mead (February 27, 1863 – April 26, 1931) was an American philosopher, sociologist and psychologist, primarily affiliated with the University of Chicago, where he was one of several distinguished pragmatists. ...


Scholastic realism

At one point, Peirce described himself as a "scholastic realist of a somewhat extreme stripe" (CP 5.470). In contrast, some writers call him an idealist, apparently on account of his defining reality as "the object of the final opinion of the scientific community", but this label is based on a peculiar sense of the word idealist and is overall misleading in the case of Peirce, as he consistently and systematically argues that reality is best viewed as independent of mind, at least of minds in particular, if not necessarily of minds in general. The problem of interpretation appears to arise from at least three sources. First, Peirce's use of the word independent needs to be understood in a way that is analogous to its definition in mathematics, where it means orthogonal, or its definition in statistics, where it means uncorrelated. In these senses, independence is a particular kind of relation, not a lack of relation, and certainly not a form of disconnection or exclusion. Second, Peirce did in fact describe himself as being in favor of objective idealism, but what he meant by that is a far cry from ordinary idealism. Third, we need to recognize that scholastic realism is one side of the realist vs. nominalist debate over universals, and not a position in the realist vs. idealist debate about a mind-independent reality. Peirce's scholastic realism in fact supplies essential support for his own thesis of objective idealism regarding the relationship between matter and mind. Two early studies on Peirce’s realism and the influence of Duns Scotus thereon, are the chapter by McKeon in Wiener and Young (1952), and that by Moore in Moore and Robin (1964). In philosophy, idealism is any theory positing the primacy of spirit, mind, or language over matter. ... This article or section may contain original research or unverified claims. ... In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. ... In probability theory and statistics, to call two real-valued random variables X and Y uncorrelated means that their correlation is zero, or, equivalently, their covariance is zero. ... Objective idealism is a metaphysics that postulates that there is in an important sense only one perceiver, and that this perceiver is one with that which is perceived. ... Idealism is an approach to philosophical enquiry that asserts that everything we experience is of a mental nature. ... Realism is commonly defined as a concern for fact or reality and rejection of the impractical and visionary. ... Nominalism is the position in metaphysics that there exist no universals outside of the mind. ... Universal has several meanings: For the concept of a universal in metaphysics, see Universal (metaphysics). ... Realism is commonly defined as a concern for fact or reality and rejection of the impractical and visionary. ... In philosophy, idealism is any theory positing the primacy of spirit, mind, or language over matter. ... This article or section may contain original research or unverified claims. ... Objective idealism is a metaphysics that postulates that there is in an important sense only one perceiver, and that this perceiver is one with that which is perceived. ... Blessed John Duns Scotus (c. ...


In his first remarks on the realist vs. nominalist debate, Peirce sided with nominalism:

Qualities are fictions; for though it is true that roses are red, yet redness is nothing, but a fiction framed for the purpose of philosophizing; yet harmless so long as we remember that the scholastic realism it implies is false. (CE 1, 307, 1865.)

Here Peirce is explicitly disparaging a position he is well-known for spending most of his life defending. How might we make sense of this apparent contradiction? The temptation is to simply say Peirce changed his mind. After all, since Peirce asserts nominalism in 1865 and scholastic realism in 1868, Peirce may have gone from denying the reality of universals to asserting it. This explanation is most famously given by Max Fisch in his "Peirce’s Progress from Nominalism toward Realism" (1967) and then again in his introduction to Volume 2 of the Chronological Edition of Peirce’s writings (1984). More recently this way of understanding Peirce has been indepenently challenged by Rosa Mayorga in her On Universals (2002) and by Robert Lane in his "Peirce's Early Realism" (2004). Both Mayorga and Lane are troubled by several instances where Peirce’s self assessment of his own intellectual development contradicts Fisch's account of Peirce development. One of these statements appears in 1893 when Peirce states that "never, during the thirty years in which I have been writing on philosophical questions, have I failed in my allegiance to realistic opinions and to certain Scotistic ideas" (CP 6.605). Remarks like these led Lane to conduct a re-evaluation of Peirce’s 1865 declarations for nomianlism, whereupon Lane discovered significant evidence for the same conclusion Mayorga had already reached two years earlier (unbenownst to Lane). Both concluded that the correct way to understand Peirce’s shift from outspoken nominalist to outspoken realist is not by reading into Peirce a change in his fundamental philosophical position, but instead to realize that Peirce merely changed his understanding and use of the terms scholastic realism and nominalism. The reason Peirce calls himself a nominalist in 1865 is because he believes realism to only come in the form offered by Plato:

It has been said that these “abstract names” [blueness, hardness, and loudness] denote qualities and connote nothing. But it seems to me the phrase “denoted object” is nothing but a roundabout expression for a thing…. To say that a quality is denoted is to say it is a thing…. [Such terms] were framed at a time when all men were realists in the scholastic sense and consequently things were meant by them, entities which had no quality but that expressed by the word. They, therefore, must denote these things and connote the qualities they relate to. (Peirce, CE 1, 311–312.)

When Peirce goes on to call universals “fictions,” he is not condemning their truth; he is simply asserting that they do not exist as particulars. This becomes clearer when in the same paper Peirce argues against psychologism in logic, by establishing the same “fictional” status for logic and mathematics that he claims for universals. Now by proving logic fictional, Peirce believes he does logic a favor, that is, by saving it from the psychologists. This suggests that Peirce employed fictional in a rather idiosyncratic way. Many things (including universals) covered by Peirce’s pre-1868 use of fictional came under his post-1868 use of real. Peirce had been using “fictional” to refer to things having no physical existence, and not to imply that something was merely the result of human imagination or fancy. By 1868 at least, Peirce had changed his mind about "reality", holding instead that "fictional" should be contrasted with "independent of what we think about it" (real). He no longer deemed existence as a physical object as a prerequisite for being real, so that a lack of physical existence no longer led Peirce to chatacterize universals as "fictional". That something has blueness can be true independent of what anyone thinks of it, and therefore it can be a part of reality despite the fact blueness never has a physical existence anywhere. Blueness is real independent of what anyone thinks, but it does not exist as an entity because it has no secondness.


Logic, mathematics, relations, and semiotics

Peirce did not live or work in a vacuum. No one who appreciates his use of phrases like laws of the symbol in their historical context can fail to hear the echoes of George Boole, nor the undertones of the symbolist movement in mathematics inspired by the writings of George Peacock. George Boole [], (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. ... George Peacock George Peacock (April 9, 1791 - November 8, 1858) was an English mathematician. ...


At the outset of his Laws of Thought, Boole tells us how he plans to evade the horns of a dilemma that would otherwise threaten to block his inquiry before he can even begin. There were four classic laws of thought recognised in European thought of the seventeenth and eighteenth century, which held sway also during nineteenth century (while subject to greater debate). ...

