View source for Charles Sanders Peirce

{{Short description|American thinker who founded pragmatism (1839–1914)}}
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{{Use mdy dates|date=January 2023|cs1-dates=y}}
{{infobox philosopher
| name             = Charles Sanders Peirce
| image            = Charles Sanders Peirce.jpg
| caption=Peirce in 1891
| birth_date       = {{birth date|1839|09|10}}
| birth_place      = [[Cambridge, Massachusetts|Cambridge]], Massachusetts, U.S.
| death_date       = {{death date and age|1914|04|19|1839|09|10}}
| death_place      = [[Milford, Pennsylvania|Milford]], Pennsylvania, U.S.
| relatives       = [[Benjamin Peirce]] (father)
| institutions     = [[Johns Hopkins University]]
| alma_mater       = [[Harvard University]]
| known_for        = <!--See {{C. S. Peirce articles}}-->
| region           = [[Western philosophy]]
| era              = [[Late modern philosophy]]
| school_tradition = {{hlist | [[Pragmatism]] | [[Pragmaticism]] }}
| main_interests   = {{hlist | [[Logic]] | mathematics | statistics<ref name="Hacking">{{cite book |author-link=Ian Hacking |author-last=Hacking |author-first=Ian |date=1990 |series=A Universe of Chance |title=The Taming of Chance |url=https://archive.org/details/isbn_9780521388849 |url-access=registration |pages=[https://archive.org/details/isbn_9780521388849/page/200 200–215] |publisher=[[Cambridge University Press]] |isbn=978-0-52138884-9}}</ref><ref name="Stigler78">{{cite journal |author-last=Stigler |author-first=Stephen M. |author-link=Stephen Stigler |date=1978 |title=Mathematical statistics in the early States |journal=Annals of Statistics |volume=6 |issue=2 |pages=239–265 [248] |doi=10.1214/aos/1176344123 |jstor=2958876 |mr=483118 |doi-access=free}}</ref> | philosophy | [[metrology]]<ref name="metr">{{cite journal |author-last=Crease |author-first=Robert P. |date=2009 |title=Charles Sanders Peirce and the first absolute measurement standard |quote=In his brilliant but troubled life, Peirce was a pioneer in both [[metrology]] and philosophy. |url=http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_62/iss_12/39_1.shtml?bypassSSO |journal=Physics Today |volume=62 |issue=12 |pages=39–44 |doi=10.1063/1.3273015 |bibcode=2009PhT....62l..39C |s2cid=121338356 |url-status=dead |archive-url=https://archive.today/20130112162124/http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_62/iss_12/39_1.shtml?bypassSSO |archive-date=January 12, 2013}}</ref> | [[chemistry]] | [[experimental psychology]]<ref name="psych">{{cite journal |doi=10.1002/1520-6696(197407)10:3<291::AID-JHBS2300100304>3.0.CO;2-N |pmid=11609224 |title=Charles S. Peirce (1839–1914): The first American experimental psychologist |date=1974 |author-last=Cadwallader |author-first=Thomas C. |journal=Journal of the History of the Behavioral Sciences |volume=10 |issue=3 |pages=291–298}}</ref> | economics<ref name="econom">{{cite magazine |author-last=Wible |author-first=James R. |date=December 2008 |url=http://www.ingentaconnect.com/content/rodopi/cpm/2008/00000005/00000002/art00003 |title=The economic mind of Charles Sanders Peirce |magazine=Contemporary Pragmatism |volume=5 |issue=2 |pages=39–67}}</ref> | [[linguistics]]<ref name="ling">{{cite web |author-link=Nöth, Winfried |author-last=Nöth |author-first=Winfried |date=2000 |url=http://www.digitalpeirce.fee.unicamp.br/ling.htm |title=Charles Sanders Peirce, Pathfinder in Linguistics}}<br/>{{cite web |url=http://www.digitalpeirce.fee.unicamp.br/ |title=Digital Encyclopedia of Charles S. Peirce |author-link=Nöth, Winfried |author-last=Nöth |author-first=Winfried |date=2000}}</ref> | [[history of science]] | [[Philosophical logic]] | [[metaphysics]] | [[epistemology]]}}
| notable_students = {{collapsible list|
{{hlist | [[John Dewey]] | [[Fabian Franklin]]<ref name="grads"/> | [[Benjamin Ives Gilman]] | [[Joseph Jastrow]] | [[Christine Ladd-Franklin|Christine Ladd]] | [[Allan Marquand]] | [[Josiah Royce]] | [[Thorstein Veblen]]<ref name="grads"/>}}
}}
| notable_ideas    = <!--Please do not populate; see {{C. S. Peirce articles}}-->
| signature        = Signature of Charles Sanders Peirce (1839–1914).png
}}
{{C. S. Peirce articles}}

'''Charles Sanders Peirce''' ({{IPAc-en|p|ɜr|s}}{{efn|"Peirce", in the case of C. S. Peirce, always rhymes with the English-language word "terse" and so, in most dialects, is pronounced exactly like the English-language word "{{audio|en-us-purse.ogg|purse}}."}}<ref>{{cite news |url=http://www.iupui.edu/~peirce/news/1_3/13_4x.htm |title=Note on the Pronunciation of 'Peirce' |website=Peirce Project Newsletter |volume=1 |issue=3–4 |date=December 1994 |access-date=2009-04-06  |archive-date=2016-03-03  |archive-url=https://web.archive.org/web/20160303204222/http://www.iupui.edu/~peirce/news/1_3/13_4x.htm |url-status=dead }}</ref> {{respell|PURSS}}; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, [[logic]]ian, and philosopher who is sometimes known as "the father of [[pragmatism]]".<ref>{{cite encyclopedia |date=1934 |title=Dictionary of American Biography |publisher=Arisbe |url=http://www.cspeirce.com/menu/library/aboutcsp/weissbio.htm |author-last=Weiss |author-first=Paul |author-link=Paul Weiss (philosopher) |article=Peirce, Charles Sanders |access-date=2007-12-12  |archive-date=2013-11-03  |archive-url=https://web.archive.org/web/20131103161340/http://www.cspeirce.com/menu/library/aboutcsp/weissbio.htm |url-status=dead }}</ref><ref>{{cite dictionary |date=1960 |title=Webster's Biographical Dictionary |dictionary=Merriam-Webster |place=Springfield, Massachusetts |orig-date=1943 |article=Peirce, Benjamin: Charles Sanders}}</ref> According to philosopher [[Paul Weiss (philosopher)|Paul Weiss]], Peirce was "the most original and versatile of America's philosophers and America's greatest logician".<ref>{{cite encyclopedia |title=Dictionary of American Biography |publisher=Internet Archive |url=https://archive.org/details/dictionaryofamer019328mbp/page/403/mode/1up?q=peirce&view=theater |date=1934 |author-link=Paul Weiss (philosopher) |author-last=Weiss |author-first=Paul |article=Peirce, Charles Sanders}}</ref> [[Bertrand Russell]] wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever". 

Educated as a chemist and employed as a scientist for thirty years, Peirce meanwhile made major contributions to logic, such as theories of [[Algebraic logic|relations]] and [[Quantifier (logic)|quantification]]. [[Clarence Irving Lewis|C. I. Lewis]] wrote, "The contributions of C. S. Peirce to symbolic logic are more numerous and varied than those of any other writer—at least in the nineteenth century." For Peirce, logic also encompassed much of what is now called [[epistemology]] and the [[philosophy of science]]. He saw logic as the formal branch of [[semiotics]] or study of [[Sign (semiotics)|signs]], of which he is a founder, which foreshadowed the debate among [[logical positivists]] and proponents of [[philosophy of language]] that dominated 20th-century Western philosophy. Peirce's study of signs also included a [[Categories (Peirce)|tripartite theory of predication]].  

Additionally, he defined the concept of [[abductive reasoning]], as well as rigorously formulating [[mathematical induction]] and [[deductive reasoning]]. He was one of the [[founders of statistics]]. As early as 1886, he saw that [[logic gate|logical operations could be carried out by electrical switching circuits]]. The same idea was used decades later to produce digital computers.<ref name="P2M">{{cite book |author-last=Peirce |author-first=Charles Sanders |url=https://archive.org/details/writingsofcharle0002peir/page/5 |title=Writings of Charles S. Peirce |date=1886 |isbn=978-0-25337201-7 |pages=5:541–543 |chapter=Letter, Peirce to A. Marquand |publisher=Indiana University Press |chapter-url=https://books.google.com/books?id=DnvLHp919_wC&q=Marquand |url-access=registration}} See {{cite journal |author-last=Burks |author-first=Arthur W. |author-link=Arthur W. Burks |date=1978 |title=Charles S. Peirce, ''The new elements of mathematics'' |url=https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-84/issue-5/Review-Charles-S-Peirce-The-new-elements-of-mathematics/bams/1183541145.full |format=PDF |department=Book Review |journal=Bulletin of the American Mathematical Society |series=Eprint |volume=84 |issue=5 |pages=913–918 |doi=10.1090/S0002-9904-1978-14533-9 |doi-access=free}} Also {{cite book |author-last=Houser |author-first=Nathan |title=Writings of Charles S. Peirce |volume=5 |page=xliv |chapter=Introduction}}</ref>

In [[metaphysics]], Peirce was an "[[Objective idealism|objective idealist]]" in the tradition of German philosopher [[Immanuel Kant]] as well as a [[Scotistic realism|scholastic realist]] about universals. He also held a commitment to the ideas of continuity and chance as real features of the universe, views he labeled [[synechism]] and [[tychism]] respectively. Peirce believed an epistemic [[fallibilism]] and anti-[[skepticism]] went along with these views. 

==Biography==

=== Early life ===
[[File:Charles Sanders Peirce's birthplace building.jpg|thumb|left|upright=1.25|Peirce's birthplace. Now part of [[Lesley University]]'s Graduate School of Arts and Social Sciences.]]
Peirce was born at 3 Phillips Place in [[Cambridge, Massachusetts]]. He was the son of Sarah Hunt Mills and [[Benjamin Peirce]], himself a professor of mathematics and [[astronomy]]  at [[Harvard University]].{{efn|Benjamin was one of the founders of [[linear algebra]].}} At age&nbsp;12, Charles read his older brother's copy of [[Richard Whately]]'s ''Elements of Logic'', then the leading English-language text on the subject. So began his lifelong fascination with logic and reasoning.<ref>Fisch, Max, "[http://www.iupui.edu/~peirce/writings/v1/v1intro.htm Introduction] {{Webarchive|url=https://web.archive.org/web/20181022143324/http://www.iupui.edu/~peirce/writings/v1/v1intro.htm |date=2018-10-22  }}", ''Writings of Charles S. Peirce'', 1:xvii, find phrase "One episode".</ref> 

He suffered from his late teens onward from a nervous condition then known as "facial neuralgia", which would today be diagnosed as [[trigeminal neuralgia]]. His biographer, Joseph Brent, says that when in the throes of its pain "he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper".<ref>{{Harvnb|Brent|1998|p=40}}</ref> Its consequences may have led to the social isolation of his later life.

=== Education ===
Peirce went on to earn a Bachelor of Arts degree and a Master of Arts degree (1862) from Harvard. In 1863 the [[Lawrence Scientific School]] awarded him a Bachelor of Science degree, Harvard's first ''summa cum laude'' [[chemistry]] degree.<ref>"Peirce, Charles Sanders" (1898), ''The National Cyclopedia of American Biography'', v. 8, [https://books.google.com/books?id=1uI-AAAAYAAJ&pg=PA409&dq=%22Peirce%2C%20Charles%22 p. 409].</ref> His academic record was otherwise undistinguished.<ref>{{Harvnb|Brent|1998|pp=54–56}}</ref> At Harvard, he began lifelong friendships with [[Francis Ellingwood Abbot]], [[Chauncey Wright]], and [[William James]].<ref>{{cite book |author-last=Brent |author-first=Josep |date=1998 |title=Charles Sanders Peirce: A Life |edition=2nd |location=Bloomington |publisher=Indiana University Press |pages=363–364 |isbn=978-0-25321161-3}}<!-- |access-date=24 September 2012 --></ref> One of his Harvard instructors, [[Charles William Eliot]], formed an unfavorable opinion of Peirce. This proved fateful, because Eliot, while President of Harvard (1869–1909—a period encompassing nearly all of Peirce's working life), repeatedly vetoed Peirce's employment at the university.<ref>{{Harvnb|Brent|1998|pp=19–20, 53, 75, 245}}</ref>

=== United States Coast Survey ===
[[File:Charles Sanders Peirce in 1859.jpg|thumb|left|160px|Peirce in 1859]]
Between 1859 and 1891, Peirce was intermittently employed in various scientific capacities by the United States Coast Survey, which in 1878 was renamed the [[United States Coast and Geodetic Survey]],<ref name="Burch">Burch, Robert (2001, 2010), "[http://plato.stanford.edu/entries/peirce/ Charles Sanders Peirce]", ''Stanford Encyclopedia of Philosophy''</ref> where he enjoyed his highly influential father's protection until the latter's death in 1880.<ref>{{Harvnb|Brent|1998|p=139}}</ref> At the Survey, he worked mainly in [[geodesy]] and [[gravimetry]], refining the use of [[pendulum]]s to determine small local variations in the Earth's [[gravity]].<ref name="Burch" />

==== American Civil War ====
This employment exempted Peirce from having to take part in the [[American Civil War]]; it would have been very awkward for him to do so, as the [[Boston Brahmin]] Peirces sympathized with the [[Confederate States of America|Confederacy]].<ref>{{Harvnb|Brent|1998|pp=61–62}}</ref> No members of the Peirce family volunteered or enlisted.  Peirce grew up in a home where white supremacy was taken for granted, and slavery was considered natural.<ref>{{Harvnb|Brent|1998|p=34}}</ref> Peirce's father had described himself as a [[Secession in the United States|secessionist]] until the outbreak of the war, after which he became a [[Union (American Civil War)|Union]] partisan, providing donations to the [[United States Sanitary Commission|Sanitary Commission]], the leading Northern war charity. 

Peirce liked to use the following [[syllogism]] to illustrate the unreliability of [[Term logic|traditional]] forms of logic (for the first premise arguably [[Begging the question|assumes the conclusion]]):<ref name="Menand1">{{cite book |author-last=Menand |author-first=Louis |title=The Metaphysical Club |date=2001 |publisher=Flamingo |isbn=978-0-00712690-3 |location=London|pages=161–162}}</ref><poem>
All Men are equal in their political rights.
Negroes are Men.
Therefore, negroes are equal in political rights to whites.</poem>

==== Travels to Europe ====
He was elected a resident fellow of the [[American Academy of Arts and Sciences]] in January 1867.<ref>{{Harvnb|Brent|1998|p=69}}</ref> The Survey sent him to Europe five times,<ref>{{Harvnb|Brent|1998|p=368}}</ref> first in 1871 as part of a group sent to observe a [[solar eclipse]]. There, he sought out [[Augustus De Morgan]], [[William Stanley Jevons]], and [[William Kingdon Clifford]],<ref>{{Harvnb|Brent|1998|pp=79–81}}</ref> British mathematicians and logicians whose turn of mind resembled his own. 

==== Harvard observatory ====
From 1869 to 1872, he was employed as an assistant in Harvard's astronomical observatory, doing important work on determining the brightness of [[star]]s and the shape of the [[Milky Way]].<ref name="SP2">Moore, Edward C., and Robin, Richard S., eds., (1964), ''Studies in the Philosophy of Charles Sanders Peirce, Second Series'', Amherst: U. of Massachusetts Press. On Peirce the astronomer, see Lenzen's chapter.</ref> In 1872 he founded the [[The Metaphysical Club|Metaphysical Club]], a conversational philosophical club that Peirce, the future [[Supreme Court Justice]] [[Oliver Wendell Holmes Jr.]], the philosopher and  psychologist [[William James]], amongst others, formed in January 1872 in [[Cambridge, Massachusetts]], and dissolved in December 1872. Other members of the club included [[Chauncey Wright]], [[John Fiske (philosopher)|John Fiske]], [[Francis Ellingwood Abbot]], [[Nicholas St. John Green]], and [[Joseph Bangs Warner]].<ref>Menand (2001), p. 201.</ref>  The discussions eventually birthed Peirce's notion of pragmatism.

