Charles Sanders Peirce

Charles Sanders Peirce (pronounced purse), (September 10, 1839 – April 19, 1914) was an American polymath, born in Cambridge, Massachusetts. Although educated as a chemist and employed as a scientist for 30 years, he is now mostly seen as a philosopher. He is the greatest American builder of architectonic systems, and his admirers deem him the most important systematizer since Kant and Hegel, who were major influences. Download high resolution version (700x1072, 265 KB) Charles Sanders Peirce Credit: National Oceanic and Atmospheric Administration/Department of Commerce [1] Source http://www. ... 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 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). ... 1914 (MCMXIV) was a common year starting on Thursday. ... Leonardo da Vinci A polymath (from greek polys(πολύς) meaning much, great in quantity, and mathisi(μάθηση) meaning learning), is a person who excels in multiple fields, particularly in both arts and sciences. ... Cambridge City Hall Settled: 1630 â€“ Incorporated: 1636 Zip Code(s): 02139 â€“ Area Code(s): 617 / 857 Official website: http://www. ... Chemist Julie Perkins of Lawrence Livermore National Laboratory pours from a Florence flask. ... The physicist Albert Einstein is probably historys most widely recognized scientist. ... Philosopher in Meditation (detail), by Rembrandt. ... In philosophy, Architectonic (or archetectonic) is used to mean the scientific systematisation of all knowledge. ... 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. ...

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 Much of his huge output is still unpublished. 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, thus anticipating the digital computer. Combatants Allies: Poland, British Commonwealth, France/Free France, Soviet Union, United States, China, and others Axis Powers: Germany, Italy, Japan, and others Casualties Military dead: 17 million Civilian dead: 33 million Total dead: 50 million Military dead: 8 million Civilian dead: 4 million Total dead: 12 million World War II... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... Research is often described as an active, diligent, and systematic process of inquiry aimed at discovering, interpreting and revising facts. ... The philosophy of science is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of science, including the formal sciences, natural sciences, and social sciences. ... It has been suggested that this article or section be merged with Knowledge. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Semiotics, or semiology, is the study of signs, both individually and grouped in sign systems. ...

Life

Right from the beginning, the relations of America as New England with Europe were, from the philosophical point of view, ambiguous, when they were not simply difficult and, in the end, impossible. Peirce is in himself the ‘’resumé’’ of this story… from the rejection of European philosophical paradigms to the creation of new paradigms which are not only Peirce’s but America’s, and slowly but inevitably [those] of the global world of tomorrow. (Deledalle 2000: 3).

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 devoured an older brother's copy of Richard Whately's Elements of Logic, then the leading English language text of its kind. Thus began his lifelong fascination with logic and reasoning. He went on to obtain the BA and MA from Harvard, and in 1863 was awarded the Lawrence Scientific School's first B.Sc. in chemistry. This last degree was awarded summa cum laude; his academic record was otherwise 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 him; they clashed on later occasions. This was unfortunate, because Eliot was President of Harvard 1869-1909, a period encompassing nearly all of Peirce's working life, during which he repeatedly vetoed having Harvard employ Peirce in any capacity. For others with a similar name, see Benjamin Pierce. ... Radio telescopes are among many different tools used by astronomers Astronomy (Greek: αστρονομία = άστρον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects and phenomena that originate outside the Earths atmosphere, such as stars, planets, comets, auroras, galaxies, and the cosmic background radiation. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... Harvard University campus (old map) 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. ... 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 - Wikipedia /**/ @import /skins-1. ... William James William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... Prof. ...

United States Coast Survey

Charles was employed as a scientist by the United States Coast Survey (1859–1891), 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, sparing him a very awkward situation, as his Boston Brahmin family sympathized with the Confederacy. At the Survey, he worked mainly in geodesy and in gravimetry, refining the use of pendulums to determine small local variations in the strength of the earth's gravity. The Survey sent him to Europe five times, the first in 1871, as part of a group dispatched to observe a solar eclipse. While in Europe, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford, British mathematicians and logicians whose turn of mind resembled his own. During 1869-72, 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 1878, he was the first to define the meter as so many wavelengths of light of a certain frequency, the definition employed today. The U.S. Coast and Geodetic Survey was established by President Thomas Jefferson in 1807 as the Survey of the Coast. ... 1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ... 1891 (MDCCCXCI) was a common year starting on Thursday (see link for calendar). ... Combatants United States of America Union Confederate States of America Commanders Abraham Lincoln, Ulysses S. Grant Jefferson Davis, Robert E. Lee Strength 2,200,000 1,064,000 Casualties Killed in action: 110,000 Total dead: 360,000 Wounded: 275,200 Killed in action: 93,000 Total dead: 258,000... Motto: Deo Vindice (Latin: With God As Our Vindicator) Anthem: God Save the South (unofficial) Dixie (popular) The Bonnie Blue Flag (popular) Capital Montgomery, Alabama February 4, 1861–May 29, 1861 Richmond, Virginia May 29, 1861–April 9, 1865 Danville, Virginia April 3–April 10, 1865 Largest city New Orleans... 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. ... Note: This article contains special characters. ... 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 wavelengths that are studied in the field of optics. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