In proceeding to these inquiries, it will not be necessary to enter into the discussion of that famous question of the schools, whether Language is to be regarded as an essential instrument of reasoning, or whether, on the other hand, it is possible for us to reason without its aid. I suppose this question to be beside the design of the present treatise, for the following reason, viz., that it is the business of Science to investigate laws; and that, whether we regard signs as the representatives of things and of their relations, or as the representatives of the conceptions and operations of the human intellect, in studying the laws of signs, we are in effect studying the manifested laws of reasoning. (Boole, Laws of Thought, p. 24.)

Boole is saying that the business of science, the investigation of laws, applies itself to the laws of signs at such a level of abstraction that its results are the same no matter whether it finds those laws embodied in objects or in intellects. In short, he does not have to choose one or the other in order to begin. This simple idea is the essence of the formal approach in mathematics, and it is one of the reasons that contemporary mathematicians tend to consider structures that are isomorphic to one another as tantamount to being the same thing. Peirce avails himself of this same depth of perspective for much the same reason. It allows him to investigate the forms of triadic sign relations that exist among objects, signs, and interpretants without being blocked by the impossible task of acquiring knowledge of supposedly unknowable things in themselves, whether outward objects or the contents of other minds. Like Aristotle and Boole before him, Peirce replaces these impossible problems with the practical problem of inquiring into the sign relations that exist among commonly accessible objects and publicly accessible signs. In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of interesting mapping between objects. ...

How often do we think of the thing in algebra? When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose, coincide with the laws of multiplication in the object. Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it? It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use — whether reflected on or not — by association immediately regulate the action of the mind; and these may be regarded as laws of the symbol itself which it cannot as a symbol transgress. ("On the Logic of Science" (1865), CE 1, 173.)

The motive themes of the symbolist movement are familiar to anyone who has worked a "story problem" in a mathematics course. One learns to approach the story problem, a roughly realistic representation of a concrete set of circumstances, with the aim of abstracting the appropriate general formula from the mass of concrete details that make up the problem — not all of which data are equally pertinent to the solution and some of which may even be thrown in as distractors. The next step is to derive the logical implications of the abstract formula, generally speaking substituting specific values for some of its variables but just as often leaving other variables unfilled in. The bearing of the formula on the desired answer is obscure at first — that is what makes the problem a problem in the first place. But progressive clarification of the formula leads to an equivalent or implied formula that amounts to an abstract answer or a generic solution to the story problem. Given that, there is nothing more to do but fill in the rest of the concrete data to arrive at the concrete answer or the specific solution to the problem.


The three-phase maneuver for solving a story problem, (1) teasing out, (2) cranking the crank, (3) plugging in, can be articulated in semiotic or sign-relational terms as follows: The first phase passes from the object domain to the sign domain, the second phase passes from the sign domain to the interpretant sign domain, continuing perhaps in a relay of successive passes, and the third phase passes from the last interpretant sign domain back to the object domain.


There are a number of issues that typically arise with the continuing development of a symbolist perspective, in any field of endeavor, over the years of its natural life-cycle. We can see these issues illustrated clearly enough in our story problem paradigm, with its parsing of the problem-solving process into the three phases of abstraction, transformation, and application.

  • Once the division of labor among the three phases of the process has been in place for a sufficiently long time, each of the three phases will tend to take on a certain degree of independence, sometimes actual and sometimes merely apparent, from the other two phases.
  • As a side-effect of the increasing independence among the various phases of inquiry, there tend to develop specialized disciplines, each devoted to a single aspect of the initially interactive and integral process. A symptom of this stage of development is that references to the 'independence' of the several phases of inquiry may become confused with or even replaced by assertions of their 'autonomy' from one another.

Returning to the formal sciences of logic and mathematics and focusing on the rise of symbolic logic in particular, all of the above issues were clearly recognized and widely discussed among the movers and shakers of the symbolist movement, with especial mention of George Boole, Augustus De Morgan, Benjamin Peirce, and Charles Peirce. George Boole [], (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. ... Augustus De Morgan (June 27, 1806 – March 18, 1871) was an Indian-born British mathematician and logician. ... For others with a similar name, see Benjamin Pierce. ...


The first symptoms of a crisis typically arise in connection with questions about the status of the abstract symbols that are 'manipulated' in the transformation phase, to express it in sign-relational terms, the sign-to-sign aspect of semiosis. In the beginning, while it is still evident to everyone concerned that these symbols are mined from the matrix of their usual interpretations, which are generally more diverse than unique, these abstracted symbols are commonly referred to as 'uninterpreted symbols', the sense being that they are transiently detached from their interpretations simply for the sake of extra facility in processing the more general thrust of their meanings, after which intermediary process they will have their concrete meanings restored.


When we start to hear these abstract, general, uninterpreted symbols being described as 'meaningless' symbols, then we can be sure that a certain line in our sand-reckoning has been crossed, and that the crossers thereof have hefted or sublimated 'formalism' to the status of a full-blown Weltanschauung rather than a simple heuristic device. The term formalism describes an emphasis on form over content or meaning in the arts, literature, or philosophy. ... A world view, also spelled as worldview is a term calqued from the German word Weltanschauung (look onto the world). The German word is also in wide use in English, as well as the translated form world outlook. ... Look up Heuristic in Wiktionary, the free dictionary. ...


What we observe here is a familiar form of cyclic process, with the crest of excess followed by the slough of despond. The inflationary boom that raises 'formalism' beyond its formative sphere as one among a host of equally useful heuristic tricks to the status of a totalizing worldview leads perforce to the deflationary bust that makes of 'formalist' a pejorative term.


The point of the foregoing discussion is this, that one of the main difficulties that we have in understanding what the whole complex of words rooted in 'form' meant to Peirce is that we find ourselves, historically speaking, on opposite sides of this cycle of ideas from him.


And so we are required, as so often happens in trying to read a writer of another age, to lift the scales of the years from our eyes, to drop the reticles that have encrusted themselves on our 'reading glasses', our hermeneutic scopes, due to the interpolant philosophical schemata that have managed to enscounce themselves in our unthinking culture over the years that separate us from the writer in question. Hermeneutics (Hermeneutic means interpretive), is a branch of philosophy concerned with human understanding and the interpretation of texts. ...


Logic as formal semiotic

On the Definition of Logic. Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word "formal" in the definition is also defined. (Peirce, "Carnegie Application", NEM 4, 54). Karl Theodor Wilhelm Weierstraß (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. (The letter ß may be transliterated as ss; one often writes Weierstrass. ...

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 above. The Carnegie Institution of Washington (CIW) is a foundation established by Andrew Carnegie in 1902 to support scientific research. ...


Peirce's major discoveries in formal logic include:

  • Distinguishing (Peirce, 1885) between first-order and second-order quantification.
  • Seeing that Boolean calculations could be carried out by means of electrical switches (W5: 421–24), anticipating Claude Shannon by more than 50 years.