==== National Academy of Sciences ====
[[File:Peirce Quincuncial Projection 1879.jpg|thumb|upright=1.35|"The World on a [[Peirce quincuncial projection|Quincuncial Projection]]", 1879.<ref>{{cite journal |author-last=Peirce |author-first=Charles Sanders |date=1879 |title=A Quincuncial Projection of the Sphere |journal=American Journal of Mathematics |volume=2 |issue=4 |pages=394–397 |doi=10.2307/2369491 |jstor=2369491 |url=https://archive.org/details/sim_american-journal-of-mathematics_1879_2/page/n403/mode/2up}}</ref> Peirce's projection of a sphere onto a square [[conformal map|keeps angles true]] except at four isolated points on the equator, and has less scale variation than the [[Mercator projection]]. It can be [[Tessellation|tessellated]]; that is, multiple copies can be joined continuously edge-to-edge.]]
On April 20, 1877, he was elected a member of the [[National Academy of Sciences]].<ref>{{Harvnb|Brent|1998|p=367}}</ref> Also in 1877, he proposed measuring the meter as so many [[wavelength]]s of light of a certain [[frequency]],<ref>Fisch, Max (1983), "Peirce as Scientist, mathematician, historian, Logician, and Philosopher", ''[[#SIL|Studies in Logic]]'' (new edition), see p. x.</ref> the kind of definition employed [[Metre#Wavelength definition|from 1960 to 1983]].

In 1879 Peirce developed [[Peirce quincuncial projection]], having been inspired by [[Hermann Schwarz|H. A. Schwarz]]'s 1869 [[Schwarz–Christoffel mapping|conformal transformation of a circle onto a polygon of ''n'' sides]] (known as the Schwarz–Christoffel mapping). 

==== 1880 to 1891 ====
During the 1880s, Peirce's indifference to bureaucratic detail waxed while his Survey work's quality and timeliness waned. Peirce took years to write reports that he should have completed in months.{{according to whom|date=March 2013}} Meanwhile, he wrote entries, ultimately thousands, during 1883–1909 on philosophy, logic, science, and other subjects for the encyclopedic ''[[Century Dictionary]]''.<ref>See "[http://www.pep.uqam.ca/short.pep Peirce Edition Project (UQÀM) – in short] {{webarchive|url=https://web.archive.org/web/20110706211228/http://www.pep.uqam.ca/short.pep|date=6 July 2011}}" from [[#PEP|PEP-UQÀM]].</ref> In 1885, an investigation by the [[William B. Allison|Allison]] Commission exonerated Peirce, but led to the dismissal of Superintendent [[Julius Hilgard]] and several other Coast Survey employees for misuse of public funds.<ref>Houser, Nathan, "[http://www.iupui.edu/~peirce/writings/v5/v5intro.htm Introduction] {{Webarchive|url=https://web.archive.org/web/20110607101202/http://www.iupui.edu/~peirce/writings/v5/v5intro.htm |date=2011-06-07  }}", ''Writings of Charles S. Peirce'', 5:xxviii–xxix, find "Allison".</ref> In 1891, Peirce resigned from the Coast Survey at Superintendent [[Thomas Corwin Mendenhall]]'s request.<ref>{{Harvnb|Brent|1998|p=202}}</ref>

=== Johns Hopkins University ===
In 1879, Peirce was appointed lecturer in logic at [[Johns Hopkins University]], which had strong departments in areas that interested him, such as philosophy ([[Josiah Royce|Royce]] and [[John Dewey|Dewey]] completed 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.&nbsp;J. Sylvester]], who came to admire Peirce's work on mathematics and logic). His ''[[Charles Sanders Peirce bibliography#SIL|Studies in Logic by Members of the Johns Hopkins University]]'' (1883) contained works by himself and [[Allan Marquand]], [[Christine Ladd-Franklin|Christine Ladd]], [[Benjamin Ives Gilman]], and Oscar Howard Mitchell,<ref name="dipert">Randall R. Dipert [https://www.jstor.org/stable/40320486?seq=1 (1994) The Life and Logical Contributions of O. H. Mitchell, Peirce's Gifted Student]</ref> several of whom were his graduate students.<ref name="grads">Houser, Nathan (1989), "[http://www.iupui.edu/~peirce/writings/v4/v4intro.htm Introduction] {{Webarchive|url=https://web.archive.org/web/20100530064901/http://www.iupui.edu/~peirce/writings/v4/v4intro.htm |date=2010-05-30  }}",  ''Writings of Charles S. Peirce'', 4:xxxviii, find "Eighty-nine".</ref> Peirce's nontenured position at Hopkins was the only academic appointment he ever held.

Brent documents something Peirce never suspected, namely that his efforts to obtain academic employment, grants, and scientific respectability were repeatedly frustrated by the covert opposition of a major Canadian-American scientist of the day, [[Simon Newcomb]].<ref>{{Harvnb|Brent|1998|pp=150–154, 195, 279–280, 289}}</ref> Newcomb had been a favourite student of Peirce's father; although "no doubt quite bright", "like [[Antonio Salieri|Salieri]] in [[Amadeus (play)|Peter Shaffer's Amadeus]] he also had just enough talent to recognize he was not a genius and just enough pettiness to resent someone who was". Additionally "an intensely devout and literal-minded Christian of rigid moral standards", he was appalled by what he considered Peirce's personal shortcomings.<ref>{{cite web | url=https://www.firstthings.com/article/1993/12/003-discovering-the-american-aristotle | title=Discovering the American Aristotle &#124; Edward T. Oakes | date=December 1993 }}</ref> Peirce's efforts may also have been hampered by what Brent characterizes as "his difficult personality".<ref>{{Harvnb|Brent|1998|p=xv}}</ref> In contrast, [[Keith Devlin]] believes that Peirce's work was too far ahead of his time to be appreciated by the academic establishment of the day and that this played a large role in his inability to obtain a tenured position.<ref name="devlin_2000">{{cite book |author-link=Keith Devlin |author-first=Keith |author-last=Devlin |date=2000 |title=The Math Gene |url=https://archive.org/details/mathgene00keit |url-access=registration |publisher=Basic Books |isbn=978-0-46501619-8}}</ref>

=== Personal life ===
[[File:JulietteAndCharles.JPG|thumb|upright=1.25|Juliette and Charles by a well at their home Arisbe in 1907]]
Peirce's personal life undoubtedly worked against his professional success. After his first wife, [[Melusina Fay Peirce|Harriet Melusina Fay]] ("Zina"), left him in 1875,<ref>{{Harvnb|Brent|1998|pp=98–101}}</ref> Peirce, while still legally married, became involved with [[Juliette Peirce|Juliette]], whose last name, given variously as Froissy and Pourtalai,<ref>{{Harvnb|Brent|1998|p=141}}</ref> and nationality (she spoke French)<ref>{{Harvnb|Brent|1998|p=148}}</ref> remains uncertain.<ref>Houser, Nathan, "[http://www.iupui.edu/~peirce/writings/v6/v6intro.htm Introduction] {{Webarchive|url=https://web.archive.org/web/20110607100406/http://www.iupui.edu/~peirce/writings/v6/v6intro.htm |date=2011-06-07  }}", ''Writings of Charles S. Peirce'', 6, first paragraph.</ref> When his divorce from Zina became final in 1883, he married Juliette.<ref>{{Harvnb|Brent|1998|pp=123, 368}}</ref> That year, Newcomb pointed out to a Johns Hopkins trustee that Peirce, while a Hopkins employee, had lived and traveled with a woman to whom he was not married; the ensuing scandal led to his dismissal in January 1884.<ref>{{Harvnb|Brent|1998|pp=150–151, 368}}</ref> Over the years Peirce sought academic employment at various universities without success.<ref>In 1885 ({{Harvnb|Brent|1998|p=369}}); in 1890 and 1900 (p. 273); in 1891 (pp. 215–216); and in 1892 (pp. 151–152, 222).</ref> He had no children by either marriage.<ref>{{Harvnb|Brent|1998|p=77}}</ref>

=== Later life and poverty ===
[[File:Charles S. Peirce house PA1.jpg|thumb|left|Arisbe in 2011]]
[[File:Gravestone Charles Sanders Peirce and Juliette Peirce.jpg|thumb|Charles and Juliette Peirce's grave]]

In 1887, Peirce spent part of his inheritance from his parents to buy {{convert|2000|acre|km2|0}} of rural land near [[Milford, Pennsylvania]], which never yielded an economic return.<ref>{{Harvnb|Brent|1998|pp=191–192, 217, 270, 318, 321, 337.}}</ref> There he had an 1854 farmhouse remodeled to his design.<ref>{{Harvnb|Brent|1998|p=13}}</ref> The Peirces named the property "[[Juliette Peirce#Arisbe|Arisbe]]". There they lived with few interruptions for the rest of their lives,<ref>{{Harvnb|Brent|1998|pp=369–374}}</ref> Charles writing prolifically, with much of his work remaining unpublished to this day (see [[#Works|Works]]). Living beyond their means soon led to grave financial and legal difficulties.<ref>{{Harvnb|Brent|1998|p=191}}</ref> Charles spent much of his last two decades unable to afford heat in winter and subsisting on old bread donated by the local baker. Unable to afford new stationery, he wrote on the [[verso]] side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while.<ref>{{Harvnb|Brent|1998|p=246}}</ref> Several people, including his brother [[James Mills Peirce]]<ref>{{Harvnb|Brent|1998|p=242}}</ref> and his neighbors, relatives of [[Gifford Pinchot]], settled his debts and paid his property taxes and mortgage.<ref>{{Harvnb|Brent|1998|p=271}}</ref>

Peirce did some scientific and engineering consulting and wrote much for meager pay, mainly encyclopedic dictionary entries, and reviews for ''[[The Nation (U.S. periodical)|The Nation]]'' (with whose editor, [[Wendell Phillips Garrison]], he became friendly). He did translations for the [[Smithsonian Institution]], at its director [[Samuel Langley]]'s instigation. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried inventing.<ref>{{Harvnb|Brent|1998|pp=249–255}}</ref> He began but did not complete several books.<ref>{{Harvnb|Brent|1998|p=371}}</ref> In 1888, President [[Grover Cleveland]] appointed him to the [[Assay Commission]].<ref>{{Harvnb|Brent|1998|p=189}}</ref>

From 1890 on, he had a friend and admirer in Judge Francis C. Russell of Chicago,<ref>{{Harvnb|Brent|1998|p=370}}</ref> who introduced Peirce to editor [[Paul Carus]] and owner [[Edward C. Hegeler]] of the pioneering American philosophy journal ''[[The Monist]]'', which eventually published at least 14 articles by Peirce.<ref>{{Harvnb|Brent|1998|pp=205–206}}</ref> He wrote many texts in [[James Mark Baldwin]]'s ''[[Charles Sanders Peirce bibliography#Peirce's definitions in the Baldwin|Dictionary of Philosophy and Psychology]]'' (1901–1905); half of those credited to him appear to have been written actually by [[Christine Ladd-Franklin]] under his supervision.<ref>{{Harvnb|Brent|1998|pp=374–376}}</ref> He applied in 1902 to the newly formed [[Carnegie Institution]] for a grant to write a systematic book describing his life's work. The application was doomed; his nemesis, Newcomb, served on the Carnegie Institution executive committee, and its president had been president of Johns Hopkins at the time of Peirce's dismissal.<ref>{{Harvnb|Brent|1998|pp=279–289}}</ref>

The one who did the most to help Peirce in these desperate times was his old friend [[William James]], dedicating his ''Will to Believe'' (1897) to Peirce, and arranging for Peirce to be paid to give two series of lectures at or near Harvard (1898 and 1903).<ref>{{Harvnb|Brent|1998|pp=261–264, 290–292, 324}}</ref> Most important, each year from 1907 until James's death in 1910, James wrote to his friends in the Boston intelligentsia to request financial aid for Peirce; the fund continued even after James died. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him.<ref>{{Harvnb|Brent|1998|pp=306–307, 315–316}}</ref> It has been believed that this was also why Peirce used "Santiago" ("St. James" in English) as a middle name, but he appeared in print as early as 1890 as Charles Santiago Peirce. (See [[Charles Santiago Sanders Peirce]] for discussion and references).

==Death and legacy==
Peirce died destitute in [[Milford, Pennsylvania]], twenty years before his widow. Juliette Peirce kept the urn with Peirce's ashes at Arisbe. In 1934, Pennsylvania Governor [[Gifford Pinchot]] arranged for Juliette's burial in Milford Cemetery. The urn with Peirce's ashes was interred with Juliette.{{efn|In 2018, plans have been made to erect a memorial monument for Peirce at the site of burial – see: Justin Weinberg, [http://dailynous.com/2018/03/14/proper-memorial-monument-peirce/ 'A Proper Memorial Monument for Peirce'], website ''[[Daily Nous]]'', March 14, 2018.}}

[[Bertrand Russell]] (1959) wrote "Beyond doubt [...] he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever".<ref>Russell, Bertrand (1959), ''Wisdom of the West'', p. 276</ref> Russell and [[Alfred North Whitehead|Whitehead]]'s ''[[Principia Mathematica]]'', published from 1910 to 1913, does not mention Peirce (Peirce's work was not widely known until later).<ref name="Anellis">Anellis, Irving 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. ''Arisbe'' [http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp&br.htm Eprint] {{Webarchive|url=https://web.archive.org/web/20130924110921/http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp%26br.htm |date=2013-09-24  }}</ref> [[A. N. Whitehead]], while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and [[process metaphysics]], see Lowe 1964.<ref name="SP2" />) [[Karl Popper]] viewed Peirce as "one of the greatest philosophers of all times".<ref>Popper, Karl (1972), ''Objective Knowledge: An Evolutionary Approach'', p. 212</ref> Yet Peirce's achievements were not immediately recognized. His imposing contemporaries [[William James]] and [[Josiah Royce]]<ref>See Royce, Josiah, and Kernan, W. Fergus (1916), "Charles Sanders Peirce", ''The Journal of Philosophy, Psychology, and Scientific Method'' v. 13, pp. 701–709. ''Arisbe'' [http://www.cspeirce.com/menu/library/aboutcsp/royce/cspobit.htm Eprint]</ref> admired him and [[Cassius Jackson Keyser]], at Columbia and [[C. K. Ogden]], wrote about Peirce with respect but to no immediate effect.

The first scholar to give Peirce his considered professional attention was Royce's student [[Morris Raphael Cohen]], the editor of an anthology of Peirce's writings entitled ''[[Charles Sanders Peirce bibliography#CLL|Chance, Love, and Logic]]'' (1923), and the author of the first bibliography of Peirce's scattered writings.<ref>Ketner ''et al.'' (1986), ''[[Charles Sanders Peirce bibliography#cb|Comprehensive Bibliography]]'', p. iii</ref> [[John Dewey]] studied under Peirce at Johns Hopkins.<ref name="grads"/> From 1916 onward, Dewey's writings repeatedly mention Peirce with deference. His 1938 ''Logic: The Theory of Inquiry'' is much influenced by Peirce.<ref>[[Hookway, Christopher]] (2008), "[http://plato.stanford.edu/entries/pragmatism/ Pragmatism]", ''Stanford Encyclopedia of Philosophy''.</ref> The publication of the first six volumes of ''Collected Papers'' (1931–1935) was the most important event to date in Peirce studies and one that Cohen made possible by raising the needed funds;<ref>{{Harvnb|Brent|1998|p=8}}</ref> however it did not prompt an outpouring of secondary studies. The editors of those volumes, [[Charles Hartshorne]] and [[Paul Weiss (philosopher)|Paul Weiss]], did not become Peirce specialists. Early landmarks of the secondary literature include the monographs by Buchler (1939), [[James Feibleman|Feibleman]] (1946), and [[T. A. Goudge|Goudge]] (1950), the 1941 PhD thesis by [[Arthur W. Burks]] (who went on to edit volumes 7 and 8), and the studies edited by Wiener and Young (1952). The [[Charles S. Peirce Society]] was founded in 1946. Its ''Transactions'', an academic quarterly specializing in Peirce's pragmatism and American philosophy has appeared since 1965.<ref>{{cite web |url=http://www.iupress.indiana.edu/pages.php?pID=94&CDpath=4 |title=Transactions of the Charles S. Peirce Society |language=en |website=Indiana University Press Journals |access-date=June 17, 2017 |archive-url=https://web.archive.org/web/20151204172633/http://www.iupress.indiana.edu/pages.php?pID=94&CDpath=4 |archive-date=December 4, 2015 |url-status=dead}}</ref> (See Phillips 2014, 62 for discussion of Peirce and Dewey relative to [[transactionalism]].)