Over 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 required 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, he 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 Peirce, such as philosophy (Royce and John Dewey were students), 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. It is a fact that Clark, Wisconsin, Michigan, Cornell, Stanford, and Chicago all declined to hire him, although the precise reasons for their so doing can no longer be determined. 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 (1835-1909). 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, further claiming that Peirce experienced 8 nervous breakdowns between 1876 and 1911. Brent also believes that Peirce tried to alleviate his symptoms with ether, morphine, and cocaine. 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 thought has 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. ... Simon Newcomb. ... Bipolar disorder (previously known as manic depression) is a diagnostic category describing a class of mood disorders where the person experiences states or episodes of depression and/or mania, hypomania, and/or mixed states. ...

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), marrying her immediately upon divorcing Harriet 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, and to his being deemed morally unfit for academic employment anywhere in the USA. Peirce had no children by either marriage.

Poverty

In 1887, Peirce used an 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. He insisted on living well beyond his means, which 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. His only food was bread donated by the local baker, and he wrote on the verso side of old manuscripts because he could not afford new stationery. For a while an outstanding warrant for assault and debt led to his becoming a fugitive in New York. A variety of people including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot, paid his property taxes and mortgage, and settled other debts. 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. ... Milford is a borough located in Pike County, Pennsylvania. ... Gifford Pinchot (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). ...

During this long final twilight phase of Peirce’s life, he 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. Peirce tried his hand at inventing, and began but did not complete a number of books, all in the hope of making money. 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 Foundation is named after Andrew Carnegie, the Scottish-American idealist and industrial magnate, whose generous gift made it possible to carry out plans for the construction of the Peace Palace in 1903, the year in which it was founded. ...

The one who did the most to help Peirce in this his hour of desperate need was his old friend William James, who helped arrange four series of lectures at or near Harvard, and dedicated his Will to Believe to Peirce. 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 showed his gratitude for these remarkable gestures of friendship 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 1998: 315-16, 374). William James 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. Milford is a borough located in Pike County, Pennsylvania. ...

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 fails to mention Peirce.) While reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, Alfred North Whitehead was struck by the extent to which 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 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, working mostly in the 20th century. ... 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, OM (February 15, 1861 – December 30, 1947) was a British mathematician who became a philosopher. ... Conventional Platonic metaphysics posits the real world of metaphysical reality as being timeless. ... Sir Karl Raimund Popper, CH, KT, MA, Ph. ... William James William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... Josiah Royce (November 20, 1855, Grass Valley, California. ... 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 Peirce bibliography. From 1916 until his death, John Dewey's writings repeatedly mention Peirce with deference, and 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 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 the history of American philosophy, including pragmatism, 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 thought has 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. ...

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 (pp. 422-48) a wide-ranging survey of the impact of Peirce's thought through 1983. The history of ideas is a field of research in history and in related fields dealing with the expression, preservation, and change of human ideas over time. ...

Peirce has come to enjoy an international following. University research centers devoted to Peirce Studies and pragmatism can be found in Brazil, Finland, Germany, and Spain. There have been French and Italian Peirceans of note since 1950. For many years, the University of Toronto housed the North American philosophy department most devoted to Peirce. In recent years, Peirce scholars have clustered at Indiana University - Purdue University Indianapolis, the home of the Peirce Edition Project, and the Pennsylvania State University. To meet Wikipedias quality standards, this article or section may require cleanup. ... The University of Toronto (U of T), in Toronto, Ontario, is the largest university in Canada. ... → 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 The Pennsylvania State University (commonly known as Penn State) is a state-related land-grant university with a main campus located in State College, Pennsylvania, and 23 other campuses (some called Commonwealth Campuses) located throughout Pennsylvania. ...