A philosophy of logic, grounded in his categories and semeiotic, can be extracted from Peirce's writings. This philosophy, as well as Peirce's logical work more generally, is exposited and defended in, and in Hilary Putnam (1982), the Introduction to Houser et al (1997), and Dipert's chapter in Misak (2004). Jean Van Heijenoort (1967), Jaakko Hintikka in his chapter in Brunning and Forster (1997), and Brady (2000) 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). Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ... An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882 and continued to develop the method until his death in 1914. ... First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as there exists an x such that. ... Elsie the cat is sitting on a mat John F. Sowas conceptual graphs (CGs) are a system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. ... John Florian Sowa is the computer scientist who invented conceptual graphs, a graphic notation for logic and natural language, based on the structures in semantic networks and on the existential graphs of Charles S. Peirce. ... Jean van Heijenoort (prounounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. ... Jaakko Hintikka in 2006. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... Semantics (Greek semantikos, giving signs, significant, symptomatic, from sema, sign) refers to the aspects of meaning that are expressed in a language, code, or other form of representation. ... Proof theory, studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician. ... The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ...


Peirce's work on formal logic had admirers other than Ernst Schröder: Ernst Schröder Ernst Schröder (25 November 1841 Mannheim, Germany - 16 June 1902 Karlsruhe Germany) was a German mathematician mainly known for his work on algebraic logic. ...

  • 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.

William Kingdon Clifford William Kingdon Clifford, FRS (May 4, 1845 - March 3, 1879) was an English mathematician who also wrote a fair bit on philosophy. ... William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician known for his three volume work Logic (1921-1924). ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... Arthur Norman Prior (1914 Masterton, New Zealand - 1969 Trondheim, Norway) was one of the foremost logicians of the twentieth century. ...

Relations and relative terms

The reader of Peirce needs to be aware of the distinction between relations and relatives. Succinctly put, relations are mathematical objects and relatives are logical signs. The word relative is short for relative term, and a relative term is a type of sign that forms the main study of the logic of relatives. A relation, on the other hand, is a type of formal object that is treated in the mathematical theory of relations. There is of course an intimate relationship between the two studies, but like most intimate relationships it has its fair share of intricacies.


The following collection of definitions from one of Peirce's papers is practically indispensable for understanding the language that he used:

  • A relative, then, may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb "is" is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank.
  • A relationship, or fundamentum relationis, is a fact relative to a number of objects, considered apart from those objects, as if, after the statement of the fact, the designations of those objects had been erased.
  • A relation is a relationship considered as something that may be said to be true of one of the objects, the others being separated from the relationship yet kept in view. Thus, for each relationship there are as many relations as there are blanks. For example, corresponding to the relationship which consists in one thing loving another there are two relations, that of loving and that of being loved by. There is a nominal relative for each of these relations, as "lover of ——" and "loved by ——".
  • These nominal relatives belonging to one relationship, are in their relation to one another termed correlatives. In the case of a dyad, the two correlatives, and the corresponding relations are said, each to be the converse of the other.
  • The objects whose designations fill the blanks of a complete relative are called the correlates.
  • The correlate to which a nominal relative is attributed is called the relate.
  • In the statement of a relationship, the designations of the correlates ought to be considered as so many logical subjects and the relative itself as the predicate. The entire set of logical subjects may also be considered as a collective subject, of which the statement of the relationship is predicate.
(Peirce, CP 3.466–467, "The Logic of Relatives", The Monist 7, 161–217 (1897), CP 3.456–552).

To understand these definitions, as everywhere in Peirce's work, one needs to keep a close watch on the things that are meant as objects of discussion and thought and the things that are meant as signs and thoughts in which discussion and thought take place. Doing this is trickier than it seems at first, since many standard approaches to defining abstract, formal, or hypostatic objects approach their objects by way of formal operations on the corresponding signs. In linguistics and logic, a predicate is an expression that can be true of something. ... The Monist: An International Quarterly Journal of General Philosophical Inquiry is an American learned journal in the field of philosophy. ... Hypostatic abstraction, also known as hypostasis or subjectal abstraction, is the process or the product of a formal operation that takes an element of information, such as might be expressed in a proposition of the form X is Y, and conceives its information to consist in the relation between a...


Relatives

Main article: Logic of relatives

Logic of relatives, short for logic of relative terms, is a term used to cover the study of relations in their logical, philosophical, or semiotic aspects, as distinguished from, though closely coordinated with, their more properly formal, mathematical, or objective aspects. ...

Relations

Main article: Theory of relations

A concept of relation that suffices to begin the study of Peirce's logic, mathematics, and semiotics, making use of analogous concepts of relation that have served well enough in other areas of experience to make further experience possible, can be set out as follows. The theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another. ...

  • Defined in extension, a k-adic relation L is a set of k-tuples.
  • A k-tuple x is a sequence of k elements, x1, x2, …, xk–1, xk, called the components of the k-tuple. The components of the k-tuple x can be indicated by writing either one of the following two forms, the latter form of syntax being the one that Peirce most often used:

It is critically important to understand that a relation in extension is a set, in other words, an aggregate entity or a collection of things. More to the point, a single k-tuple is not a relation, it is only an element of a relation, what Peirce quite naturally called an elementary relation or sometimes an individual relation. In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... In mathematics, an element (also called a member) is an object contained in a set (or more generally a class). ...


In his time, Peirce found himself forced by the task of understanding the intertwined natures of science and signs to develop the logic of relations from the fairly primitive state in which he found it to a condition of readiness more qualified for the job. There was nothing very cut and dried about trying to do this from scratch, as will be evident in the appropriate Sections below when we sample the fits and starts forward, the culs-de-sac, and the many paths that had to be backtracked in order to arrive at an adequate theory of relations. For the purpose at hand, however, we can rely on the fact that few readers these days will have escaped some encounter with relational databases, and so we can draw on these resources of experience to speed the exposition of relations in general. A relational database is a database that conforms to the relational model, and refers to a databases data and schema (the databases structure of how that data is arranged). ...


Table 1 shows how the k-tuples of a k-adic relation might be conceived in tabular form, with the k-uple xi = (xi1, …, xik) = xi1 :: xik supplying the entries for the ith row of the Table.

Table 1. Relational Database
Domain 1 Domain 2 ... Domain j ... Domain k
x11 x12 ... x1j ... x1k
x21 x22 ... x2j ... x2k
... ... ... ... ... ...
xi1 xi2 ... xij ... xik
... ... ... ... ... ...
xm1 xm2 ... xmj ... xmk

For ease of exposition, Table 1 shows the generic form of a discrete k-adic relation, one that contains a countable number of k-tuples, indeed, it shows a finite k-adic relation, one that contains a finite number of k-tuples. Generalizations to relations with an infinite or even a continuous cardinality in respect of their numbers of elementary relations are possible. Indeed, it is possible to conceive of relations with infinite, continuous, or even no fixed numbers of components in their elementary relations, but finite k-adic relations are illustration enough for our immediate aims. Look up discrete in Wiktionary, the free dictionary. ... In mathematics the term countable set is used to describe the size of a set, e. ... In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... In mathematics, the cardinality of the continuum is the cardinal number of the set of real numbers R (sometimes called the continuum). ... In mathematics, the cardinality of a set is a measure of the number of elements of the set. There are two approaches to cardinality – one which compares sets directly using bijections, injections, and surjections, and another which uses cardinal numbers. ...