By 1943 such was Peirce's reputation, in the US at least, that ''Webster's Biographical Dictionary'' said that Peirce was "now regarded as the most original thinker and greatest logician of his time".<ref>{{cite dictionary |title=Peirce, Benjamin: Charles Sanders |dictionary=Webster's Biographical Dictionary |orig-date=1943 |date=1960 |place=Springfield, Massachusetts}}</ref>

In 1949, while doing unrelated archival work, the historian of mathematics [[Carolyn Eisele]] (1902–2000) chanced on an autograph letter by Peirce. So began her forty years of research on Peirce, “the mathematician and scientist,” culminating in Eisele (1976, 1979, 1985). In 1952, the [[Scotland|Scottish]] philosopher [[W. B. Gallie]] had his book ''Peirce and pragmatism''<ref>{{cite book |last1=Gallie |first1=W.B. |title=Peirce and pragmatism |date=1952 |publisher=Penguin Books |location=Harmondsworth, Middlesex |url=https://archive.org/details/piercepragmatism/mode/2up |access-date=27 February 2025}}</ref> published, which introduced the work of Peirce to an international readership. [[A.J. Ayer]], the English philosopher, provided the Editorial Foreword to Gallie's book. In it he credited Peirce's philosophy as being 'not only of great historical significance, as one of the original sources of American pragmatism, but also extremely important in itself.' Ayer concluded: 'it is clear from Professor Gallie’s exposition of his doctrines that he is a philosopher from whom we still have much to learn.'<ref>{{cite book |last1=Gallie |first1=W.B. |title=Peirce and pragmatism |date=1952 |publisher=Penguin Books |location=Harmondsworth, Middlesex |url=https://archive.org/details/piercepragmatism/page/n1/mode/2up |access-date=26 February 2025 }}</ref>

Beginning around 1960, Max Fisch (1900-1995),<ref>{{cite journal |last1=Marshall |first1=David L. |title=Historical and Philosophical Stances: Max Harold Fisch, A Paradigm for Intellectual Historians |journal=European Journal of Pragmatism and American Philosophy |date=2016 |volume=8 |issue=VIII-2 |page=248-274 |url=https://journals.openedition.org/ejpap/647 |access-date=27 February 2025 |issn=2036-4091}}</ref> the philosopher and [[history of ideas|historian of ideas]], emerged as an authority on Peirce (Fisch, 1986).<ref name="Fisch">Fisch, Max (1986), ''Peirce, Semeiotic, and Pragmatism'', Kenneth Laine Ketner and Christian J. W. Kloesel, eds., Bloomington, Indiana: Indiana U. Press</ref> He included many of his relevant articles in a survey (Fisch 1986: 422–448) of the impact of Peirce's thought through 1983.

Peirce has gained an international following, marked by university research centers devoted to Peirce studies and [[pragmatism]] in Brazil ([[#CIEP|CeneP/CIEP]] and [[#CEP|Centro de Estudos de Pragmatismo]]), Finland ([[#HPRC|HPRC]] and [[#CDPT|{{Not a typo|Commens}}]]), Germany ([[#IRGAI|Wirth's group]], [[#RGSEME|Hoffman's and Otte's group]], and Deuser's and Härle's group<ref>Theological Research Group in C.S. Peirce's Philosophy (Hermann Deuser, Justus-Liebig-Universität Gießen; Wilfred Härle, Philipps-Universität Marburg, Germany).</ref>), France ([[#LIRSCE|L'I.R.S.C.E.]]), Spain ([[#GEP|GEP]]), and Italy ([[#CSPI|CSP]]). His writings have been translated into several languages, including German, French, Finnish, Spanish, and Swedish. Since 1950, there have been French, Italian, Spanish, British, and Brazilian Peirce scholars of note. For many years, the North American philosophy department most devoted to Peirce was the [[University of Toronto]], thanks in part to the leadership of [[T. A. Goudge|Thomas Goudge]] and David Savan. In recent years, U.S. Peirce scholars have clustered at [[IUPUI|Indiana University – Purdue University Indianapolis]], home of the [[#PEP|Peirce Edition Project]] (PEP) –, and [[Pennsylvania State University]].

{{Blockquote|Currently, considerable interest is being taken in Peirce's ideas by researchers wholly outside the arena of academic philosophy. The interest comes from industry, business, technology, intelligence organizations, and the military; and it has resulted in the existence of a substantial number of agencies, institutes, businesses, and laboratories in which ongoing research into and development of Peircean concepts are being vigorously undertaken.|Robert Burch, 2001, updated 2010<ref name="Burch"/>}}

In recent years, Peirce's [[wikt:trichotomy|trichotomy]] of signs is exploited by a growing number of practitioners for marketing and design tasks.

[[John Deely]] writes that Peirce was the last of the "moderns" and "first of the postmoderns". He lauds Peirce's doctrine of signs as a contribution to the dawn of the [[Postmodern]] epoch. Deely additionally comments that "Peirce stands...in a position analogous to the position occupied by [[Augustine of Hippo|Augustine]] as last of the Western [[Church Fathers|Fathers]] and first of the medievals".<ref>''Postmodernism and Christian Philosophy''. [https://www3.nd.edu/~maritain/ama/Ciapalo/Ciapalo05.pdf ''Quid Sit Postmodernismus?''], p. 93, [https://web.archive.org/web/20211216161244/https://www3.nd.edu/~maritain/ama/Ciapalo/Ciapalo05.pdf ''archived''.]</ref>

==Works==
{{see also|Charles Sanders Peirce bibliography}}
Peirce's reputation rests largely on academic papers published in American scientific and scholarly journals such as ''Proceedings of the [[American Academy of Arts and Sciences]]'', the ''Journal of Speculative Philosophy'', ''[[The Monist]]'', ''[[Popular Science]] Monthly'', the ''[[American Journal of Mathematics]]'', ''Memoirs of the [[United States National Academy of Sciences|National Academy of Sciences]]'', ''[[The Nation (U.S. periodical)|The Nation]]'', and others. See [[Charles Sanders Peirce bibliography#Articles by Peirce, published in his lifetime|Articles by Peirce, published in his lifetime]] for an extensive list with links to them online. The only full-length book (neither extract nor pamphlet) that Peirce authored and saw published in his lifetime<ref>[[Arthur Burks|Burks, Arthur]], Introduction, ''Collected Papers of Charles Sanders Peirce'', 7, p. xi.</ref> was ''[[Charles Sanders Peirce bibliography#PR|Photometric Researches]]'' (1878), a 181-page monograph on the applications of spectrographic methods to astronomy. While at Johns Hopkins, he edited ''[[#SIL|Studies in Logic]]'' (1883), containing chapters by himself and his [[#GS|graduate students]]. Besides lectures during his years (1879–1884) as lecturer in Logic at Johns Hopkins, he gave at least nine series of lectures, many now published; see [[Charles Sanders Peirce bibliography#Lectures by Peirce|Lectures by Peirce]].

After Peirce's death, [[Harvard University]] obtained from Peirce's widow the papers found in his study, but did not microfilm them until 1964. Only after Richard Robin (1967)<ref>Robin, Richard S. (1967), ''[http://www.iupui.edu/~peirce/robin/robin.htm Annotated Catalogue of the Papers of Charles S. Peirce] {{Webarchive|url=https://web.archive.org/web/20191027010841/http://www.iupui.edu/~peirce/robin/robin.htm |date=2019-10-27  }}''. Amherst MA: [[University of Massachusetts Press]].</ref> catalogued this ''[[Nachlass]]'' did it become clear that Peirce had left approximately 1,650 unpublished manuscripts, totaling over 100,000&nbsp;pages,<ref>"The manuscript material now (1997) comes to more than a hundred thousand pages. These contain many pages of no philosophical interest, but the number of pages on philosophy certainly number much more than half of that. Also, a significant but unknown number of manuscripts have been lost." – Joseph Ransdell (1997), "Some Leading Ideas of Peirce's Semiotic", [http://www.cspeirce.com/menu/library/aboutcsp/ransdell/leading.htm#note2 end note 2] {{Webarchive|url=https://web.archive.org/web/20080114022817/http://www.cspeirce.com/menu/library/aboutcsp/ransdell/leading.htm#note2 |date=2008-01-14  }}, 1997 light revision of 1977 version in ''Semiotica'' 19:157–178.</ref> mostly still unpublished except [[Charles Sanders Peirce bibliography#mf|on microfilm]]. On the vicissitudes of Peirce's papers, see Houser (1989).<ref>Houser, Nathan, "The Fortunes and Misfortunes of the Peirce Papers", Fourth Congress of the [[IASS]], Perpignan, France, 1989. ''Signs of Humanity'', v. 3, 1992, pp. 1259–1268. [http://www.cspeirce.com/menu/library/aboutcsp/houser/fortunes.htm Eprint]</ref> Reportedly the papers remain in unsatisfactory condition.<ref>Memorandum to the President of Charles S. Peirce Society by Ahti-Veikko Pietarinen, U. of Helsinki, March 29, 2012. [http://www.helsinki.fi/~pietarin/Memorandum-Peirce%20Society-Pietarinen-2012.pdf Eprint].</ref>

The first published anthology of Peirce's articles was the one-volume ''[[Charles Sanders Peirce bibliography#CLL|Chance, Love and Logic: Philosophical Essays]]'', edited by [[Morris Raphael Cohen]], 1923, still in print. [[Charles Sanders Peirce bibliography#Other collections|Other one-volume anthologies]] were published in 1940, 1957, 1958, 1972, 1994, and 2009, most still in print. The main posthumous editions<ref>See for example "[http://www.helsinki.fi/science/commens/collections.html Collections of Peirce's Writings]" at ''Commens'', U. of Helsinki.</ref> of Peirce's works in their long trek to light, often multi-volume, and some still in print, have included:

1931–1958: ''[[Charles Sanders Peirce bibliography#CP|Collected Papers of Charles Sanders Peirce]]'' (CP), 8 volumes, includes many published works, along with a selection of previously unpublished work and a smattering of his correspondence. This long-time standard edition drawn from Peirce's work from the 1860s to 1913 remains the most comprehensive survey of his prolific output from 1893 to 1913. It is organized thematically, but texts (including lecture series) are often split up across volumes, while texts from various stages in Peirce's development are often combined, requiring frequent visits to editors' notes.<ref>See 1987 review by B. Kuklick (of ''Peirce'' by [[Christopher Hookway]]), in ''British Journal for the Philosophy of Science''v. 38, n. 1, pp. 117–119. [https://archive.today/20120708211504/http://bjps.oxfordjournals.org/cgi/pdf_extract/38/1/117 First page].</ref> Edited (1–6) by [[Charles Hartshorne]] and [[Paul Weiss (philosopher)|Paul Weiss]] and (7–8) by [[Arthur Burks]], in print and online.

1975–1987: [[Charles Sanders Peirce bibliography#CN|''Charles Sanders Peirce: Contributions to'' The Nation]], 4 volumes, includes Peirce's more than 300 reviews and articles published 1869–1908 in ''[[The Nation]]''. Edited by Kenneth Laine Ketner and James Edward Cook, online.

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

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

1982–now: ''[[Charles Sanders Peirce bibliography#W|Writings of Charles S. Peirce, A Chronological Edition]]'' (W), Volumes 1–6 & 8, of a projected 30. The limited coverage, and defective editing and organization, of the ''Collected Papers'' led Max Fisch and others in the 1970s to found the [http://peirce.iupui.edu/ Peirce Edition Project] (PEP), whose mission is to prepare a more complete critical chronological edition. Only seven volumes have appeared to date, but they cover the period from 1859 to 1892, when Peirce carried out much of his best-known work. ''Writings of Charles S. Peirce'', 8 was published in November 2010; and work continues on ''Writings of Charles S. Peirce'', 7, 9, and 11. In print and online.

1985: ''[[Charles Sanders Peirce bibliography#HP|Historical Perspectives on Peirce's Logic of Science: A History of Science]]'', 2 volumes. Auspitz has said,<ref>Auspitz, Josiah Lee (1994), "The Wasp Leaves the Bottle: Charles Sanders Peirce", ''The American Scholar'', v. 63, n. 4, Autumn 1994, 602–618. ''Arisbe'' [http://www.cspeirce.com/menu/library/aboutcsp/auspitz/escape.htm Eprint] {{Webarchive|url=https://web.archive.org/web/20131103161015/http://www.cspeirce.com/menu/library/aboutcsp/auspitz/escape.htm |date=2013-11-03  }}.</ref> "The extent of Peirce's immersion in the science of his day is evident in his reviews in the ''Nation'' [...] and in his papers, grant applications, and publishers' prospectuses in the history and practice of science", referring latterly to ''Historical Perspectives''. Edited by Carolyn Eisele, back in print.

1992: ''[[Charles Sanders Peirce bibliography#RLT|Reasoning and the Logic of Things]]'' collects in one place Peirce's 1898 series of lectures invited by William James. Edited by Kenneth Laine Ketner, with commentary by [[Hilary Putnam]], in print.

1992–1998: ''[[Charles Sanders Peirce bibliography#EP|The Essential Peirce]]'' (EP), 2 volumes, is an important recent sampler of Peirce's philosophical writings. Edited (1) by Nathan Hauser and Christian Kloesel and (2) by ''Peirce Edition Project'' editors, in print.

1997: ''[[Charles Sanders Peirce bibliography#PPM|Pragmatism as a Principle and Method of Right Thinking]]'' collects Peirce's 1903 Harvard "Lectures on Pragmatism" in a study edition, including drafts, of Peirce's lecture manuscripts, which had been previously published in abridged form; the lectures now also appear in ''The Essential Peirce'', 2. Edited by Patricia Ann Turisi, in print.

2010: ''[[Charles Sanders Peirce bibliography#PMSW|Philosophy of Mathematics: Selected Writings]]'' collects important writings by Peirce on the subject, many not previously in print. Edited by Matthew E. Moore, in print.

==Mathematics==
Peirce's most important work in pure mathematics was in logical and foundational areas. He also worked on [[linear algebra]], [[Matrix (mathematics)|matrices]], various geometries, [[topology]] and [[Listing number]]s, [[Bell number]]s, [[Graph theory|graph]]s, the [[four-color problem]], and the nature of continuity.

He worked on applied mathematics in economics, engineering, and map projections, and was especially active in [[probability]] and statistics.<ref name="Burks">[[Arthur W. Burks|Burks, Arthur W.]], "Review: Charles S. Peirce, ''The new elements of mathematics''", ''Bulletin of the American Mathematical Society'' v. 84, n. 5 (1978), [https://projecteuclid.orgeuclid.bams/1183541145 pp. 913–918 (PDF)].</ref>

;Discoveries
<div style="float:right;width:8.5em;text-align:center;margin-right:20px;border:solid 1px #bbb"><div style="margin:2px;background-color:#dddddd;font-size:40pt;height:50pt;line-height:100%">↓</div> <div style="font-size:8pt;line-height:150%">The [[Logical NOR|Peirce arrow]], <br>symbol for "(neither) ... '''nor''' ...", also called the ''Quine dagger''</div></div>
Peirce made a number of striking discoveries in formal logic and foundational mathematics, nearly all of which came to be appreciated only long after he died:

In 1860,<ref>Peirce (1860 MS), "Orders of Infinity", [http://www.iupui.edu/~peirce/PEP_news_Sept2010.pdf ''News from the Peirce Edition Project'', September 2010] {{Webarchive|url=https://web.archive.org/web/20130329072747/http://www.iupui.edu/~peirce/PEP_news_Sept2010.pdf |date=2013-03-29  }} (PDF), p. 6, with the manuscript's text. Also see logic historian Irving Anellis's [http://thread.gmane.org/gmane.science.philosophy.peirce/6621/focus=6626 November 11, 2010 comment] {{Webarchive|url=https://web.archive.org/web/20170423131106/http://thread.gmane.org/gmane.science.philosophy.peirce/6621/focus=6626 |date=April 23, 2017 }} at peirce-l.</ref> he suggested a cardinal arithmetic for infinite numbers, years before any work by [[Georg Cantor]] (who completed [[Georg Cantor#Teacher and researcher|his dissertation in 1867]]) and without access to [[Bernard Bolzano]]'s 1851 (posthumous) ''Paradoxien des Unendlichen''.