Works

Peirce's reputation is based in large part 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 corresondence, fill the eight volumes of the Collected Papers of Charles Sanders Peirce, published between 1931 and 1958. A first taste of Peirce's philosophical writings can be found in the two volumes of The Essential Peirce (Houser and Kloesel (eds.) 1992, Peirce Edition Project (eds.) 1998). 1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ... 1958 (MCMLVIII) was a common year starting on Wednesday of the Gregorian calendar. ...

The only book-length account of his own investigations that 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, the sum of which writing is reprinted in Contributions to 'The Nation' (Ketner and Cook, 1975-1987). 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) published his catalog of this legacy, did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totalling 80,000 pages. A number of these works were published in Eisele (1976, 1985), but most of them remain as yet unpublished. For more on the vicissitudes of Peirce's papers, see (Houser 1989). Harvard University campus (old map) Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ...

The increasingly apparent limitations of the Collected Papers, with respect to coverage and organization both, led Max Fisch and others in the 1970's to establish the Peirce Edition Project, whose mission is to prepare a more complete critical edition, known as the Writings, organized chronologically. A mere half dozen of the anticipated 30-plus volumes have appeared to date, but they cover a period from 1859 to 1890 when Peirce carried out some of his most important work.

On a New List of Categories (1867)

Main article: On a New List of Categories

Logic of Relatives (1870)

Main article: 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)

Main article: 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)

Main article: The Simplest Mathematics

Kaina Stoicheia (1904)

Main article: Kaina Stoicheia

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 secondly 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 was a working scientist for 30 years, and arguably was a professional philosopher only during the five years he lectured at Johns Hopkins. He learned philosophy mainly by reading a few pages of Kant's Critique of Pure Reason in the original German, every day while a Harvard undergraduate. His writings bear on a wide array of disciplines, including astronomy, metrology, geodesy, mathematics, logic, philosophy, the history and philosophy of science, linguistics, economics, and psychology. This work has become the subject of renewed interest and approval, resulting in a revival inspired not only by his anticipations of recent scientific developments but also by his demonstration of how philosophy can be applied effectively to human problems. 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. ... This article or section is incomplete and may require cleanup and/or expansion. ... Radio telescopes are among many different tools used by astronomers Astronomy (Greek: αστρονομία = άστρον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects and phenomena that originate outside the Earths atmosphere, such as stars, planets, comets, auroras, galaxies, and the cosmic background radiation. ... Metrology is variously described as the science of measurement; the science of accuracy and precision; the history of measures; the history of measurement and other definitions. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Philosopher in Meditation (detail), by Rembrandt. ... 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 human language, and someone who engages in this study is called a linguist. ... Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ... Psychology (Gk: psyche, soul or mind + logos, speech) is an academic and applied field involving the study of the mind, brain, and behavior, both human and nonhuman. ...

Peirce's writings repeatedly refer to a system of three categories, named Firstness, Secondness, and Thirdness, devised early in his career in reaction to his reading of Aristotle, Kant, and Hegel. He later initiated the philosophical tendency known as pragmatism, a variant of which his life-long friend William James made popular. Peirce believed that any truth is provisional, and that the truth of any proposition cannot be certain but only probable. The name he gave to this state of affairs was "fallibilism". This fallibilism and pragmatism may be seen as playing roles in his work similar to those of skepticism and positivism, respectively, in the work of others. 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 (Ancient Greek: AristotélÄ“s 384 – March 7, 322 BCE) was an ancient 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... William James William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... 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. ... The neutrality of this article is disputed. ... Positivism can have several meanings. ...

Pragmatism

Peirce's recipe for pragmatic thinking, going under the label of pragmatism and also known as pragmaticism, is recapitulated in several versions of the so-called pragmatic maxim. Here is one of his more emphatic statements of it: To meet Wikipedias quality standards, this article or section may require cleanup. ... 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). ...

Pragmaticism was originally enounced in the form of a maxim, as follows: 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).

William James, among others, regarded two of Peirce's papers, "The Fixation of Belief" (1877) and "How to Make Our Ideas Clear" (1878) as being the origin of pragmatism. Peirce conceived pragmatism to be a method for clarifying the meaning of difficult ideas through the application of the pragmatic maxim. He differed from William James and the early John Dewey, in some of their tangential enthusiasms, in being decidedly more rationalistic and realistic, in several senses of those terms, throughout the preponderance of his own philosophical moods. William James William James (January 11, 1842 – August 26, 1910) was a pioneering American psychologist and philosopher. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... An idea (Greek: ιδέα) is a specific thought which arises in the mind. ... 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). ... John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thought has been greatly influential in the United States and around the world. ...