Dyadic relations

Main article: Binary relation

In mathematics, a binary relation (or a dyadic relation) is an arbitrary association of elements of one set with elements of another (perhaps the same) set. ...

Triadic relations

Main article: Triadic relation
This completes the classification of dual relatives founded on the difference of the fundamental forms A : A and A : B. Similar considerations applied to triple relatives would give rise to a highly complicated development, inasmuch as here we have no less than five fundamental forms of individuals, namely:
(A : A) : A (A : A) : B (A : B) : A (B : A) : A (A : B) : C.
(Peirce, CP 3.229, "On the Algebra of Logic", American Journal of Mathematics 3, 15–57 (1880), CP 3.154–251).

In logic, mathematics, and semiotics, a triadic relation or a ternary relation is an important special case of a polyadic or finitary relation, one in which the number of places in the relation is three. ...

Theory of categories

Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: "Category" from Aristotle and Kant, "Functor" from Carnap (Logische Syntax der Sprache), and "natural transformation" from then current informal parlance. (Saunders Mac Lane, Categories for the Working Mathematician, 29–30.)

Mac Lane did not mention Peirce among the objects of his sincerest flattery, but he might as well have, for his mention of Aristotle and Kant well enough credits his deep indebtedness to the pursers of them all. As Richard Feynman was fond of observing, 'the same questions have the same answers', and the problem that a system of categories is aimed to 'beautify' is the same sort of beast whether it's Aristotle, Kant, Peirce, Carnap, or Eilenberg and Mac Lane that bends the bow. What is that problem? To answer that, let's begin again at the source: Richard Phillips Feynman (May 11, 1918 – February 15, 1988; surname pronounced ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... Samuel Eilenberg (September 30, 1913-January 30, 1998) was a Polish mathematician. ...

Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called 'animals' (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.


Things are univocally named, when not only they bear the same name but the name means the same in each case -- has the same definition corresponding. Thus a man and an ox are called 'animals'. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called 'animals', you give that particular name in both cases the same definition. (Aristotle, Categories, 1.1a1–12.)

In the logic of Aristotle categories are adjuncts to reasoning that are designed to resolve equivocations and thus to prepare ambiguous signs, that are otherwise recalcitrant to being ruled by logic, for the application of logical laws. An equivocation is a variation in meaning, or a manifold of sign senses, and so Peirce's claim that three categories are sufficient amounts to an assertion that all manifolds of meaning can be unified in just three steps.


The following passage is critical to the understanding of Peirce's Categories:

I will now say a few words about what you have called Categories, but for which I prefer the designation Predicaments, and which you have explained as predicates of predicates. That wonderful operation of hypostatic abstraction by which we seem to create entia rationis that are, nevertheless, sometimes real, furnishes us the means of turning predicates from being signs that we think or think through, into being subjects thought of. We thus think of the thought-sign itself, making it the object of another thought-sign. Thereupon, we can repeat the operation of hypostatic abstraction, and from these second intentions derive third intentions. Does this series proceed endlessly? I think not. What then are the characters of its different members? My thoughts on this subject are not yet harvested. I will only say that the subject concerns Logic, but that the divisions so obtained must not be confounded with the different Modes of Being: Actuality, Possibility, Destiny (or Freedom from Destiny). On the contrary, the succession of Predicates of Predicates is different in the different Modes of Being. Meantime, it will be proper that in our system of diagrammatization we should provide for the division, whenever needed, of each of our three Universes of modes of reality into Realms for the different Predicaments. (Peirce, CP 4.549, "Prolegomena to an Apology for Pragmaticism", Monist, 16, 492–546 (1906), CP 4.530–572.) Hypostatic abstraction, also known as hypostasis or subjectal abstraction, is the process or the product of a formal operation that takes an element of information, such as might be expressed in a proposition of the form X is Y, and conceives its information to consist in the relation between a...

The first thing that we need to extract from this text is the fact that Categories are predicates of predicates, in effect, types of relations.


Logical graphs

Main article: Logical graph

A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. ...

Mathematics

It may be added that algebra was formerly called Cossic, in English, or the Rule of Cos; and the first algebra published in England was called "The Whetstone of Wit", because the author supposed that the word cos was the Latin word so spelled, which means a whetstone. But in fact, cos was derived from the Italian, cosa, thing, the thing you want to find, the unknown quantity whose value is sought. It is the Latin caussa, a thing aimed at, a cause. (C.S. Peirce, "Elements of Mathematics", MS 165 (c. 1895), NEM 2, 50.)

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

  • 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.

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had recently revived after long years of neglect by logicians. Much of the actual mathematics of relations that is taken for granted today was borrowed from Peirce, not always with all due credit (Anellis 1995). 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 abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. ... NAND Logic gate The Sheffer stroke, written | or ↑, denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as not both. It is also called the alternative denial, since it says in effect that at least one of its operands is false. ... NAND Logic gate The Sheffer stroke, written | or ↑, denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as not both. It is also called the alternative denial, since it says in effect that at least one of its operands is false. ... note that demorgans laws are also a big part in circut design. ... Vertical bar, or pipe is the name of the ASCII character at position 124 (decimal). ... This article or section is in need of attention from an expert on the subject. ... Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician and philosopher. ... In mathematics, the Peano axioms (or Peano postulates) are a set of second-order axioms proposed by Giuseppe Peano which determine the theory of arithmetic. ... Julius Wilhelm Richard Dedekind (October 6, 1831 - February 12, 1916) was a German mathematician and Ernst Eduard Kummers closest follower in arithmetic. ... Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher. ... In set theory, an infinite set is a set that is not a finite set. ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... In mathematics, a bijection, bijective function, or one-to-one correspondence is a function that is both injective (one-to-one) and surjective (onto), and therefore bijections are also called one-to-one and onto. ... A is a subset of B If X and Y are sets and every element of X is also an element of Y, then we say or write: X is a subset of (or is included in) Y; X ⊆ Y; Y is a superset of (or includes) X; Y... Logic of Relatives (1870), more precisely, Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Booles Calculus of Logic, is the title of a 60 page memoir that Charles Sanders Peirce published in the Memoirs of the American Academy of Arts... The theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another. ... Augustus De Morgan (June 27, 1806 – March 18, 1871) was an Indian-born British mathematician and logician. ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... Relational algebra, an offshoot of first-order logic, is a set of relations closed under operators. ... Edgar Ted Codd Edgar Frank Codd (August 23, 1923 – April 18, 2003) was a British computer scientist who made seminal contributions to the theory of relational databases. ... Arthur Walter Burks (born October 13, 1915 in Duluth, Minnesota) is an American mathematician who in the 1940s as a senior engineer on the project contributed to the design of the ENIAC, the first general-purpose electronic digital computer. ... The relational model for database management is a database model based on predicate logic and set theory. ... The term or expression database originated within the computer industry. ...