In 1880–1881,<ref>Peirce (MS, winter of 1880–1881), "A Booli<!-- sic! -->an Algebra with One Constant", ''Collected Papers of Charles Sanders Peirce'', 4.12–20, ''Writings of Charles S. Peirce'', 4:218–221. Google [https://archive.org/details/writingsofcharle0002peir <!-- quote=378 Winter. --> Preview]. See Roberts, Don D. (1973), ''The Existential Graphs of Charles S. Peirce'', p. 131.</ref> he showed how [[Boolean algebra (logic)|Boolean algebra]] could be done via a [[Functional completeness|repeated sufficient single binary operation]] ([[logical NOR]]), anticipating [[Henry M. Sheffer]] by 33&nbsp;years. (See also [[De Morgan's Laws]].)

In 1881,<ref>Peirce (1881), "On the Logic of Number", ''American Journal of Mathematics'' v. 4, pp. [https://books.google.com/books?id=LQgPAAAAIAAJ&pg=PA85 85–95]. Reprinted (CP 3.252–288), (''Writings of Charles S. Peirce'', 4:299–309). See Shields, Paul (1997), "Peirce's Axiomatization of Arithmetic", in Houser ''et al.'', eds., ''Studies in the Logic of Charles S. Peirce''.</ref> he set out the [[Peano axioms|axiomatization of natural number arithmetic]], a few years before [[Richard Dedekind]] and [[Giuseppe Peano]]. In the same paper Peirce gave, years before Dedekind, the first purely cardinal definition of a finite set in the sense now known as "[[Dedekind-finite]]", and implied by the same stroke an important formal definition of an [[infinite set]] (Dedekind-infinite), as a [[Set (mathematics)|set]] that can be put into a [[one-to-one correspondence]] with one of its proper [[subsets]].

In 1885,<ref name="CSP1885">Peirce (1885), "On the Algebra of Logic: A Contribution to the Philosophy of Notation", ''American Journal of Mathematics'' 7, two parts, first part published 1885, pp. [https://books.google.com/books?id=lwYPAAAAIAAJ&&pg=PA180 180–202] (see Houser in [http://www.iupui.edu/~peirce/writings/v4/v4introx.htm#21note linked paragraph] {{Webarchive|url=https://web.archive.org/web/20160212172608/http://www.iupui.edu/~peirce/writings/v4/v4introx.htm#21note |date=2016-02-12  }} in "Introduction" in ''Writings of Charles S. Peirce'', 4). Presented, National Academy of Sciences, Newport, RI, October 14–17, 1884 (see ''The Essential Peirce'', 1, [http://www.iupui.edu/~peirce/ep/ep1/heads/ep1heads.htm#16 Headnote 16] {{Webarchive|url=https://web.archive.org/web/20141019135652/http://www.iupui.edu/~peirce/ep/ep1/heads/ep1heads.htm#16 |date=2014-10-19  }}). 1885 is the year usually given for this work. Reprinted ''Collected Papers of Charles Sanders Peirce'', 3.359–403, ''Writings of Charles S. Peirce'', 5:162–190, ''The Essential Peirce'', 1:225–228, in part.</ref> he distinguished between first-order and second-order quantification.<ref name="Putnam">Putnam, Hilary (1982), "Peirce the Logician", ''Historia Mathematica'' 9, 290–301. Reprinted, pp. 252–260 in Putnam (1990), ''Realism with a Human Face'', Harvard. [http://www.jfsowa.com/peirce/putnam.htm Excerpt with article's last five pages].</ref>{{efn|It was in Peirce's 1885 "On the Algebra of Logic". See Byrnes, John (1998), "Peirce's First-Order Logic of 1885", ''Transactions of the Charles S. Peirce Society'' v. 34, n. 4, pp. 949–976.}} In the same paper he set out what can be read as the first (primitive) [[axiomatic set theory]], anticipating [[Zermelo]] by about two decades (Brady 2000,<ref name="Brady">Brady, Geraldine (2000), ''From Peirce to Skolem: A Neglected Chapter in the History of Logic'', North-Holland/Elsevier Science BV, Amsterdam, Netherlands.</ref> pp.&nbsp;132–133).
[[File:PeirceAlphaGraphs.svg|thumb|upright=1.35|[[Existential graph]]s: Alpha graphs]]
In 1886, he saw that Boolean calculations could be carried out via electrical switches,<ref name="P2M"/> anticipating [[Claude Shannon]] by more than 50 years. 
By the later 1890s<ref>See Peirce (1898), Lecture 3, "The Logic of Relatives" (not the 1897 ''Monist'' article), ''[[#RLT|Reasoning and the Logic of Things]]'', pp. 146–164 [151]</ref> he was devising [[existential graph]]s, a diagrammatic notation for the [[predicate calculus]]. Based on them are [[John F. Sowa]]'s [[conceptual graph]]s and Sun-Joo Shin's [[diagrammatic reasoning]].

;''The New Elements of Mathematics''

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

;Nature of mathematics

Peirce agreed with [[Auguste Comte]] in regarding mathematics as more basic than philosophy and the special sciences (of nature and mind). Peirce [[Classification of the sciences (Peirce)|classified]] mathematics into three subareas: (1) mathematics of logic, (2) discrete series, and (3) pseudo-continua (as he called them, including the [[real numbers]]) and continua. Influenced by his father [[Benjamin Peirce|Benjamin]], Peirce argued that mathematics studies purely hypothetical objects and is not just the science of quantity but is more broadly the science which draws necessary conclusions; that mathematics aids logic, not vice versa; and that logic itself is part of philosophy and is the science ''about'' drawing conclusions necessary and otherwise.<ref>Peirce (1898), "The Logic of Mathematics in Relation to Education" in ''Educational Review'' v. 15, pp. [https://archive.org/stream/educationalrevie15newyuoft#page/209/mode/1up 209–216] (via ''Internet Archive''). Reprinted ''Collected Papers of Charles Sanders Peirce'', 3.553–562. See also his "The Simplest Mathematics" (1902 MS), ''Collected Papers of Charles Sanders Peirce'', 4.227–323.</ref>

===Mathematics of logic===
<div style="padding:5px;width:40%;border: 1px solid #a2a9b1; float:right;">Mathematical logic and foundations, some noted articles
* "On an Improvement in Boole's Calculus of Logic" (1867)
* "Description of a Notation for the Logic of Relatives" (1870)
* "On the Algebra of Logic" (1880)
* "A Boolian{{sic}} Algebra with One Constant" (1880 MS)
* "On the Logic of Number" (1881)
* "Note B: The Logic of Relatives" (1883)
* "On the Algebra of Logic: A Contribution to the Philosophy of Notation" (1884/1885)
* "The Logic of Relatives" (1897)
* "The Simplest Mathematics" (1902 MS)
* "Prolegomena to an Apology for Pragmaticism" (1906, on existential graphs)
</div>
===Probability and statistics===
Peirce held that science achieves statistical probabilities, not certainties, and that spontaneity ("absolute chance") is real (see [[Tychism]] on his view). Most of his statistical writings promote the [[Frequency probability|frequency interpretation]] of probability (objective ratios of cases), and many of his writings express skepticism about (and criticize the use of) [[statistical model|probability]] when such models are not based on objective [[randomization]].{{efn|Peirce condemned the use of "certain [[likelihood function|likelihoods]]" (''The Essential Peirce'', 2:108–109) even more strongly than he criticized [[Bayesian statistics|Bayesian methods]]. Peirce used [[Bayesian inference]] in criticizing parapsychology (''Writings of Charles S. Peirce'', 6:76).}} Though Peirce was largely a frequentist, his [[possible world semantics]] introduced the [[propensity probability|"propensity" theory of probability]] before [[Karl Popper]].<ref>Miller, Richard W. (1975), "Propensity: Popper or Peirce?", ''[[British Journal for the Philosophy of Science]]'', v. 26, n. 2, pp. 123–132. {{doi|10.1093/bjps/26.2.123}}. [https://wayback.archive-it.org/all/20190412103703/https://academic.oup.com/bjps/article-abstract/26/2/123/1513234?redirectedFrom=fulltext Eprint].</ref><ref>[[Susan Haack|Haack, Susan]] and Kolenda, Konstantin (1977), "Two Fallibilists in Search of the Truth", ''Proceedings of the Aristotelian Society'', Supplementary Volumes, v. 51, pp. 63–104. {{JSTOR|4106816}}</ref> Peirce (sometimes with [[Joseph Jastrow]]) investigated the [[Bayesian probability|probability judgments]] of experimental subjects, "perhaps the very first" elicitation and estimation of [[subjective probability|subjective probabilities]] in [[experimental psychology]] and (what came to be called) [[Bayesian statistics]].<ref name="Stigler78" />

Peirce formulated modern statistics in "[[Charles Sanders Peirce bibliography#illus|Illustrations of the Logic of Science]]" (1877–1878) and "[[Charles Sanders Peirce bibliography#SIL|A Theory of Probable Inference]]" (1883). With a [[repeated measures design]], Charles Sanders Peirce and Joseph Jastrow introduced [[Blind experiment|blinded]], [[Randomized controlled trial|controlled randomized experiments]] in 1884<ref>Peirce CS, Jastrow J. [http://psychclassics.yorku.ca/Peirce/small-diffs.htm On Small Differences in Sensation]. Memoirs of the National Academy of Sciences 1885; 3:73–83.</ref> (Hacking 1990:205)<ref name="Hacking" /> (before [[Ronald A. Fisher]]).<ref name="Stigler78" /> He invented [[optimal design]] for experiments on gravity, in which he "[[analysis of variance|corrected the means]]". He used [[correlation]] and [[smoothing]]. Peirce extended the work on [[Peirce's criterion|outliers]] by [[Benjamin Peirce]], his father.<ref name="Stigler78" /> He introduced the terms "[[Confidence interval|confidence]]" and "[[Likelihood function|likelihood]]" (before [[Jerzy Neyman]] and [[Ronald A. Fisher|Fisher]]). (See [[Stephen Stigler]]'s historical books and [[Ian Hacking]] 1990.<ref name="Hacking" />)

== As a philosopher ==
Peirce was a working scientist for 30 years, and arguably was a professional philosopher only during the five years he lectured at Johns Hopkins. He learned philosophy mainly by reading, each day, a few pages of [[Immanuel Kant]]'s ''[[Critique of Pure Reason]]'', in the original German, while a Harvard undergraduate. His writings bear on a wide array of disciplines, including mathematics, [[logic]], philosophy, statistics, [[astronomy]],<ref name="SP2" /> [[metrology]],<ref name="metr" /> [[geodesy]], [[experimental psychology]],<ref name="psych" /> economics,<ref name="econom" /> [[linguistics]],<ref name="ling" /> and the [[history and philosophy of science]]. This work has enjoyed renewed interest and approval, a revival inspired not only by his anticipations of recent scientific developments but also by his demonstration of how philosophy can be applied effectively to human problems.

Peirce's philosophy includes a pervasive three-category system: belief that truth is immutable and is both independent from actual opinion ([[fallibilism]]) and discoverable (no radical skepticism), logic as formal semiotic on signs, on arguments, and on inquiry's ways—including philosophical [[pragmatism]] (which he founded), [[#Critical common-sensism|critical common-sensism]], and [[scientific method]]—and, in metaphysics: [[Scotistic realism|Scholastic realism]], e.g. [[John Duns Scotus]], belief in God, freedom, and at least an attenuated immortality, [[objective idealism]], and belief in the reality of continuity and of absolute chance, mechanical necessity, and creative love.<ref name=evolove/> In his work, fallibilism and pragmatism may seem to work somewhat like [[skepticism]] and [[positivism]], respectively, in others' work.  However, for Peirce, fallibilism is balanced by an [[Pragmatism#antiskep|anti-skepticism]] and is a basis for belief in the reality of absolute chance and of continuity,<ref name="FCE">Peirce (1897) "Fallibilism, Continuity, and Evolution", ''Collected Papers of Charles Sanders Peirce'', 1.141–175 ([http://www.textlog.de/4248.html Eprint]), placed by the ''Collected Papers of Charles Sanders Peirce'', editors directly after "F.R.L." (1899, ''Collected Papers of Charles Sanders Peirce'', 1.135–140).</ref> and pragmatism commits one to anti-[[nominalist]] belief in the reality of the general (CP 5.453–457).

For Peirce, First Philosophy, which he also called cenoscopy, is less basic than mathematics and more basic than the special sciences (of nature and mind). It studies positive phenomena in general, phenomena available to any person at any waking moment, and does not settle questions by resorting to special experiences.<ref name="phil">Peirce (1903), ''Collected Papers of Charles Sanders Peirce'', 1.180–202 and (1906) "The Basis of Pragmaticism", ''The Essential Peirce'', 2:372–373, see "[http://www.helsinki.fi/science/commens/terms/philosophy.html Philosophy]" at ''Commens Digital Companion to C.S. Peirce''.</ref> He [[Classification of the sciences (Peirce)|divided]] such philosophy into (1) phenomenology (which he also called phaneroscopy or categorics), (2) normative sciences (esthetics, ethics, and logic), and (3) metaphysics; his views on them are discussed in order below.

Peirce did not write extensively in aesthetics and ethics,<ref>"[http://agora.phi.gvsu.edu/kap/CSP_Bibliography/CSP_norm_bib.pdf Charles S. Peirce on Esthetics and Ethics: A Bibliography] {{webarchive|url=https://web.archive.org/web/20030406170524/http://agora.phi.gvsu.edu/kap/CSP_Bibliography/CSP_norm_bib.pdf|date=6 April 2003}}" (PDF) by Kelly A. Parker in 1999.</ref> but came by 1902 to hold that aesthetics, ethics, and logic, in that order, comprise the normative sciences.<ref>Peirce (1902 MS), Carnegie Application, edited by Joseph Ransdell, [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm Memoir 2] {{Webarchive|url=https://web.archive.org/web/20131103160621/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm |date=2013-11-03  }}, see table.</ref> He characterized aesthetics as the study of the good (grasped as the admirable), and thus of the ends governing all conduct and thought.<ref>See [http://www.helsinki.fi/science/commens/terms/esthetics.html Esthetics] at ''Commens Digital Companion to C.S. Peirce''.</ref>

===Influence and legacy===
[[Umberto Eco]] described Peirce as "undoubtedly the greatest unpublished writer of our generation"<ref>{{cite journal |last1=Eco |first1=Umberto |title=Peirce's Notion of Interpretant |journal=[[Modern Language Notes]] |date=December 1976 |volume=91 |issue=6}}</ref> and by [[Karl Popper]] as "one of the greatest philosophers of all time".<ref>{{cite book |last1=George Frederick Simkin |first1=Colin |title=Popper's Views on Natural and Social Science |date=1993 |publisher=E.J. Brill |page=41}}</ref> The [[Internet Encyclopedia of Philosophy]] says of Peirce that although "long considered an eccentric figure whose contribution to pragmatism was to provide its name and whose importance was as an influence upon James and Dewey, Peirce's significance in his own right is now largely accepted."<ref>{{cite web |last1=Atkin |first1=Albert |title=Charles Sanders Peirce (1839–1914) |url=https://iep.utm.edu/peirce-charles-sanders/ |publisher=[[Internet Encyclopedia of Philosophy]]}}</ref>

==Pragmatism==
{{Main|Pragmaticism|Pragmatic maxim|Pragmatic theory of truth#Peirce}}
<div style="padding:5px;font-size:94%;max-width:22em; border: 1px solid #a2a9b1; float:right;">Some noted articles and lectures
* [[s:Author:Charles Sanders Peirce#Articles in The Popular Science Monthly Project|Illustrations of the Logic of Science]] (1877–1878): <br>inquiry, pragmatism, statistics, inference
# The Fixation of Belief (1877)
# How to Make Our Ideas Clear (1878)
# The Doctrine of Chances (1878)
# The Probability of Induction (1878)
# The Order of Nature (1878)
# Deduction, Induction, and Hypothesis (1878)
* The Harvard lectures on pragmatism (1903)
* What Pragmatism Is (1905)
* Issues of Pragmaticism (1905)
* Pragmatism (1907 MS in ''The Essential Peirce'', 2)</div> Peirce's recipe for pragmatic thinking, which he called ''[[pragmatism]]'' and, later, ''[[pragmaticism]]'', is recapitulated in several versions of the so-called ''[[pragmatic maxim]]''. Here is one of his more [[Pragmatic maxim#2|emphatic reiterations]] of it:

{{quote|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.}}

As a movement, pragmatism began in the early 1870s in discussions among Peirce, [[William James]], and others in [[the Metaphysical Club]]. James among others regarded some articles by Peirce such as "[[s:The Fixation of Belief|The Fixation of Belief]]" (1877) and especially "[[s:How to Make Our Ideas Clear|How to Make Our Ideas Clear]]" (1878) as foundational to [[pragmatism]].<ref>James, William (1897), ''The Will to Believe'', see p. 124.</ref> Peirce (CP 5.11–12), like James (''[[s:Pragmatism: A New Name for Some Old Ways of Thinking|Pragmatism: A New Name for Some Old Ways of Thinking]]'', 1907), saw pragmatism as embodying familiar attitudes, in philosophy and elsewhere, elaborated into a new deliberate method for fruitful thinking about problems. Peirce differed from 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.