Peirce's pragmatism may be understood as a method of sorting out conceptual confusions by linking the meaning of concepts to their operational or practical consequences. This pragmatism bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavellian search for mercenary or political advantage. Rather, Peirce sought an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond the usual duo of foundational alternatives, namely: Detail of the portrait of Machiavelli, ca 1500, in the robes of a Florentine public official Niccolò Machiavelli (May 3, 1469—June 21, 1527) was an Italian political philosopher during the Renaissance. ...

• Deduction from self-evident truths, or rationalism;

• Induction from experiential phenomena, or empiricism.

His approach is often confused with the latter form of foundationalism, but is distinct from it by virtue of the following three dimensions: In traditional Aristotelian logic, deductive reasoning is inference in which the conclusion is of no greater generality than the premises, as opposed to abductive and inductive reasoning, where the conclusion is of greater generality than the premises. ... Rationalism, also known as the rationalist movement, is a philosophical doctrine that asserts that the truth can best be discovered by reason and factual analysis, rather than faith, dogma or religious teaching. ... // 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... ...

• Active process of theory generation, with no prior assurance of truth;

• Subsequent application of the contingent theory, aimed toward developing its logical and practical consequences;

• Evaluation of the provisional theory's utility for the anticipation of future experience, and that in dual senses of the word: prediction and control. Peirce's 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.

A theory that proves itself more successful in predicting and controlling our world than its rivals is said to be nearer the truth. This is an operational notion of truth employed by scientists. Unlike the other pragmatists, Peirce never explicitly advanced a theory of truth. But his scattered comments about truth have proved influential to several epistemic truth theorists, and as a useful foil for deflationary and correspondence theories of truth. 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. ... Physiognomy (Gk. ... Scientific method refers to a body of techniques for the investigation of phenomena and the acquisition of new knowledge of the natural world, as well as the correction and integration of previous knowledge, based on observable, empirical, measurable evidence, and subject to laws of reasoning. ... It has been suggested that this article or section be merged with Knowledge. ...

Pragmatism is regarded as a distinctively American philosophy. As advocated by James, John Dewey, Ferdinand Canning Scott Schiller, George Herbert Mead, and others, it has proved durable and popular. But Peirce did not seize on this fact to enhance his reputation. 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). John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thought has 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. ... Pragmaticism was a term used by Charles Sanders Peirce for his philosophy, in order to distance himself from pragmatism of William James ...

Scholastic realism

Peirce’s confession to being a “scholastic realist of a somewhat extreme stripe” (CP 5.470) is well known and baffles some. He has been described by careless writers as an idealist (“reality” = “the object of the final opinion of the scientific community”), but this description is inaccurate, since he believed that reality was best described 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. ... Reality in everyday usage means everything that exists. The term Reality, in its widest sense, includes everything that is, whether it is observable, accessible or understandable by science, philosophy, theology or any other system of analysis. ... 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 which asserts that all that exists is in and of the mind. ... 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. ... Reality in everyday usage means everything that exists. The term Reality, in its widest sense, includes everything that is, whether it is observable, accessible or understandable by science, philosophy, theology or any other system of analysis. ... 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 two of the Chronological Edition of Peirce’s writings (1984). However, 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 statemesnts 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.” (6.605, italics mine) 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, i.e., 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; it has no secondness).

Formal perspective

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. (George Boole, Laws of Thought, p. 24) George Boole [], (November 2, 1815 Lincoln, Lincolnshire, England – December 8, 1864 Ballintemple, Cork City, Ireland) was a mathematician and philosopher. ...

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).

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 could fail to hear the echoes of Boole, nor indeed the background stirrings of the contemporary Zeitgeist in mathematics that went under the name of the 'symbolist movement', the clarion call to which is commonly attributed to George Peacock (1791-1858). If Peirce appears at times to march out of step, it is because he hears the beat of many different drummers, not just one. Look up Zeitgeist in Wiktionary, the free dictionary. ... George Peacock George Peacock (April 9, 1791 - November 8, 1858) was an English mathematician. ...

The main themes of the symbolist movement, though they may have presented novelties to the general understanding of mathematics in the 19th Century, are nowadays familiar to anyone who has had a brush with the 'art of the story problem' in an elementary algebra course. There one learns to approach the story problem, a roughly realistic representation of a concrete circumstance, with the aim to abstract or to 'tease out' a general formula from the concrete data that specify the situation. Next one proceeds to 'crank the formula', starting from a form that is true but problematically obscure in its implications, and, circumstances warranting, continuing until a logically equivalent or a lower implied form is reached, but one that is maximally clarified in its implications. That most clear result one dubs the 'abstract answer' or the 'general solution' to the story problem, leaving nothing more to do but 'plug in' the concrete data that came with the story problem to arrive at the 'concrete answer' or the 'specific solution'.