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, titled The New Elements of Mathematics in allusion to Euclid's Elements, that presented mathematics from a novel standpoint. Euclid, is also referred to as Euclid of Alexandria, (Greek: , 330 BC– 275 BC), a Greek mathematician, who lived in the city of Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323 BC–283 BC), is often considered to be the father of geometry. His most popular work... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems...


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", CE 3, 68–69.)

All through the 1860's, the young but rapidly maturing Peirce was busy establishing a conceptual basecamp and a technical supply line for the intellectual adventures of a lifetime. Taking the longview of this activity and trying to choose the best titles for the story, it all seems to have something to do with the dynamics of inquiry. This broad subject area has a part that is given by nature and a part that is ruled by nurture. On first approach, it is possible to see a question of articulation and a question of explanation: Inquiry is any proceeding or process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. ... Galunggung in 1982, showing a combination of natural events. ... Nurture is usually defined as the process of caring for and teaching a child as they grow. ... Articulation may refer to several topics: In speech, linguistics, and communication: Topic-focus articulation Articulation score Place of articulation Manner of articulation In music: Musical articulations (staccato, legato, etc) In education: Articulation (education) In sociology: Articulation (sociology) This is a disambiguation page — a navigational aid which lists other pages... An explanation is a statement which points to causes, context and consequences of some object (or process, state of affairs etc. ...

  • 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?

The pursuit of answers to these questions finds them to be so entangled with each other that it's ultimately impossible to comprehend them apart from each other, but for the sake of exposition it's convenient to organize our study of Peirce's assault on the summa by following first the trails of thought that led him to develop a theory of signs, one that has come to be known as 'semiotic', and tracking next the ways of thinking that led him to develop a theory of inquiry, one that would be up to the task of saying 'how science works'. In cognitive psychology a representation is a hypothetical internal cognitive symbol that represents external reality. ... Wikipedia does not yet have an article with this exact name. ... Semiotics (also spelled Semeiotics) is the study of signs and sign systems. ...


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. Staying within the bounds of what will give us a more solid basis for understanding Peirce, it serves to consider the following loci in Aristotle: Inference is the act or process of deriving a conclusion based solely on what one already knows. ... Information is the result of processing, manipulating and organizing data in a way that adds to the knowledge of the person receiving it. ... Wikipedia does not yet have an article with this exact name. ... In semiotics, a sign is generally defined as, ...something that stands for something else, to someone in some capacity. ... Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ...

In addition to the three elements of inference, that Peirce would assay to be irreducible, Aristotle analyzed several types of compound inference, most importantly the type 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'. Psychology is an academic and applied discipline involving the scientific study of mental processes and behavior. ... On the Soul (or De Anima) is a writing by Aristotle, outlining his philosophical views on the nature of living things. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... De Interpretatione or Hermeneutics (Peri Hermeneias) is a work of the ancient Greek philosopher Aristotle, mainly on the philosophy of language. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... Abduction, or abductive reasoning, is the process of reasoning to the best explanations. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it. ... Prior Analytics is Aristotles work on deductive reasoning, part of his Organon, the organ of logical and scientific methods. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... Irreducible can refer to: irreducible (mathematics) irreducible (philosophy) This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Aristotle (Greek: AristotélÄ“s) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Analogy is either the cognitive process of transferring or giving information from a particular subject (the analogue or source) to another particular subject (the target), or a linguistic expression corresponding to such a process. ... Look up Example in Wiktionary, the free dictionary. ... Since the late 1960s, the word paradigm (IPA: ) has referred to a thought pattern in any scientific discipline or other epistemological context. ...


Inquiry is a form of reasoning process, in effect, a particular way of conducting thought, and thus it can be said to institute a specialized manner, style, or turn of thinking. Philosophers of the school that is commonly called 'pragmatic' hold that all thought takes place in signs, where 'sign' is the word they use for the broadest conceivable variety of characters, expressions, formulas, messages, signals, 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 allows us to 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.

The distinction between signs denoting and objects denoted is critical to the discussion of Peirce's theory of signs. Wherever needed in the rest of this article, therefore, in order to mark this distinction a little more emphatically than usual, double quotation marks placed around a given sign, for example, a string of zero or more characters, will be used to create a new sign that denotes the given sign as its object. Aristotelian logic, also known as syllogistic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. ... Semiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ...


Theory of signs, or semiotic

To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs. - C.S. Peirce, CP5.254

Peirce referred to his general study of signs, based on the concept of a triadic sign relation, as semiotic or semeiotic, either of which terms are currently used in either singular of plural form. Peirce began writing on semeiotic in the 1860s, around the time that he devised his system of three categories. He eventually defined semiosis as an "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". (Houser 1998: 411, written 1907). This triadic relation grounds the semeiotic. In logic, mathematics, and semiotics, a triadic relation or a ternary relation is an important special case of a polyadic or finitary relation, one in which the number of places in the relation is three. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... Semiotics (also spelled Semeiotics) is the study of signs and sign systems. ... Semeiotic is a term used by Charles Sanders Peirce to distinguish his theory of sign relations from other approaches to the same subject matter. ... Semiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. ...


A sign (a.k.a. a representamen) is not necessarily a linguistic symbol, and is something interpretable as saying something about something. An object (a.k.a. a semiotic object) is a subject matter of a sign and an interpretant. An interpretant (a.k.a. an interpretant sign) is a sign's effect on the mind which comprehends it; it is an interpretation in the sense of product or content (rather than act or activity) of interpretation, and is the sign's clarified meaning or ramification, a clarified idea of the difference which the sign's being true would make. The sign stands for the object to the interpretant. The object determines (in Peirce's sense of "specializes," bestimmt) the sign to determine the interpretant to be related to the object as the sign is related to the object. Therefore this determines the interpretant as a sign to determine a still further interpretant, and semiosis ever continues. 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. Some understanding needed by the mind depends on familiarity with the object; in order to know what a given sign stands for, the mind needs some experience of that sign's object collaterally to that sign or sign system. An interpretant, in Semiotics, is the effect of a sign on someone who reads or comprehends it. ...