In 1905 Peirce coined the new name [[pragmaticism]] "for the precise purpose of expressing the original definition", saying that "all went happily" with James's and [[F.C.S. Schiller]]'s variant uses of the old name "pragmatism" and that he coined the new name because of the old name's growing use in "literary journals, where it gets abused". Yet he cited as causes, in a 1906 manuscript, his differences with James and Schiller and, in a 1908 publication, his differences with James as well as literary author [[Giovanni Papini]]'s declaration of pragmatism's indefinability. Peirce in any case regarded his views that truth is immutable and infinity is real, as being opposed by the other pragmatists, but he remained allied with them on other issues.<ref>See [[Pragmaticism#Pragmaticism's name]] for discussion and references.</ref>{{circular reference|date=March 2024}}

Pragmatism begins with the idea that belief is that on which one is prepared to act. Peirce's pragmatism is a method of clarification of conceptions of objects. It equates any conception of an object to a conception of that object's effects to a general extent of the effects' conceivable implications for informed practice. It is a method of sorting out conceptual confusions occasioned, for example, by distinctions that make (sometimes needed) formal yet not practical differences. He formulated both pragmatism and statistical principles as aspects of scientific logic, in his "Illustrations of the Logic of Science" series of articles. In the second one, "[[s:How to Make Our Ideas Clear|How to Make Our Ideas Clear]]", Peirce discussed three grades of clearness of conception:

# Clearness of a conception familiar and readily used, even if unanalyzed and undeveloped.
# Clearness of a conception in virtue of clearness of its parts, in virtue of which logicians called an idea "distinct", that is, clarified by analysis of just what makes it applicable. Elsewhere, echoing Kant, Peirce called a likewise distinct definition "nominal" (CP 5.553).
# Clearness in virtue of clearness of conceivable practical implications of the object's conceived effects, such that fosters fruitful reasoning, especially on difficult problems. Here he introduced that which he later called the [[pragmatic maxim]].

By way of example of how to clarify conceptions, he addressed conceptions about truth and the real as questions of the [[#Presuppositions of logic|presuppositions of reasoning]] in general. In clearness's second grade (the "nominal" grade), he defined truth as a sign's correspondence to its object, and the real as the object of such correspondence, such that truth and the real are independent of that which you or I or any actual, definite [[Community of inquiry|community of inquirers]] think. After that needful but confined step, next in clearness's third grade (the pragmatic, practice-oriented grade) he defined truth as that opinion which ''would'' be reached, sooner or later but still inevitably, by research taken far enough, such that the real does depend on that ideal final opinion—a dependence to which he appeals in theoretical arguments elsewhere, for instance for the long-run validity of the rule of induction.<ref name="Induction">"That the rule of induction will hold good in the long run may be deduced from the principle that reality is only the object of the final opinion to which sufficient investigation would lead", in Peirce (1878 April), "The Probability of Induction", p. [https://archive.org/stream/popscimonthly12yoummiss#page/728/mode/1up 718] (via ''Internet Archive'' ) in ''Popular Science Monthly'', v. 12, pp. 705–718. Reprinted in ''Collected Papers of Charles Sanders Peirce'', 2.669–693, ''Writings of Charles S. Peirce'', 3:290–305, ''The Essential Peirce'', 1:155–169, elsewhere.</ref> Peirce argued that even to argue against the independence and discoverability of truth and the real is to presuppose that there is, about that very question under argument, a truth with just such independence and discoverability.

Peirce said that a conception's meaning consists in "[[Pragmatic maxim#2|all general modes of rational conduct]]" implied by "acceptance" of the conception—that is, if one were to accept, first of all, the conception as true, then what could one conceive to be consequent general modes of rational conduct by all who accept the conception as true?—the whole of such consequent general modes is the whole meaning. His pragmatism does not equate a conception's meaning, its intellectual purport, with the conceived benefit or cost of the conception itself, like a meme (or, say, propaganda), outside the perspective of its being true, nor, since a conception is general, is its meaning equated with any definite set of actual consequences or upshots corroborating or undermining the conception or its worth. His pragmatism also bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and [[Machiavelli]]an search for mercenary or political advantage. Instead the pragmatic maxim is the heart of his pragmatism as a method of experimentational mental [[Pragmatic maxim#6|reflection]]<ref>Peirce (1902), ''Collected Papers of Charles Sanders Peirce'', 5.13 note 1.</ref> arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances—a method hospitable to the formation of explanatory hypotheses, and conducive to the use and improvement of verification.<ref>See ''Collected Papers of Charles Sanders Peirce'', 1.34 [http://www.textlog.de/4220.html Eprint] (in "The Spirit of Scholasticism"), where Peirce ascribed the success of modern science less to a novel interest in verification than to the improvement of verification.</ref>

Peirce's pragmatism, as method and theory of definitions and conceptual clearness, is part of his theory of inquiry,<ref>See [[Joseph Morton Ransdell|Joseph Ransdell]]'s comments and his tabular list of titles of Peirce's proposed list of memoirs in 1902 for his Carnegie application, [http://www.cspeirce.com/menu/library/bycsp/l75/intro/l75intro.htm Eprint]</ref> which he variously called speculative, general, formal or [[universal rhetoric]] or simply methodeutic.<ref name="rhetoric">See [http://www.helsinki.fi/science/commens/terms/rhetoricspec.html rhetoric definitions] at ''Commens Digital Companion to C.S. Peirce''.</ref> He applied his pragmatism as a method throughout his work.

===Theory of inquiry===
{{See also|Inquiry}}

In "[[wikisource:The_Fixation_of_Belief|The Fixation of Belief]]" (1877), Peirce gives his take on the psychological origin and aim of inquiry. On his view, individuals are motivated to inquiry by desire to escape the feelings of anxiety and unease which Peirce takes to be characteristic of the state of doubt. Doubt is described by Peirce as an "uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief."  Peirce uses words like "irritation" to describe the experience of being in doubt and to explain why he thinks we find such experiences to be motivating.  The irritating feeling of doubt is appeased, Peirce says, through our efforts to achieve a settled state of satisfaction with what we land on as our answer to the question which led to that doubt in the first place.  This settled state, namely, belief, is described by Peirce as "a calm and satisfactory state which we do not wish to avoid."  Our efforts to achieve the satisfaction of belief, by whichever methods we may pursue, are what Peirce calls "inquiry".  Four methods which Peirce describes as having been actually pursued throughout the history of thought are summarized below in the section after next. 

====Critical common-sensism====
Critical common-sensism,<ref>Peirce (1905), "Issues of Pragmaticism", ''The Monist'', v. XV, n. 4, pp. [[iarchive:monist18instgoog/page/n532|481–499]]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 5.438–463. Also important: ''Collected Papers of Charles Sanders Peirce'', 5.497–525.</ref> treated by Peirce as a consequence of his pragmatism, is his combination of [[Scottish School of Common Sense|Thomas Reid's common-sense philosophy]] with a [[fallibilism]] that recognizes that propositions of our more or less vague common sense now indubitable may later come into question, for example because of transformations of our world through science. It includes efforts to raise genuine doubts in tests for a core group of common indubitables that change slowly, if at all.

====Rival methods of inquiry====
In "[[s:The Fixation of Belief|The Fixation of Belief]]" (1877), Peirce described inquiry in general not as the pursuit of truth ''per se'' but as the struggle to move from irritating, inhibitory doubt born of surprise, disagreement, and the like, and to reach a secure belief, belief being that on which one is prepared to act. That let Peirce frame scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal, quarrelsome, or [[hyperbolic doubt]], which he held to be fruitless. Peirce sketched four methods of settling opinion, ordered from least to most successful:

# The method of {{em|tenacity}} (policy of sticking to initial belief) – which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. The method goes against the social impulse and easily falters since one may well notice when another's opinion seems as good as one's own initial opinion. Its successes can be brilliant but tend to be transitory.
# The method of {{em|authority}} – which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lasting, but it cannot regulate people thoroughly enough to withstand doubts indefinitely, especially when people learn about other societies present and past.
# The method of the {{em|a priori}} – which promotes conformity less brutally but fosters opinions as something like tastes, arising in conversation and comparisons of perspectives in terms of "what is agreeable to reason". Thereby it depends on fashion in [[paradigm]]s and goes in circles over time. It is more intellectual and respectable but, like the first two methods, sustains accidental and capricious beliefs, destining some minds to doubt it.
# The method of {{em|science}} – wherein inquiry supposes that the real is discoverable but independent of particular opinion, such that, unlike in the other methods, inquiry can, by its own account, go wrong ([[fallibilism]]), not only right, and thus purposely tests itself and criticizes, corrects, and improves itself.

Peirce held that, in practical affairs, slow and stumbling ratiocination is often dangerously inferior to instinct and traditional sentiment, and that the scientific method is best suited to theoretical research,<ref>Peirce, "Philosophy and the Conduct of Life", Lecture 1 of the 1898 Cambridge (MA) Conferences Lectures, ''Collected Papers of Charles Sanders Peirce'', 1.616–648 in part and ''[[#RLT|Reasoning and the Logic of Things]]'', 105–122, reprinted in ''The Essential Peirce'', 2:27–41.</ref> which in turn should not be trammeled by the other methods and practical ends; reason's "first rule"<ref name="FRL" /> is that, in order to learn, one must desire to learn and, as a corollary, must not block the way of inquiry. [[Scientific method]] excels over the others finally by being deliberately designed to arrive—eventually—at the most secure beliefs, upon which the most successful practices can be based. Starting from the idea that people seek not truth ''per se'' but instead to subdue irritating, inhibitory doubt, Peirce showed how, through the struggle, some can come to submit to truth for the sake of belief's integrity, seek as truth the guidance of potential conduct correctly to its given goal, and wed themselves to the scientific method.

====Scientific method====
Insofar as clarification by pragmatic reflection suits explanatory hypotheses and fosters predictions and testing, pragmatism points beyond the usual duo of foundational alternatives: [[deductive reasoning|deduction]] from self-evident truths, or ''[[rationalism]]''; and [[inductive reasoning|induction]] from experiential phenomena, or ''[[empiricism]]''.

Based on his critique of three [[#Modes of inference|modes of argument]] and different from either [[foundationalism]] or [[coherentism]], Peirce's approach seeks to justify claims by a three-phase dynamic of inquiry:

# Active, [[abductive reasoning|abductive]] genesis of theory, with no prior assurance of truth;
# Deductive application of the contingent theory so as to clarify its practical implications;
# Inductive testing and evaluation of the utility of the provisional theory in anticipation of future experience, in both senses: ''[[prediction]]'' and ''control''.

Thereby, Peirce devised an approach to inquiry far more solid than the flatter image of inductive generalization ''simpliciter'', which is a mere re-labeling of phenomenological patterns. Peirce's pragmatism was the first time the [[scientific method]] was proposed as an [[epistemology]] for philosophical questions.

A theory that succeeds better than its rivals in predicting and controlling our world is said to be nearer the truth. This is an operational notion of truth used by scientists.

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

Abduction, deduction, and induction make incomplete sense in isolation from one another but comprise a cycle understandable as a whole insofar as they collaborate toward the common end of inquiry. In the pragmatic way of thinking about conceivable practical implications, every thing has a purpose, and, as possible, its purpose should first be denoted. Abduction hypothesizes an explanation for deduction to clarify into implications to be tested so that induction can evaluate the hypothesis, in the struggle to move from troublesome uncertainty to more secure belief. No matter how traditional and needful it is to study the modes of inference in abstraction from one another, the integrity of inquiry strongly limits the effective [[modularity (programming)|modularity]] of its principal components.

Peirce's outline of the scientific method in §III–IV of "A Neglected Argument"<ref name="NA">Peirce (1908), "[[wikisource:A Neglected Argument for the Reality of God|A Neglected Argument for the Reality of God]]", published in large part, ''Hibbert Journal'' v. 7, 90–112. Reprinted with an unpublished part, ''Collected Papers of Charles Sanders Peirce'', 6.452–485, ''Selected Writings'' pp. 358–379, ''The Essential Peirce'', 2:434–450, ''Peirce on Signs'' 260–278.</ref> is summarized below (except as otherwise noted). There he also reviewed plausibility and inductive precision (issues of [[#Modes of inference|critique of arguments]]).

# ''Abductive'' (or retroductive) phase. Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicated phenomenon. The modicum of success in our guesses far exceeds that of random luck, and seems born of attunement to nature by developed or inherent instincts, especially insofar as best guesses are optimally plausible and simple in the sense of the "facile and natural", as by [[Galileo]]'s natural light of reason and as distinct from "logical simplicity".<ref>See also Nubiola, Jaime (2004), "[http://www.unav.es/users/LumeNaturale.html Il Lume Naturale: Abduction and God]", ''Semiotiche'' I/2, 91–102.</ref> Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and it has no substitute in expediting us toward new truths.<ref>Peirce (c. 1906), "PAP (Prolegomena to an Apology for Pragmatism)" (MS 293), ''[[#NEM|The New Elements of Mathematics]]'' v. 4, pp. 319–320, first quote under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Digital Companion to C. S. Peirce''.</ref> In 1903, Peirce called pragmatism "the logic of abduction".<ref>Peirce (1903), "Pragmatism – The Logic of Abduction", ''Collected Papers of Charles Sanders Peirce'', 5.195–205, especially 196. [http://www.textlog.de/7663.html Eprint].</ref> Coordinative method leads from abducting a plausible hypothesis to judging it for its testability<ref>Peirce, Carnegie application, MS L75.279–280: [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 Memoir 27] {{Webarchive|url=https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 |date=2011-05-24  }}, Draft B.</ref> and for how its trial would economize inquiry itself.<ref name="econ">See MS L75.329–330, from Draft D of [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 Memoir 27] {{Webarchive|url=https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 |date=2011-05-24  }} of Peirce's application to the Carnegie Institution: {{quote|Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuretic and is the first question of heuretic, is to be governed by economical considerations.}}</ref> The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if not costly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has plausibility or reasoned objective probability, while [[Subjective probability|subjective likelihood]], though reasoned, can be misleadingly seductive. Guesses can be selected for trial strategically, for their caution (for which Peirce gave as example the game of [[Twenty Questions]]), breadth, or incomplexity.<ref>Peirce, C. S., "On the Logic of Drawing Ancient History from Documents", ''The Essential Peirce'', 2, see pp. 107–109. On Twenty Questions, see 109: {{quote|Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do.}}</ref> One can discover only that which would be revealed through their sufficient experience anyway, and so the point is to expedite it; economy of research demands the leap, so to speak, of abduction and governs its art.<ref name="econ" />

# ''Deductive'' phase. Two stages:
:i. Explication. Not clearly premised, but a deductive analysis of the hypothesis so as to render its parts as clear as possible.
:ii. Demonstration: Deductive Argumentation, [[Euclid]]ean in procedure. Explicit deduction of consequences of the hypothesis as predictions about evidence to be found. [[Corollary|Corollarial]] or, if needed, Theorematic.