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 Lincoln, Lincolnshire, England – December 8, 1864 Ballintemple, Cork City, Ireland) was a 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 word formalism has several meanings: A certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems specifically associated with David Hilbert. ... 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. ... Heuristic is the art and science of discovery and invention. ...

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. ...

On Peirce and his contemporaries Ernst Schröder and Frege, Hilary Putnam (1982) wrote: 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. ... Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Hilary Whitehall Putnam (born July 31, 1926) is a key figure in the philosophy of mind during the 20th century. ...

When I started to trace the later development of logic, the first thing I did was to look at Schröder's Vorlesungen über die Algebra der Logik. This book … has a third volume on the logic of relations (Algebra und Logik der Relative, 1895). [These] three volumes were the best-known logic text in the world among advanced students, and they can safely be taken to represent what any mathematician interested in the study of logic would have had to know, or at least become acquainted with in the 1890s.

While, to my knowledge, no one except Frege ever published a single paper in Frege's notation, many famous logicians adopted Peirce-Schröder notation, and famous results and systems were published in it. Löwenheim stated and proved the Löwenheim-Skolem theorem … in Peirce's notation. In fact, there is no reference in Löwenheim's paper to any logic other than Peirce's. To cite another example, Zermelo presented his axioms for set theory in Peirce–Schröder notation, and not, as one might have expected, in Russell–Whitehead notation. Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Leopold Löwenheim (1878, Krefeld Germany - 1957, Berlin) was a German mathematician, known for his work in mathematical logic. ... In mathematical logic, the classic Löwenheim-Skolem theorem states that any infinite model M has a countably infinite submodel N that satisfies exactly the same set of first-order sentences that M satisfies. ... Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician and philosopher. ... Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ... 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. ...

One can sum up these simple facts (which anyone can quickly verify) as follows: Frege certainly discovered the quantifier first (four years before O. H. Mitchell did so, going by publication dates, which are all we have as far as I know). But Leif Ericson probably discovered America 'first' (forgive me for not counting the native Americans, who of course really discovered it 'first'). If the effective discoverer, from a European point of view, is Christopher Columbus, that is because he discovered it so that it stayed discovered (by Europeans, that is), so that the discovery became known (by Europeans). Frege did 'discover' the quantifier in the sense of having the rightful claim to priority; but Peirce and his students discovered it in the effective sense. The fact is that until Russell appreciated what he had done, Frege was relatively obscure, and it was Peirce who seems to have been known to the entire world logical community. How many of the people who think that 'Frege invented [formal] logic' are aware of these facts? In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... A statue of Leif Ericson near the Minnesota State Capitol in St. ... The Americas (sometimes referred to as America) is the area including the land mass located between the Pacific Ocean and the Atlantic Ocean, generally divided into North America and South America. ... A Hupa man, 1923 The term indigenous peoples of the Americas encompasses the inhabitants of the Americas before the arrival of the European explorers in the 15th century, as well as many present-day ethnic groups who identify themselves with those historical peoples. ... For information about the film director, see Chris Columbus. ...

The main evidence for Putnam's claims is Peirce (1885), published in the premier American mathematical journal of the day. Peano, Ernst Schröder, among others, cited this article. Peirce was apparently ignorant of Frege's work, despite their rival achievements in logic, philosophy of language, and the foundations of mathematics. Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician 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. ... Philosophy of language is the branch of philosophy that studies language. ... Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...

Peirce's other major discoveries in formal logic include:

• Distinguishing (Peirce, 1885) between first-order and second-order quantification.

• Seeing that Boolean calculations could be carried out by means of electrical switches (W5:421-24), anticipating Claude Shannon by more than 50 years.

• Devising the existential graphs, a diagrammatic notation for the predicate calculus. These graphs form the basis of the conceptual graphs of John F. Sowa, and of Sun-Joo Shin's diagrammatic reasoning.

A philosophy of logic, grounded in his categories and semeiotic, can be extracted from Peirce's writings. This philosophy, as well as Peirce's logical work more generally, is exposited and defended in , 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, invented 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. ... John F. Sowas Conceptual Graphs allow the graphical statement of logic propositions, or predicates. ... 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 (born January 12, 1929, Vantaa, Finland) is a philosopher and logician. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ... In the main, semantics (from the Greek and in greek letters σημαντικός or in latin letters semantikós, or significant meaning, der