Signhood is a way of being in relation, not a way of being in itself. The role of sign is constituted as one among three, where roles in general are distinct even when the things filling them are not distinct. In other words, the question of what is a sign depends on the question of sign relation, which depends on the question of triadic relation. This, in turn, depends on the question of relation itself; and, to the traditional ways of extension and intension, which Peirce regards as necessary but insufficient, Peirce adds a third approach, the way of information -- including the idea of change of information -- in order to integrate the other two approaches in a unified whole. In semiotics, a sign is generally defined as, ...something that stands for something else, to someone in some capacity. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... In logic, mathematics, and semiotics, a triadic relation or a ternary relation is an important special case of a polyadic or finitary relation, one in which the number of places in the relation is three. ... In mathematics, a finitary relation is defined by one of the formal definitions given below. ... In any of several studies that treat the use of signs, for example, linguistics, logic, mathematics, semantics, and semiotics, the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties... Intension refers to the meanings or characteristics encompassed by a given word. ... Semiotic information theory considers the information content of signs and expressions as it is conceived within the semiotic or sign-relational framework developed by Charles Sanders Peirce. ...


Sign relations

Main article: Sign relation

With that hasty map of relations and relatives sketched above, we may now trek into the terrain of sign relations, the main subject matter of Peirce's semeiotic, or theory of signs. A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... Semeiotic is a term used by Charles Sanders Peirce to distinguish his theory of sign relations from other approaches to the same subject matter. ...


Types of signs

Peirce proposes several typologies and definitions of the signs (which he also at times called "representamens"). More than 76 definitions of what a sign is have been collected throughout Peirce's work. Some canonical typologies can nonetheless be observed, one crucial one being the distinction between "icons", "indices" and "symbols" (CP 2.228, CP 2.229 and CP 5.473). This typology emphasizes how the sign alternatively refers to its object (1) iconically, by virtue of the sign's relation to itself (or its ground), (2) indexically, by virtue of the sign's relation to its object, and (3) symbolically, by virtue of the sign's relation to its interpretant. A sign may compound these modes, for example, a roadside sign displaying a fork both (1) portrays and (2) indicates a rest stop, and (3) does so in keeping with some pronounced stylistic conventions which add something of a symbolic dimension. (Peirce also elaborates further typologies based on other criteria).

  1. An icon is a sign that denotes its object by virtue of a quality which is shared by them but which the icon has irrespectively of the object. The icon, for example, a portrait or a diagram, resembles or imitates its object. The icon has, of itself, a certain character or aspect, one which the object also has (or is supposed to have) and which lets the icon be interpreted as a sign even if the object does not exist. The icon signifies essentially on the basis of its ground. Peirce defined the ground as the pure abstraction of a quality, and the sign's ground as the respect in which it resembles its object.
  2. An index is a sign that denotes its object by virtue of an actual connection involving them, one that he also calls a real relation in virtue of its being irrespective of interpretation. It is in any case a relation which is in fact, in contrast to the icon, which has only a ground for denotation of its object, and in contrast to the symbol, which denotes by an interpretive habit or law. If the indexical relation is a resistance or reaction physically or causally connecting an index to its object, then the index is a reagent, for example, smoke coming from a building is a reagent index of fire. Such an index refers to the object because that index is really affected or modified by the object, and is the only kind of index which can be used in order to ascertain facts about its object. Peirce also usually held that an index does not have to be an actual individual fact or thing, but can be a general; a disease symptom is general, its occurrence singular; and he usually considered a designation to be an index, for example, a pronoun, a proper name, or a label on a diagram, actually directing or compelling the mind's attention toward the object just as a reagent does. (In 1903 Peirce said that only an individual is an index (EP 2.274) and called designations "subindices or hyposemes," classing them as symbols; he allowed of a "degenerate index" indicating a non-individual object, as exemplified by an individual thing indicating its own characteristics. But by 1904 he returned to allowing indices to be generals and to classing designations as indices.)
  3. A symbol is a sign that denotes its object solely by virtue of the fact that it will be interpreted to do so. The symbol does not depend on having any resemblance or actual connection to the denoted object but is fundamentally conventional, so that the signifying relationship must be learned and agreed upon, for example, the word cat. A symbol thus denotes, primarily, by virtue of its interpretant. Its sign-action (semeiosis) is ruled by a convention, a more or less systematic set of associations that ensures its interpretation.

These definitions are specific to Peirce's theory of signs and are not exactly equivalent to more general uses of the terms icon, index, or symbol. Christ the Redeemer (1410s, by Andrei Rublev) An icon (from Greek , eikon, image) is an image, picture, or representation; it is a sign or likeness that stands for an object by signifying or representing it, or by analogy, as in semiotics; in computers an icon is a symbol on the... Look up Index in Wiktionary, the free dictionary. ...


Theory of inquiry

Main article: Inquiry
Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:
Do not block the way of inquiry.
Although it is better to be methodical in our investigations, and to consider the economics of research, yet there is no positive sin against logic in trying any theory which may come into our heads, so long as it is adopted in such a sense as to permit the investigation to go on unimpeded and undiscouraged. On the other hand, to set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning, as it is also the one to which metaphysicians have in all ages shown themselves the most addicted. (Peirce, "F.R.L." (c. 1899), CP 1.135–136.)

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. Borrowing a brace of concepts from Aristotle, Peirce examined three fundamental modes of reasoning that play a role in inquiry, processes that are currently known as abductive, deductive, and inductive inference. Wikipedia does not yet have an article with this exact name. ... A mental model is an explanation in someones thought process for how something works in the real world. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... Wikipedia does not yet have an article with this exact name. ... Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... This article is in need of attention. ... Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ...


In the roughest terms, abduction is what we use to generate a likely hypothesis or an initial diagnosis in response to a phenomenon of interest or a problem of concern, while deduction is used to clarify, to derive, and to explicate the relevant consequences of the selected hypothesis, and induction is used to test the sum of the predictions against the sum of the data. Abduction, or abductive reasoning, is the process of reasoning to the best explanations. ... Look up Hypothesis in Wiktionary, the free dictionary. ... In general, a diagnosis (plural diagnoses) covers a broad spectrum, or spectra, of testing in some form of analysis; such tests based on some collective reasoning is called the method of diagnostics, leading then to the results of those tests by ideal (ethics) would then be considered a diagnosis, but... This article does not cite its references or sources. ... Look up Problem in Wiktionary, the free dictionary. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Look up Hypothesis in Wiktionary, the free dictionary. ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. ...


These three processes typically operate in a cyclic fashion, systematically operating to reduce the uncertainties and the difficulties that initiated the inquiry in question, and in this way, to the extent that inquiry is successful, leading 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. Personification of knowledge (Greek Επιστημη, Episteme) in Celsus Library in Ephesos, Turkey. ... Skill is human (usually learned) ability to perform actions. ... In music and music theory augmentation is the lengthening or widening of rhythms, melodies, intervals, chords. ... Look up competence, incompetence in Wiktionary, the free dictionary. ... This article needs to be cleaned up to conform to a higher standard of quality. ...