# ''Inductive'' phase. Evaluation of the hypothesis, inferring from observational or experimental tests of its deduced consequences. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real "is only the object of the final opinion to which sufficient investigation would lead";<ref name="Induction" /> in other words, anything excluding such a process would never be real. Induction involving the ongoing accumulation of evidence follows "a method which, sufficiently persisted in", will "diminish the error below any predesignate degree". Three stages:
:i. Classification. Not clearly premised, but an inductive classing of objects of experience under general ideas.
:ii. Probation: direct Inductive Argumentation. Crude or Gradual in procedure. Crude Induction, founded on experience in one mass (CP 2.759), presumes that future experience on a question will not differ utterly from all past experience (CP 2.756). Gradual Induction makes a new estimate of the proportion of truth in the hypothesis after each test, and is Qualitative or Quantitative. Qualitative Gradual Induction depends on estimating the relative evident weights of the various qualities of the subject class under investigation (CP 2.759; see also ''Collected Papers of Charles Sanders Peirce'', 7.114–120). Quantitative Gradual Induction depends on how often, in a fair sample of instances of ''S'', ''S'' is found actually accompanied by ''P'' that was predicted for ''S'' (CP 2.758). It depends on measurements, or statistics, or counting.
:iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result".

====Against Cartesianism====
Peirce drew on the methodological implications of the [[#Four incapacities|four incapacities]]—no genuine introspection, no intuition in the sense of non-inferential cognition, no thought but in signs, and no conception of the absolutely incognizable—to attack philosophical [[René Descartes|Cartesianism]], of which he said that:<ref name="SCFI" />

# "It teaches that philosophy must begin in universal doubt" – when, instead, we start with preconceptions, "prejudices [...] which it does not occur to us ''can'' be questioned", though we may find reason to question them later. "Let us not pretend to doubt in philosophy what we do not doubt in our hearts."
# "It teaches that the ultimate test of certainty is...in the individual consciousness" – when, instead, in science a theory stays on probation till agreement is reached, then it has no actual doubters left. No lone individual can reasonably hope to fulfill philosophy's multi-generational dream. When "candid and disciplined minds" continue to disagree on a theoretical issue, even the theory's author should feel doubts about it.
# It trusts to "a single thread of inference depending often upon inconspicuous premisses" – when, instead, philosophy should, "like the successful sciences", proceed only from tangible, scrutinizable premisses and trust not to any one argument but instead to "the multitude and variety of its arguments" as forming, not a chain at least as weak as its weakest link, but "a cable whose fibers", soever "slender, are sufficiently numerous and intimately connected".
# It renders many facts "absolutely inexplicable, unless to say that 'God makes them so' is to be regarded as an explanation"{{efn|Peirce believed in God. See section [[#Philosophy: metaphysics]].}} – when, instead, philosophy should avoid being "unidealistic",{{efn|However, Peirce disagreed with Hegelian [[absolute idealism]]. See for example ''Collected Papers of Charles Sanders Peirce'', 8.131.}} misbelieving that something real can defy or evade all possible ideas, and supposing, inevitably, "some absolutely inexplicable, unanalyzable ultimate", which explanatory surmise explains nothing and so is inadmissible.

==Theory of categories==
{{Main|Categories (Peirce)}}

On May 14, 1867, the 27-year-old Peirce presented a paper entitled "On a New List of Categories" to the [[American Academy of Arts and Sciences]], which published it the following year. The paper outlined a theory of predication, involving three universal categories that Peirce developed in response to reading [[Aristotle]], [[Immanuel Kant]], and [[G. W. F. Hegel]], categories that Peirce applied throughout his work for the rest of his life.<ref name="Burch" /> Peirce scholars generally regard the "New List" as foundational or breaking the ground for Peirce's "architectonic", his blueprint for a pragmatic philosophy. In the categories one will discern, concentrated, the pattern that one finds formed by the three grades of clearness in "[[s:How to Make Our Ideas Clear|How To Make Our Ideas Clear]]" (1878 paper foundational to pragmatism), and in numerous other trichotomies in his work.

[[wikisource:On_a_New_List_of_Categories|"On a New List of Categories"]] is cast as a Kantian deduction; it is short but dense and difficult to summarize. The following table is compiled from that and later works.<ref>See in "Firstness", "Secondness", and "Thirdness" in [http://www.helsinki.fi/science/commens/dictionary.html ''Commens Digital Companion to C.S. Peirce''].</ref> In 1893, Peirce restated most of it for a less advanced audience.<ref>Peirce (1893), "The Categories" MS 403. ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/bycsp.htm#NLOC-R Eprint] {{Webarchive|url=https://web.archive.org/web/20140731071800/http://cspeirce.com/menu/library/bycsp/bycsp.htm#NLOC-R |date=2014-07-31  }}, edited by [[Joseph Morton Ransdell|Joseph Ransdell]], with information on the re-write, and interleaved with the 1867 "New List" for comparison.</ref> {{C. S. Peirce categorial table}}

== Logic, or semiotic ==
In 1918, the logician [[Clarence Irving Lewis|C.&nbsp;I. Lewis]] wrote, "The contributions of C.S. Peirce to symbolic logic are more numerous and varied than those of any other writer—at least in the nineteenth century."<ref>Lewis, Clarence Irving (1918), ''A Survey of Symbolic Logic'', see ch. 1, §7 "Peirce", pp. 79–106, see [https://archive.org/stream/surveyofsymbolic00lewiiala#page/79/mode/1up p. 79] (''Internet Archive''). Note that Lewis's bibliography lists works by Frege, tagged with asterisks as important.</ref> 

=== Relational logic ===
Beginning with his first paper on the [[Charles Sanders Peirce bibliography#LOR1870|"Logic of Relatives" (1870)]], Peirce extended the [[theory of relations]] pioneered by [[Augustus De Morgan]].{{efn|Much of the mathematics of relations now taken for granted was "borrowed" from Peirce, not always with all due credit; on that and on how the young [[Bertrand Russell]], especially his ''Principles of Mathematics'' and ''[[Principia Mathematica]]'', did not do Peirce justice, see Anellis (1995).<ref name="Anellis"/>}} Beginning in 1940, [[Alfred Tarski]] and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of [[relation algebra]].

Relational logic gained applications. In mathematics, it influenced the abstract analysis of [[E. H. Moore]] and the [[Lattice (order)|lattice theory]] of [[Garrett Birkhoff]]. In computer science, the [[relational model]] for [[database]]s was developed with Peircean ideas in work of [[Edgar F. Codd]], who was a doctoral student<ref>Avery, John (2003) ''Information theory and evolution'', p. 167; also Mitchell, Melanie, "[http://web.cecs.pdx.edu/~mm/MMScientificAncestry.html My Scientific Ancestry] {{Webarchive|url=https://web.archive.org/web/20141008181914/http://web.cecs.pdx.edu/~mm/MMScientificAncestry.html|date=October 8, 2014}}".</ref> of [[Arthur W. Burks]], a Peirce scholar. In economics, relational logic was used by [[Frank P. Ramsey]], [[John von Neumann]], and [[Paul Samuelson]] to study preferences and utility and by [[Kenneth J. Arrow]] in ''[[Social Choice and Individual Values]]'', following Arrow's association with Tarski at [[City College of New York]].

=== Quantifiers ===
On Peirce and his contemporaries [[Ernst Schröder (mathematician)|Ernst Schröder]] and [[Gottlob Frege]], [[Hilary Putnam]] (1982)<ref name="Putnam" /> documented that Frege's work on the logic of quantifiers had little influence on his contemporaries, although it was published four years before the work of Peirce and his student Oscar Howard Mitchell. Putnam found that mathematicians and logicians learned about the logic of quantifiers through the independent work of Peirce and Mitchell, particularly through Peirce's "On the Algebra of Logic: A Contribution to the Philosophy of Notation"<ref name="CSP1885" /> (1885), published in the premier American mathematical journal of the day, and cited by [[Peano]] and Schröder, among others, who ignored Frege. They also adopted and modified Peirce's notations, typographical variants of those now used. Peirce apparently was ignorant of Frege's work, despite their overlapping achievements in logic, [[philosophy of language]], and the [[foundations of mathematics]].

Peirce's work on formal logic had admirers besides [[Ernst Schröder (mathematician)|Ernst Schröder]]:
* Philosophical algebraist [[William Kingdon Clifford]]<ref>Beil, Ralph G. and Ketner, Kenneth (2003), "Peirce, Clifford, and Quantum Theory", ''International Journal of Theoretical Physics'' v. 42, n. 9, pp. 1957–1972.</ref> and logician [[William Ernest Johnson]], both British;
* The Polish school of logic and foundational mathematics, including [[Alfred Tarski]];
* [[Arthur Prior]], who praised and studied Peirce's logical work in a 1964 paper<ref name="SP2" /> and in ''Formal Logic'' (saying on page 4 that Peirce "perhaps had a keener eye for essentials than any other logician before or since").

=== Philosophy of logic ===
A philosophy of logic, grounded in his categories and semiotic, can be extracted from Peirce's writings and, along with Peirce's logical work more generally, is exposited and defended in Hilary Putnam (1982);<ref name="Putnam" /> the Introduction in Nathan Houser ''et al.'' (1997);<ref>Houser, Roberts, and Van Evra, eds. (1997), ''Studies in the Logic of Charles Sanders Peirce'', Indiana U., Bloomington, IN.</ref> and [[Randall Dipert]]'s chapter in [[Cheryl Misak]] (2004).<ref>Misak, ed. (2004), ''The Cambridge Companion to Peirce'', Cambridge U., UK.</ref>{{Semiotics}}

==== Logic as philosophical ====
Peirce regarded logic ''per se'' as a division of philosophy, as a normative science based on esthetics and ethics, as more basic than metaphysics,<ref name="FRL">Peirce (1899 MS), "F.R.L." [First Rule of Logic], ''Collected Papers of Charles Sanders Peirce'', 1.135–140, [https://web.archive.org/web/20120106071421/http://www.princeton.edu/~batke/peirce/frl_99.htm Eprint]</ref> and as "the art of devising methods of research".<ref name="ars">Peirce (1882), "Introductory Lecture on the Study of Logic" delivered September 1882, ''Johns Hopkins University Circulars'', v. 2, n. 19, pp. [https://books.google.com/books?id=E0YFAAAAQAAJ&pg=PA11&dq=%22art+of+devising+methods+of+research%22 11–12] (via Google), November 1882. Reprinted (''The Essential Peirce'', 1:210–214; ''Writings of Charles S. Peirce'', 4:378–382; ''Collected Papers of Charles Sanders Peirce'', 7.59–76). The definition of logic quoted by Peirce is by [[Peter of Spain (author)|Peter of Spain]].</ref> More generally, as inference, "logic is rooted in the social principle", since inference depends on a standpoint that, in a sense, is unlimited.<ref>Peirce (1878), "The Doctrine of Chances", ''Popular Science Monthly'', v. 12, pp. 604–615 (CP 2.645–668, ''Writings of Charles S. Peirce'', 3:276–290, ''The Essential Peirce'', 1:142–154). {{quote|...&nbsp;death makes the number of our risks, the number of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great. ... logicality inexorably requires that our interests shall ''not'' be limited. ... Logic is rooted in the social principle.}}</ref> Peirce called (with no sense of deprecation) "mathematics of logic" much of the kind of thing which, in current research and applications, is called simply "logic". He was productive in both (philosophical) logic and logic's mathematics, which were connected deeply in his work and thought.

Peirce argued that logic is formal semiotic: the formal study of signs in the broadest sense, not only signs that are artificial, linguistic, or symbolic, but also signs that are semblances or are indexical such as reactions. Peirce held that "all this universe is perfused with signs, if it is not composed exclusively of signs",<ref>Peirce, ''Collected Papers of Charles Sanders Peirce'', 5.448 footnote, from "The Basis of Pragmaticism" in 1906.</ref> along with their representational and inferential relations. He argued that, since all thought takes time, all thought is in signs<ref name="QFM">Peirce, (1868), "Questions concerning certain Faculties claimed for Man", ''Journal of Speculative Philosophy'' v. 2, n. 2, [https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA103 pp. 103–114]. On thought in signs, see p. 112. Reprinted ''Collected Papers of Charles Sanders Peirce'', 5.213–263 (on thought in signs, see 253), ''Writings of Charles S. Peirce'', 2:193–211, ''The Essential Peirce'', 2:11–27. ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/question/qu-frame.htm Eprint] {{Webarchive|url=https://web.archive.org/web/20071014064210/http://cspeirce.com/menu/library/bycsp/question/qu-frame.htm |date=2007-10-14  }}.</ref> and sign processes ("semiosis") such as the inquiry process. He [[Classification of the sciences (Peirce)|divided]] logic into: (1) speculative grammar, or stechiology, on how signs can be meaningful and, in relation to that, what kinds of signs there are, how they combine, and how some embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative or [[universal rhetoric]], or methodeutic,<ref name="rhetoric"/> the philosophical theory of inquiry, including pragmatism.

==== Presuppositions of logic ====
In his "F.R.L." [First Rule of Logic] (1899), Peirce states that the first, and "in one sense, the sole", rule of reason is that, ''to learn, one needs to desire to learn'' and desire it without resting satisfied with that which one is inclined to think.<ref name="FRL"/> So, the first rule is, ''to wonder''. Peirce proceeds to a critical theme in research practices and the shaping of theories:

<blockquote><poem>...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.</poem></blockquote>

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

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

The First Rule of Logic pertains to the mind's presuppositions in undertaking reason and logic; presuppositions, for instance, that truth and the real do not depend on yours or my opinion of them but do depend on representational relation and consist in the destined end in investigation taken far enough ([[#defs|see below]]). He describes such ideas as, collectively, hopes which, in particular cases, one is unable seriously to doubt.<ref>Peirce (1902), The Carnegie Institute Application, Memoir 10, MS L75.361–362, ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-04.htm#m10 Eprint] {{Webarchive|url=https://web.archive.org/web/20110524021037/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-04.htm#m10 |date=2011-05-24  }}.</ref>

==== Four incapacities ====
<div style="padding:5px;font-size:94%;width:auto; border: 1px solid #a2a9b1; float:right;">The ''Journal of Speculative Philosophy'' series (1868–1869), including
* Questions concerning certain Faculties claimed for Man (1868)
* Some Consequences of Four Incapacities (1868)
* Grounds of Validity of the Laws of Logic:<br>Further Consequences of Four Incapacities (1869)</div> In three articles in 1868–1869,<ref name="QFM"/><ref name="SCFI">Peirce (1868), "Some Consequences of Four Incapacities", ''Journal of Speculative Philosophy'' v. 2, n. 3, [https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA140 pp. 140–157]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 5.264–317, ''Writings of Charles S. Peirce'', 2:211–242, ''The Essential Peirce'', 1:28–55. ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/conseq/cn-frame.htm Eprint].</ref><ref name="GVLL">Peirce, "Grounds of Validity of the Laws of Logic: Further Consequences of Four Incapacities", ''Journal of Speculative Philosophy'' v. II, n. 4, [https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA193 pp. 193–208]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 5.318–357, ''Writings of Charles S. Peirce'', 2:242–272 (''Peirce Edition Project'', [http://www.iupui.edu/~peirce/writings/v2/w2/w2_23/v2_23.htm Eprint] {{Webarchive|url=https://web.archive.org/web/20100528064903/http://www.iupui.edu/~peirce/writings/v2/w2/w2_23/v2_23.htm |date=2010-05-28  }}), ''The Essential Peirce'', 1:56–82.</ref> Peirce rejected mere verbal or [[hyperbolic doubt]] and first or ultimate principles, and argued that we have (as he numbered them<ref name="SCFI"/>):
# No power of Introspection. All knowledge of the internal world comes by hypothetical reasoning from known external facts.
# No power of Intuition (cognition without logical determination by previous cognitions). No cognitive stage is absolutely first in a process. All mental action has the form of inference.
# No power of thinking without signs. A cognition must be interpreted in a subsequent cognition in order to be a cognition at all.
# No conception of the absolutely incognizable.
(The above sense of the term "intuition" is almost Kant's, said Peirce. It differs from the current looser sense that encompasses instinctive or anyway half-conscious inference.)

Peirce argued that those incapacities imply the reality of the general and of the continuous, the validity of the modes of reasoning,<ref name="GVLL"/> and the falsity of philosophical [[René Descartes|Cartesianism]] ([[#Against Cartesianism|see below]]).

Peirce rejected the conception (usually ascribed to Kant) of the unknowable thing-in-itself<ref name="SCFI"/> and later said that to "dismiss make-believes" is a prerequisite for pragmatism.<ref>Peirce (1905), "What Pragmatism Is", ''The Monist'', v. XV, n. 2, pp. 161–181, [https://archive.org/details/monist18instgoog/page/n201 see 167]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 5.411–437, see 416. ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/whatis/whatpragis.htm Eprint].</ref>

==== Logic as formal semiotic ====
Peirce sought, through his wide-ranging studies through the decades, formal philosophical ways to articulate thought's processes, and also to explain the workings of science. These inextricably entangled questions of a dynamics of inquiry rooted in nature and nurture led him to develop his semiotic with very broadened conceptions of signs and inference, and, as its culmination, a theory of inquiry for the task of saying 'how science works' and devising research methods. This would be logic by the medieval definition taught for centuries: art of arts, science of sciences, having the way to the principles of all methods.<ref name="ars"/> Influences radiate from points on parallel lines of inquiry in [[Aristotle]]'s work, in such ''loci'' as: the basic terminology of [[psychology]] in ''[[On the Soul]]''; the founding description of [[sign relation]]s in ''[[On Interpretation]]''; and the differentiation of [[inference]] into three modes that are commonly translated into English as ''[[Abductive reasoning|abduction]]'', ''[[Deductive reasoning|deduction]]'', and ''[[Inductive reasoning|induction]]'', in the ''[[Prior Analytics]]'', as well as inference by [[analogy]] (called ''paradeigma'' by Aristotle), which Peirce regarded as involving the other three modes.

Peirce began writing on semiotic in the 1860s, around the time when he devised his system of three categories. He called it both ''[[semiotic]]'' and ''semeiotic''. Both are current in singular and plural. He based it on the conception of a triadic [[sign relation]], and defined ''[[semiosis]]'' as "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".<ref>Peirce 1907, ''Collected Papers of Charles Sanders Peirce'', 5.484. Reprinted, ''The Essential Peirce'', 2:411 in "Pragmatism" (398–433).</ref> As to signs in thought, Peirce emphasized the reverse: "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."<ref name="QFM"/>

Peirce held that all thought is in signs, issuing in and from interpretation, where ''sign'' is the word for the broadest variety of conceivable semblances, diagrams, metaphors, symptoms, signals, designations, symbols, texts, even mental concepts and ideas, all as determinations of a mind or ''quasi-mind'', that which at least functions like a mind, as in the work of crystals or bees<ref>See "[http://www.helsinki.fi/science/commens/terms/quasimind.html Quasi-mind]" in ''Commens Digital Companion to C.S. Peirce''.</ref>—the focus is on sign action in general rather than on psychology, linguistics, or social studies (fields which he also pursued).

Inquiry is a kind of inference process, a manner of thinking and semiosis. Global divisions of ways for phenomena to stand as signs, and the subsumption of inquiry and thinking within inference as a sign process, enable the study of inquiry on semiotics' three levels:

# Conditions for meaningfulness. Study of significatory elements and combinations, their grammar.
# Validity, conditions for true representation. Critique of arguments in their various separate modes.
# Conditions for determining interpretations. Methodology of inquiry in its mutually interacting modes.

Peirce uses examples often from common experience, but defines and discusses such things as assertion and interpretation in terms of philosophical logic. In a formal vein, Peirce said:

{{quote|''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 [[Weierstrass]]ian severity, and that is perfectly evident. The word "formal" in the definition is also defined.<ref>Peirce, "Carnegie Application", ''[[#NEM|The New Elements of Mathematics]]'' v. 4, p. 54.</ref>}}

== Signs ==
{{Main|Semiotic theory of Charles Sanders Peirce}}
{{See also|Representation (arts)#Peirce and representation|Sign (semiotics)#Triadic signs}}
{{Hatnote|A list of noted writings by Peirce on signs and sign relations is at [[Semiotic theory of Charles Sanders Peirce#References and further reading|Semiotic theory of Charles Sanders Peirce § References and further reading]].}}

=== Sign relation ===
Peirce's theory of signs is known to be one of the most complex semiotic theories due to its generalistic claim. Anything is a sign—not absolutely as itself, but instead in some relation or other. The ''[[sign relation]]'' is the key. It defines three roles encompassing (1) the sign, (2) the sign's subject matter, called its ''object'', and (3) the sign's meaning or ramification as formed into a kind of effect called its ''interpretant'' (a further sign, for example a translation). It is an irreducible ''[[triadic relation]]'', according to Peirce. The roles are distinct even when the things that fill those roles are not. The roles are but three; a sign of an object leads to one or more interpretants, and, as signs, they lead to further interpretants.

''Extension × intension = information.'' Two traditional approaches to sign relation, necessary though insufficient, are the way of ''[[Extension (semantics)|extension]]'' (a sign's objects, also called breadth, denotation, or application) and the way of ''[[intension]]'' (the objects' characteristics, qualities, attributes referenced by the sign, also called depth, [[Comprehension (logic)|comprehension]], significance, or connotation). Peirce adds a third, the way of ''[[Logic of information|information]]'', including change of information, to integrate the other two approaches into a unified whole.<ref>Peirce (1867), "Upon Logical Comprehension and Extension" (CP 2.391–426), ([http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm ''Writings of Charles S. Peirce'', 2:70–86] {{Webarchive|url=https://web.archive.org/web/20191209161818/http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm |date=2019-12-09  }}).</ref> For example, because of the equation above, if a term's total amount of information stays the same, then the more that the term 'intends' or signifies about objects, the fewer are the objects to which the term 'extends' or applies.

''Determination.'' A sign depends on its object in such a way as to represent its object—the object enables and, in a sense, determines the sign. A physically causal sense of this stands out when a sign consists in an indicative reaction. The interpretant depends likewise on both the sign and the object—an object determines a sign to determine an interpretant. But this determination is not a succession of dyadic events, like a row of toppling dominoes; sign determination is triadic. For example, an interpretant does not merely represent something which represented an object; instead an interpretant represents something ''as'' a sign representing the object. The object (be it a quality or fact or law or even fictional) determines the sign to an interpretant through one's collateral experience<ref name="collateral">See pp. 404–409 in "Pragmatism" in ''The Essential Peirce'', 2. Ten quotes on collateral experience from Peirce provided by Joseph Ransdell can be viewed [http://lyris.ttu.edu/read/messages?id=57101 here] at peirce-l's Lyris archive. Note: Ransdell's quotes from ''Collected Papers of Charles Sanders Peirce'', 8.178–179 are also in ''The Essential Peirce'', 2:493–494, which gives their date as 1909; and his quote from ''Collected Papers of Charles Sanders Peirce'', 8.183 is also in ''The Essential Peirce'', 2:495–496, which gives its date as 1909.</ref> with the object, in which the object is found or from which it is recalled, as when a sign consists in a chance semblance of an absent object. Peirce used the word "determine" not in a strictly deterministic sense, but in a sense of "specializes", ''bestimmt'',<ref name="determined">Peirce, letter to William James, dated 1909, see ''The Essential Peirce'', 2:492.</ref> involving variable amount, like an influence.<ref name="Marty">See "[http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm 76 definitions of the sign by C. S. Peirce]", collected by Robert Marty (U. of Perpignan, France).</ref> Peirce came to define representation and interpretation in terms of (triadic) determination.<ref>Peirce, A Letter to Lady Welby (1908), ''[[#SS|Semiotic and Significs]]'', pp. 80–81: {{quote|I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former. My insertion of "upon a person" is a sop to Cerberus, because I despair of making my own broader conception understood.}}</ref> The object determines the sign to determine another sign—the interpretant—to be related to the object ''as the sign is related to the object'', hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself, and is definitive of sign, object, and interpretant in general.<ref name="Marty"/>

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

# A ''sign'' (or ''representamen''){{efn|''Representamen'' ({{IPAc-en|ˌ|r|ɛ|p|r|ɪ|z|ɛ|n|ˈ|t|eɪ|m|ə|n}} {{respell|REP|ri|zen|TAY|mən}}) was adopted ([[wikt:representamen|not coined]]) by Peirce as his technical term for the ''sign'' as covered in his theory, in case a divergence should come to light between his theoretical version and the popular senses of the word "sign". He eventually stopped using "representamen". See ''The Essential Peirce'', 2:272–273 and ''[[#SS|Semiotic and Significs]]'' p. 193, quotes in "[http://www.helsinki.fi/science/commens/terms/representamen.html Representamen]" at ''Commens Digital Companion to C.S. Peirce''.}} represents, in the broadest possible sense of "represents". It is something interpretable as saying something about something. It is not necessarily symbolic, linguistic, or artificial—a cloud might be a sign of rain for instance, or ruins the sign of ancient civilization.<ref>{{cite book |author-last=Eco |author-first=Umberto |title=Semiotics and the Philosophy of Language |date=1984 |publisher=Indiana University Press |location=Bloomington & Indianapolis |isbn=978-0-25320398-4 |page=[https://archive.org/details/semioticsphiloso00ecou/page/15 15] |url=https://archive.org/details/semioticsphiloso00ecou/page/15}}</ref> As Peirce sometimes put it (he defined ''sign'' at least 76 times<ref name="Marty"/>), the sign stands ''for'' the object ''to'' the interpretant. A sign represents its object in some respect, which respect is the sign's ''ground''.<ref name="ground"/>
# An ''object'' (or ''semiotic object'') is a subject matter of a sign and an interpretant. It can be anything thinkable, a quality, an occurrence, a rule, etc., even fictional, such as [[Prince Hamlet]].<ref name="fictive">Peirce (1909), A Letter to William James, ''The Essential Peirce'', 2:492–502. Fictional object, 498. Object as universe of discourse, 492. See "[http://www.helsinki.fi/science/commens/terms/dynamicalobject.html Dynamical Object]" at ''Commens Digital Companion to C.S. Peirce''.</ref> All of those are special or partial objects. The object most accurately is the [[universe of discourse]] to which the partial or special object belongs.<ref name="fictive"/> For instance, a perturbation of Pluto's orbit is a sign about Pluto but ultimately not only about Pluto. An object either (i) is ''immediate'' to a sign and is the object as represented in the sign or (ii) is a ''dynamic'' object, the object as it really is, on which the immediate object is founded "as on bedrock".<ref>See "Immediate Object", etc., at [http://www.helsinki.fi/science/commens/dictionary.html ''Commens Digital Companion to C.S. Peirce''].</ref>
# An ''[[interpretant]]'' (or ''interpretant sign'') is a sign's meaning or ramification as formed into a kind of idea or effect, an interpretation, human or otherwise. An interpretant is a sign (a) of the object and (b) of the interpretant's "predecessor" (the interpreted sign) as a sign of the same object. An interpretant either (i) is ''immediate'' to a sign and is a kind of quality or possibility such as a word's usual meaning, or (ii) is a ''dynamic'' interpretant, such as a state of agitation, or (iii) is a ''final'' or ''normal'' interpretant, a sum of the lessons which a sufficiently considered sign ''would'' have as effects on practice, and with which an actual interpretant may at most coincide.
Some of the understanding needed by the mind depends on familiarity with the object. To know what a given sign denotes, the mind needs some experience of that sign's object, experience outside of, and collateral to, that sign or sign system. In that context Peirce speaks of collateral experience, collateral observation, collateral acquaintance, all in much the same terms.<ref name="collateral"/>

=== Classes of signs ===
{{C. S. Peirce ninefold sign table}}

Among Peirce's many sign typologies, three stand out, interlocked. The first typology depends on the sign itself, the second on how the sign stands for its denoted object, and the third on how the sign stands for its object to its interpretant. Also, each of the three typologies is a three-way division, a [[Trichotomy (philosophy)|trichotomy]], via Peirce's three phenomenological [[#Theory of categories|categories]]: (1) quality of feeling, (2) reaction, resistance, and (3) representation, mediation.<ref name="9signs"/>

I. ''Qualisign, sinsign, legisign'' (also called'' tone, token, type,'' and also called ''potisign, actisign, famisign''):<ref name="terms">On the varying terminology, look up in [http://www.helsinki.fi/science/commens/dictionary.html ''Commens Digital Companion to C.S. Peirce''].</ref> This typology classifies every sign according to the sign's own phenomenological category—the qualisign is a quality, a possibility, a "First"; the sinsign is a reaction or resistance, a singular object, an actual event or fact, a "Second"; and the legisign is a habit, a rule, a representational relation, a "Third".

II. ''Icon, index, symbol'': This typology, the best known one, classifies every sign according to the category of the sign's way of denoting its object—the icon (also called semblance or likeness) by a quality of its own, the index by factual connection to its object, and the symbol by a habit or rule for its interpretant.

III. ''Rheme, dicisign, argument'' (also called ''sumisign, dicisign, suadisign,'' also ''seme, pheme, delome,''<ref name="terms"/> and regarded as very broadened versions of the traditional ''term, proposition, argument''): This typology classifies every sign according to the category which the interpretant attributes to the sign's way of denoting its object—the rheme, for example a term, is a sign interpreted to represent its object in respect of quality; the dicisign, for example a proposition, is a sign interpreted to represent its object in respect of fact; and the argument is a sign interpreted to represent its object in respect of habit or law. This is the culminating typology of the three, where the sign is understood as a structural element of inference.

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

== Modes of inference ==
{{Main|Inquiry}}

Borrowing a brace of concepts from [[Aristotle]], Peirce examined three basic modes of [[inference]]—''[[abductive reasoning|abduction]]'', ''[[deductive reasoning|deduction]]'', and ''[[Inductive reasoning|induction]]''—in his "critique of arguments" or "logic proper". Peirce also called abduction "retroduction", "presumption", and, earliest of all, "hypothesis". He characterized it as guessing and as inference to an explanatory hypothesis. He sometimes expounded the modes of inference by transformations of the categorical [[Syllogism#Barbara (AAA-1)|syllogism Barbara (AAA)]], for example in "Deduction, Induction, and Hypothesis" (1878).<ref>''Popular Science Monthly'', v. 13, pp. 470–482, see [https://books.google.com/books?id=u8sWAQAAIAAJ&pg=PA472 472] or [[s:Popular Science Monthly/Volume 13/August 1878/Illustrations of the Logic of Science VI|the book at Wikisource]]. ''Collected Papers of Charles Sanders Peirce'', 2.619–644 [623]</ref> He does this by rearranging the ''rule'' (Barbara's major premise), the ''case'' (Barbara's minor premise), and the ''result'' (Barbara's conclusion):

{{col-begin}}
{{col-break}}
Deduction.

''Rule:'' All the beans from this bag are white. <br>
''Case:'' These beans are beans from this bag. <br>
<math>\therefore</math> ''Result:'' These beans are white.
{{col-break|gap=1%}}
Induction.

''Case:'' These beans are &#91;randomly selected&#93; from this bag.<br>
''Result:'' These beans are white.<br>
<math>\therefore</math> ''Rule:'' All the beans from this bag are white.
{{col-break|gap=1%}}
Hypothesis (Abduction).