In the pragmatic way of thinking every thing has a purpose, and the purpose of any thing is the first thing that we should try to note about it. The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call 'knowledge' or 'certainty'. It needs to be appreciated that the three kinds of inference, insofar as they contribute to the end of inquiry, describe a cycle that can be understood only as a whole, and none of the three makes complete sense in isolation from the others. Purpose is the quality of one being determined to do or achieve a goal deliberately. ... Wikipedia does not yet have an article with this exact name. ... This article is about the mental state. ... Look up belief in Wiktionary, the free dictionary. ... Personification of knowledge (Greek Επιστημη, Episteme) in Celsus Library in Ephesos, Turkey. ... A related article is titled uncertainty. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ...


For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and that induction can evaluate. This places a mild but meaningful constraint on 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. In a similar fashion, 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. Abduction, or abductive reasoning, is the process of reasoning to the best explanations. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. ... A constraint is a limitation of possibilities. ... An explanation is a statement which points to causes, context and consequences of some object (or process, state of affairs etc. ... This article or section may contain original research or unverified claims. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... Look up integrity in Wiktionary, the free dictionary. ... Modularity is a concept that has applications in the contexts of computer science, particularly programming, as well as cognitive science in investigating the structure of mind. ...


If we then think to inquire, 'What sort of constraint, exactly, does pragmatic thinking place on our guesses?', we have asked the question that is generally recognized as the problem of 'giving a rule to abduction'. Peirce's way of answering it is given in terms of the so-called 'pragmatic maxim', and this in turn gives us a clue as to the central role of abductive reasoning in Peirce's pragmatic philosophy. A constraint is a limitation of possibilities. ... Abduction, or abductive reasoning, is the process of reasoning to the best explanations. ... The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce (1839-1914). ...


Logic of information

Main article: Logic of information

Peirce was a pioneer in the study of information, lecturing on what he called the laws of information as early as 1865. The logic of information, or the logical theory of information, considers the information content of logical signs and expressions along the lines initially developed by Charles Sanders Peirce. ...

Let us now return to the 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), CE 1, 467.)

References

  • The following abbreviations are used in the text to refer to standard works in the Peirce literature:
CE n, m = Writings of Charles S. Peirce: A Chronological Edition, vol. n, page m.
CP n.m = Collected Papers of Charles Sanders Peirce, vol. n, paragraph m.
CTN n, m = Contributions to 'The Nation' , vol. n, page m.
EP n, m = The Essential Peirce: Selected Philosophical Writings, vol. n, page m.
NEM n, m = The New Elements of Mathematics by Charles S. Peirce, vol. n, page m.
SIL m = Studies in Logic by Members of the Johns Hopkins University, page m.
SS m = Semiotic and Significs … Charles S. Peirce and Lady Welby, page m.
SW m = Charles S. Peirce, Selected Writings, page m.
  • Anellis, I.H. (1995), "Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic", Modern Logic 5, 270–328. Eprint.
  • Boole, George (1854), An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan, 1854. Reprinted with corrections, Dover Publications, New York, NY, 1958.
  • Dewey, John (1910), How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991.
  • Haack, Susan (1998), Manifesto of a Passionate Moderate, The University of Chicago Press, Chicago, IL.
  • Houser, Nathan (1989), "The Fortunes and Misfortunes of the Peirce Papers", Fourth Congress of the International Association for Semiotic Studies, Perpignan, France, 1989. Published, pp. 1259–1268 in Signs of Humanity, vol. 3, Michel Balat and Janice Deledalle–Rhodes (eds.), Gérard Deledalle (gen. ed.), Mouton de Gruyter, Berlin, Germany, 1992. Eprint.
  • Peirce, C.S. (1877), "The Fixation of Belief", Popular Science Monthly 12, 1–15, 1877. Reprinted, CP 5.358–387. Eprint.
  • Peirce, C.S. (1878), "How to Make Our Ideas Clear", Popular Science Monthly 12, 286–302, 1878. Reprinted, CP 5.388–410. Eprint.
  • Peirce, C.S. (1899), "F.R.L." [First Rule of Logic], unpaginated manuscript, c. 1899. Reprinted, CP 1.135–140. Eprint.
  • Peirce, C.S., "Application of C.S. Peirce to the Executive Committee of the Carnegie Institution" (1902 July 15). Published, "Parts of Carnegie Application" (L75), pp. 13–73 in The New Elements of Mathematics by Charles S. Peirce, Volume 4, Mathematical Philosophy, Carolyn Eisele (ed.), Mouton Publishers, The Hague, Netherlands, 1976. Eprint, Joseph Ransdell (ed.).
  • Peirce, C.S., The Essential Peirce, Selected Philosophical Writings, Volume 1 (1867–1893), Nathan Houser and Christian Kloesel (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1992.
  • Peirce, C.S., The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1998.
  • Robin, Richard S. (1967), Annotated Catalogue of the Papers of Charles S. Peirce, University of Massachusetts Press, Amherst, MA, 1967. Eprint.
  • Taylor, Barry N. (Ed.), The International System of Units (NIST Special Publication 330), Superintendent of Documents, Washington, DC, 2001. PDF text.

Aristotle (Greek: AristotélÄ“s) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... The Loeb Classical Library is a series of books, today published by the Harvard University Press, which present important works of ancient Greek and Latin Literature in a way designed to make the text accessible to the broadest possible audience, by presenting the original Greek or Latin text on each... William Heinemann was the founder of a publishing house in London, England that bears his name. ... The Loeb Classical Library is a series of books, today published by the Harvard University Press, which present important works of ancient Greek and Latin Literature in a way designed to make the text accessible to the broadest possible audience, by presenting the original Greek or Latin text on each... William Heinemann was the founder of a publishing house in London, England that bears his name. ... Prior Analytics is Aristotles work on deductive reasoning, part of his Organon, the organ of logical and scientific methods. ... The Loeb Classical Library is a series of books, today published by the Harvard University Press, which present important works of ancient Greek and Latin Literature in a way designed to make the text accessible to the broadest possible audience, by presenting the original Greek or Latin text on each... George Boole [], (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. ... Macmillan Publishers Ltd, also known as The Macmillan Group, is a privately-held international publishing company owned by Georg von Holtzbrinck Publishing Group. ... Dover Publications is a book publisher founded in 1941. ... Edward N. Zalta is a Senior Research Scholar at the Center for the Study of Language and Information. ... The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ... John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ... Daniel Collamore Heath (1843-1908) D.C. Heath and Company is a small publishing company located at 125 Spring Street in Lexington, Massachusetts. ... Susan Haack (born 1945) is a professor of philosophy and law, and is currently on the faculty at the University of Miami in Florida. ... Jean van Heijenoort (prounounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. ... Henry George Liddell (1811‑1898)was a British historian and academic, editor at Charterhouse and Christ Church, Oxford, of which in 1855 he became Dean. ... There are several individuals called Robert Scott, including: Robert Scott, New Zealand radio broadcaster www. ... Oxford University Press (OUP) is a highly-respected publishing house and a department of the University of Oxford in England. ... Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ... Springer Science+Business Media or Springer (IPA: ) is a worldwide publishing company based in Germany which focuses on academic journals and books in the fields of science, technology and medicine. ... July 15 is the 196th day (197th in leap years) of the year in the Gregorian Calendar, with 169 days remaining. ...

Bibliography

A bibliography of Peirce's works may be found at the above location. Charles Sanders Peirce (Bibliography). ...


See also

Abstraction

Continuous predicate is a term coined by Charles Sanders Peirce (1839-1914) to describe a special type of relational predicate that results as the limit of a recursive process of hypostatic abstraction. ... Hypostatic abstraction, also known as hypostasis or subjectal abstraction, is the process or the product of a formal operation that takes an element of information, such as might be expressed in a proposition of the form X is Y, and conceives its information to consist in the relation between a... A hypostatic object, also known in certain senses as an abstract object or a formal object, is an object of discussion or thought that results as the normal product of a process of hypostatic abstraction. ... Prescisive abstraction or prescision, variously spelled as precisive abstraction or prescission, is a formal operation that marks, selects, or singles out one feature of a concrete experience to the disregard of others. ...

Contemporaries

John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ... For other people named William James see William James (disambiguation) William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... Ernst Schröder Ernst Schröder (25 November 1841 Mannheim, Germany - 16 June 1902 Karlsruhe Germany) was a German mathematician mainly known for his work on algebraic logic. ...

Information, inquiry, logic, semiotics

Ampheck, from Greek double-edged, is a term coined by Charles Sanders Peirce for either one of the pair of logically dual operators, variously referred to as Peirce arrows, Sheffer strokes, or NAND and NNOR. Either of these logical operators is a sole sufficient operator for deriving or generating all... In logic, the comprehension of an object is the totality of intensions, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the totality of intensions that are pertinent to the context of a given discussion. ... An entitative graph is an element of the graphical syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. ... An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882 and continued to develop the method until his death in 1914. ... Wikipedia does not yet have an article with this exact name. ... The book Laws of Form (hereinafter abbreviated LoF), by G. Spencer-Brown, describes three distinct logical systems: The primary arithmetic (described in Chapter 4), which can be interpreted as Boolean arithmetic; The primary algebra (chapter 6), an algebraic structure that is a provocative and economical notation for the two-element... The logic of information, or the logical theory of information, considers the information content of logical signs and expressions along the lines initially developed by Charles Sanders Peirce. ... Logic of relatives, short for logic of relative terms, is a term used to cover the study of relations in their logical, philosophical, or semiotic aspects, as distinguished from, though closely coordinated with, their more properly formal, mathematical, or objective aspects. ... A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. ... A logical matrix, in the finite dimensional case, is a k-dimensional array with entries from the boolean domain B = {0, 1}. Such a matrix affords a matrix representation of a k-adic relation. ... NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ... NOR Logic Gate The logical NOR or joint denial is a boolean logic operator which produces a result that is the inverse of logical or. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Peirces law in logic is named after the philosopher and logician Charles Sanders Peirce. ... In linguistics and semiotics, pragmatics is concerned with bridging the explanatory gap between sentence meaning and speakers meaning. ... A relative term, also called a rhema or a rheme, is a logical term that requires reference to any number of other objects, called the correlates of the term, in order to denote a definite object, called the relate (pronounced with the accent on the first syllable) of the relative... Semeiotic is a term used by Charles Sanders Peirce to distinguish his theory of sign relations from other approaches to the same subject matter. ... Semiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. ... Semiotics, or semiology, is the study of signs and symbols, both individually and grouped in sign systems. ... Semiotic information theory considers the information content of signs and expressions as it is conceived within the semiotic or sign-relational framework developed by Charles Sanders Peirce. ... In semantics and linguistics, the semiotic triangle is a figure that is used to explain the relationship between Concepts, Symbols and Objects. ... In semiotics, a sign is generally defined as, ...something that stands for something else, to someone in some capacity. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ... Sole sufficient operator, or sole sufficient connective, is a term used to describe an operator that is sufficient by itself to generate all of the operators in a specified class of operators. ...

Mathematics

In mathematics, a binary relation (or a dyadic relation) is an arbitrary association of elements of one set with elements of another (perhaps the same) set. ... Kaina Stoicheia (Καινα στοιχεια) or New Elements is the title of several manuscript drafts of a document that Charles Sanders Peirce wrote circa 1904, intended as a preface to a book on the foundations of mathematics. ... A quincuncial map is a conformal map projection that is conformal everywhere except at the corners of the inner hemisphere. ... In mathematics, a finitary relation is defined by one of the formal definitions given below. ... In logic and mathematics, the composition of relations is the generalization of the composition of functions. ... In logic and mathematics, relation construction and relational constructibility have to do with the ways that one relation is determined by an indexed family or a sequence of other relations, called the relation dataset. ... In logic and mathematics, relation reduction and relational reducibility have to do with the extent to which a given relation is determined by an indexed family or a sequence of other relations, called the relation dataset. ... The theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another. ... In logic, mathematics, and semiotics, a triadic relation or a ternary relation is an important special case of a polyadic or finitary relation, one in which the number of places in the relation is three. ...

Philosophy

For themes emphasized by Charles Peirce, see Pragmaticism. ... Pragmaticism was a term used by Charles Sanders Peirce for his philosophy, in order to distance himself from pragmatism of William James ... The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce (1839-1914). ... Pragmatic theory of truth refers to those accounts, definitions, and theories of the concept truth that distinguish the philosophies of pragmatism and pragmaticism. ...

External links

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  • Philosophie et sémiotique de Peirce, Raymond Robert Tremblay.
  • Portions of the above article are adapted from the Nupedia article, "Charles S. Peirce", by Jaime Nubiola.

  Results from FactBites:
 
Peirce (405 words)
Charles Sanders Peirce studied philosophy and chemistry at Harvard, where his father, Benjamin Peirce, was professor of mathematics and astronomy.
Peirce's early philosophical development relied on a Kantian theory of judgment, but careful study of the logic of relations led him to abandon syllogistic methods in favor of the study of language and belief.
Benjamin Peirce by Ivor Grattan-Guinness and Alison Walsh.
Charles Peirce (327 words)
Charles Sanders Peirce (September 10, 1839 - April 19, 1914) was an American mathematician, philosopher and logician.
He is considered to be the founder of pragmatism and the father of modern semiotics.  In recent decades, his thought has enjoyed renewed appreciation.  At present, he is widely regarded as an innovator in many fields, especially the methodology of research and the philosophy of science.
Peirce, Charles S.  The Essential Peirce, 2 vols.  Edited by N.  Houser, et al.  Bloomington, IN: Indiana University Press, 1992-98.  An excellent edition of Peirce's most relevant philosophical works.  The introductions to both volumes by Houser are the best brief presentation of Peirce written to date.
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