''Rule:'' All the beans from this bag are white.<br>
''Result:'' These beans [oddly] are white.<br>
<math>\therefore</math> ''Case:'' These beans are from this bag.
{{col-end}}

In 1883, in "A Theory of Probable Inference" (''[[#SIL|Studies in Logic]]''), Peirce equated hypothetical inference with the induction of characters of objects (as he had done in effect before<ref name="SCFI"/>). Eventually dissatisfied, by 1900 he distinguished them once and for all and also wrote that he now took the syllogistic forms and the doctrine of logical extension and comprehension as being less basic than he had thought. In 1903 he presented the following logical form for abductive inference:<ref>See, under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Digital Companion to C.S. Peirce'', the following quotes:
* On correction of "A Theory of Probable Inference", see quotes from "Minute Logic", ''Collected Papers of Charles Sanders Peirce'', 2.102, c. 1902, and from the Carnegie Application (L75), 1902, ''Historical Perspectives on Peirce's Logic of Science'' v. 2, pp. 1031–1032.
* On new logical form for abduction, see quote from Harvard Lectures on Pragmatism, 1903, ''Collected Papers of Charles Sanders Peirce'', 5.188–189.
See also Santaella, Lucia (1997) "The Development of Peirce's Three Types of Reasoning: Abduction, Deduction, and Induction", 6th Congress of the [[IASS]]. [http://www.pucsp.br/~lbraga/epap_peir1.htm Eprint].</ref>

{{quote|The surprising fact, C, is observed;
: But if A were true, C would be a matter of course,
: Hence, there is reason to suspect that A is true.}}

The logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something ''must'' be; Induction shows that something ''actually is'' operative; Abduction merely suggests that something ''may be''."<ref>"Lectures on Pragmatism", 1903, ''Collected Papers of Charles Sanders Peirce'', 5.171.</ref> Peirce did not remain quite convinced that one logical form covers all abduction.<ref>A Letter to J. H. Kehler (dated 1911), ''[[#NEM|The New Elements of Mathematics]]'' v. 3, pp. 203–204, see in "[http://www.helsinki.fi/science/commens/terms/retroduction.html Retroduction]" at ''Commens Digital Companion to C.S. Peirce''.</ref> In his [[methodeutic]] or theory of inquiry (see below), he portrayed abduction as an economic initiative to further inference and study, and portrayed all three modes as clarified by their coordination in essential roles in inquiry: hypothetical explanation, deductive prediction, inductive testing

== Metaphysics ==
Peirce [[Classification of the sciences (Peirce)|divided]] metaphysics into (1) ontology or general metaphysics, (2) [[wikt:psychical|psychical]] or religious metaphysics, and (3) physical metaphysics.

=== Ontology ===
On the issue of universals, Peirce was a [[Scotistic realism|scholastic realist]], declaring the reality of [[Problem of universals|generals]] as early as 1868.<ref>Peirce (1868), "Nominalism versus Realism", ''Journal of Speculative Philosophy'' v. 2, n. 1, pp. [https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA57 57–61]. Reprinted (CP 6.619–624), ([http://www.iupui.edu/~peirce/writings/v2/w2/w2_14/v2_14.htm ''Writings of Charles S. Peirce'', 2:144–153] {{Webarchive|url=https://web.archive.org/web/20080531074944/http://www.iupui.edu/~peirce/writings/v2/w2/w2_14/v2_14.htm |date=2008-05-31  }}).</ref> According to Peirce, his category he called "thirdness", the more general facts about the world, are extra-mental realities. Regarding [[Modal logic|modalities]] (possibility, necessity, etc.), he came in later years to regard himself as having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote:

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

Peirce retained, as useful for some purposes, the definitions in terms of information states, but insisted that the pragmaticist is committed to a strong [[modal realism]] by conceiving of objects in terms of predictive general conditional propositions about how they ''would'' behave under certain circumstances.<ref>On developments in Peirce's realism, see:
* Peirce (1897), "The Logic of Relatives", ''The Monist'' v. VII, n. 2 pp. 161–217, see [https://books.google.com/books?id=pa0LAAAAIAAJ&pg=PA206 206] (via Google). Reprinted ''Collected Papers of Charles Sanders Peirce'', 3.456–552.
* Peirce (1905), "Issues of Pragmaticism", ''The Monist'' v. XV, n. 4, pp. 481–499, see [https://archive.org/details/monist18instgoog/page/n568 495–496] (via Google). Reprinted (CP 5.438–463, see 453–457).
* Peirce (c. 1905), Letter to Signor Calderoni, ''Collected Papers of Charles Sanders Peirce'', 8.205–213, see 208.
* Lane, Robert (2007), "Peirce's Modal Shift: From Set Theory to Pragmaticism", ''Journal of the History of Philosophy'', v. 45, n. 4.</ref>

==== Continua ====
Continuity and [[synechism]] are central in Peirce's philosophy: "I did not at first suppose that it was, as I gradually came to find it, the master-Key of philosophy".<ref>Peirce (1893–1894, MS 949, p. 1)</ref>

From a mathematical point of view, he embraced [[Infinitesimal|infinitesimals]] and worked long on the mathematics of continua. He long held that the real numbers constitute a pseudo-continuum;<ref>Peirce (1903 MS), ''Collected Papers of Charles Sanders Peirce'', 6.176: "But I now define a ''pseudo-continuum'' as that which modern writers on the theory of functions call a ''continuum''. But this is fully represented by [...] the totality of real values, rational and irrational [...]."</ref> that a true continuum is the real subject matter of ''analysis situs'' ([[topology]]); and that a true continuum of instants exceeds—and within any lapse of time has room for—any [[Aleph number]] (any infinite ''multitude'' as he called it) of instants.<ref>Peirce (1902 MS) and [[Joseph Morton Ransdell|Ransdell, Joseph]], ed. (1998), "Analysis of the Methods of Mathematical Demonstration", [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm#m4 Memoir 4] {{Webarchive|url=https://web.archive.org/web/20131103160621/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm#m4 |date=2013-11-03  }}, Draft C, MS L75.90–102, see 99–100. (Once there, scroll down).</ref>

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

* Peirce (1908), "Some Amazing Mazes (Conclusion), Explanation of Curiosity the First", ''The Monist'', v. 18, n. 3, pp. 416–444, see [[iarchive:bub_gb_CqsLAAAAIAAJ_2/page/n544|463–464]]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 4.594–642, see 642.
* Havenel, Jérôme (2008), "Peirce's Clarifications on Continuity", ''Transactions'' Winter 2008 pp. 68–133, see 119. [https://www.jstor.org/pss/40321237 Abstract].</ref>

=== Psychical or religious metaphysics ===
Peirce believed in God, and characterized such belief as founded in an instinct explorable in musing over the worlds of ideas, brute facts, and evolving habits—and it is a belief in God not as an ''actual'' or ''existent'' being (in Peirce's sense of those words), but all the same as a ''real'' being.<ref name="Godasreal">Peirce in his 1906 "Answers to Questions concerning my Belief in God", ''Collected Papers of Charles Sanders Peirce'', 6.495, [http://users.xplornet.com/~gnox/CSPgod.htm Eprint] {{webarchive |url=https://web.archive.org/web/20080223094243/http://users.xplornet.com/~gnox/CSPgod.htm |date=February 23, 2008}}, reprinted in part as "The Concept of God" in ''Philosophical Writings of Peirce'', J. Buchler, ed., 1940, pp. 375–378: {{quote|I will also take the liberty of substituting "reality" for "existence." This is perhaps overscrupulosity; but I myself always use ''exist'' in its strict philosophical sense of "react with the other like things in the environment." Of course, in that sense, it would be fetichism to say that God "exists." The word "reality," on the contrary, is used in ordinary parlance in its correct philosophical sense. [....] I define the ''real'' as that which holds its characters on such a tenure that it makes not the slightest difference what any man or men may have ''thought'' them to be, or ever will have ''thought'' them to be, here using thought to include, imagining, opining, and willing (as long as forcible ''means'' are not used); but the real thing's characters will remain absolutely untouched.}}</ref> In "[[s:A Neglected Argument for the Reality of God|A Neglected Argument for the Reality of God]]" (1908),<ref name="NA"/> Peirce sketches, for God's reality, an argument to a hypothesis of God as the Necessary Being, a hypothesis which he describes in terms of how it would tend to develop and become compelling in musement and inquiry by a normal person who is led, by the hypothesis, to consider as being purposed the features of the worlds of ideas, brute facts, and evolving habits (for example scientific progress), such that the thought of such purposefulness will "stand or fall with the hypothesis"; meanwhile, according to Peirce, the hypothesis, in supposing an "infinitely incomprehensible" being, starts off at odds with its own nature as a purportively true conception, and so, no matter how much the hypothesis grows, it both (A) inevitably regards itself as partly true, partly vague, and as continuing to define itself without limit, and (B) inevitably has God appearing likewise vague but growing, though God as the Necessary Being is not vague or growing; but the hypothesis will hold it to be ''more'' false to say the opposite, that God is purposeless. Peirce also argued that the will is free<ref>See his [[Charles Sanders Peirce bibliography#MMS|"The Doctrine of Necessity Examined" (1892) and "Reply to the Necessitarians" (1893)]], to both of which editor [[Paul Carus]] responded.</ref> and (see [[Synechism]]) that there is at least an attenuated kind of immortality.

=== Physical metaphysics ===
Peirce held the view, which he called [[objective idealism]], that "matter is effete mind, inveterate habits becoming physical laws".<ref>Peirce (1891), "The Architecture of Theories",'' [[The Monist]]'' v. 1, pp. [https://archive.org/stream/monistquart01hegeuoft#page/161/mode/1up 161–176], see [https://archive.org/stream/monistquart01hegeuoft#page/170/mode/1up p. 170], via ''Internet Archive''. Reprinted (CP 6.7–34) and (''The Essential Peirce'', 1:285–297, see p. 293).</ref> Peirce observed that "[[George Berkeley|Berkeley]]'s metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop".<ref>Peirce, C.S. (1871), Review: Fraser's Edition of the ''Works of George Berkeley'' in ''North American Review'' 113(October):449–472, reprinted in ''[[Charles Sanders Peirce bibliography#CP|Collected Papers of Charles Sanders Peirce]]'' v. 8, paragraphs 7–38 and in ''[[Charles Sanders Peirce bibliography#W|Writings of Charles S. Peirce]]'' v. 2, pp. 462–486. ''Peirce Edition Project'' [http://www.iupui.edu/~peirce/writings/v2/w2/w2_48/v2_48.htm Eprint] {{Webarchive|url=https://web.archive.org/web/20180706131637/http://www.iupui.edu/~peirce/writings/v2/w2/w2_48/v2_48.htm |date=2018-07-06  }}.</ref> 

Peirce asserted the reality of (1) "absolute chance" or randomness (his [[Tychism|tychist]] view), (2) "mechanical necessity" or physical laws ([[Ananke|anancist]] view), and (3) what he called the "law of love" ([[Agapism|agapist]] view), echoing his [[#Theory of categories|categories]] Firstness, Secondness, and Thirdness, respectively.<ref name=evolove/> He held that fortuitous variation (which he also called "sporting"), mechanical necessity, and creative love are the three modes of evolution (modes called "tychasm", "anancasm", and "agapasm")<ref>See "tychism", "tychasm", "tychasticism", and the rest, at http://www.helsinki.fi/science/commens/dictionary.html {{Webarchive |url=https://web.archive.org/web/20100822160927/http://www.helsinki.fi/science/commens/dictionary.html |date=August 22, 2010}} ''Commens Digital Companion to C.S. Peirce''. https://web.archive.org/web/20111024011940/http://www.helsinki.fi/science/commens/dictionary.html</ref> of the cosmos and its parts. He found his conception of agapasm embodied in [[Lamarckism|Lamarckian evolution]]; the overall idea in any case is that of evolution tending toward an end or goal, and it could also be the evolution of a mind or a society; it is the kind of evolution which manifests workings of mind in some general sense. He said that overall he was a synechist, holding with reality of continuity,<ref name=evolove>Peirce (1893), "Evolutionary Love", ''The Monist'' v. 3, pp. 176–200. Reprinted ''Collected Papers of Charles Sanders Peirce'', 6.278–317, ''The Essential Peirce'', 1:352–372. ''Arisbe'' [http://www.cspeirce.com/menu/library/bycsp/evolove/evolove.htm Eprint] {{webarchive |url=https://web.archive.org/web/20070520131053/http://www.cspeirce.com/menu/library/bycsp/evolove/evolove.htm |date=May 20, 2007}}</ref> especially of space, time, and law.<ref>See p. 115 in ''[[#RLT|Reasoning and the Logic of Things]]'' (Peirce's 1898 lectures).</ref>

===Some noted articles===
{{Unreferenced section|date=March 2025}}
* The ''Monist'' Metaphysical Series (1891–1893)
** The Architecture of Theories (1891)
** The Doctrine of Necessity Examined (1892)
** The Law of Mind (1892)
** Man's Glassy Essence (1892)
** Evolutionary Love (1893)
* Immortality in the Light of Synechism (1893 MS)

== Philosophy of science ==
{{Main|Classification of the sciences (Peirce)}}

Peirce outlined two fields, "Cenoscopy" and "Science of Review", both of which he called philosophy. Both included philosophy about science. In 1903 he arranged them, from more to less theoretically basic, thus:<ref name="phil"/> 

# Science of Discovery.
## Mathematics.
## Cenoscopy (philosophy as discussed earlier in this article – categorial, normative, metaphysical), as First Philosophy, concerns positive phenomena in general, does not rely on findings from special sciences, and includes the ''general'' study of inquiry and scientific method.
## Idioscopy, or the Special Sciences (of nature and mind).
# Science of Review, as Ultimate Philosophy, arranges "... the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science". His examples included [[Alexander von Humboldt|Humboldt]]'s ''[[Alexander Von Humboldt#Cosmos|Cosmos]]'', [[Auguste Comte|Comte]]'s ''[[Course of Positive Philosophy|Philosophie positive]]'', and [[Herbert Spencer|Spencer]]'s ''Synthetic Philosophy''.
# Practical Science, or the Arts.

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

==See also==
{{div col|colwidth=20em}}
* [[Howland will forgery trial]]
* [[Hypostatic abstraction]]
* {{slink|Idea|Charles Sanders Peirce}}
* ''[[Laws of Form]]''
* [[List of American philosophers]]
* [[Logical machine]]
* [[Logical matrix]]
* [[Mathematical psychology]]
* {{slink|Normal distribution|Naming}}
* [[Peircean realism]]
* [[Pragmatics]]
* {{slink|Problem of universals|Peirce}}
* {{slink|Quantification (science)|History}}
* [[Relation algebra]]
* [[Truth table]]
* [[Philosophy of science]]
{{div col end}}

===Contemporaries associated with Peirce===
{{div col|colwidth=20em}}
* [[Oliver Wendell Holmes Jr.]]
* [[George Herbert Mead]]
{{div col end}}

==Notes==
{{notelist}}
== References ==
{{Reflist}}

==External links==
{{Sister project links|v=no|b=no|n=no|wikt=no|species=no|m=no|mw=no|c=Category:Charles Sanders Peirce}}
* [https://arisbe.sitehost.iu.edu/ Arisbe: The Peirce Gateway], Joseph Ransdell, ed. {{Webarchive|url=https://web.archive.org/web/20221130013710/https://arisbe.sitehost.iu.edu/ |date=2022-11-30}}. Includes over 100 annotated writings by Peirce, hundreds of papers on Peirce, and archives of a Peirce email forum.
* [https://web.archive.org/web/20030806032358/http://www.indiana.edu/~sign/ Center for Applied Semiotics (CAS)] (1998–2003), Donald Cunningham & Jean Umiker-Sebeok, Indiana U.
* {{anchor|CIEP}}{{lang|pt|[http://estudospeirceanos.wordpress.com/ Centro Internacional de Estudos Peirceanos] (CIEP)}} and previously {{lang|pt|[https://web.archive.org/web/20120516140053/http://www.pucsp.br/pos/cos/cepe/ Centro de Estudos Peirceanos] (CeneP), Lucia Santaella}} et al., Pontifical Catholic U. of {{lang|pt|São Paulo}} (PUC-SP), Brazil. In Portuguese, some English.
* {{anchor|CEP}}[https://www.pragmatismopucsp.com.br/ Centro de Estudos de Pragmatismo] (CEP), Ivo Assad Ibri, Pontifical Catholic U. of São Paulo (PUC-SP), Brazil. In Portuguese. 
*"[https://web.archive.org/web/20071011065724/http://revistas.pucsp.br/index.php/cognitiofilosofia/about Cognitio ]". ''Journal on Pragmatism'' organized by the Centre for Pragmatism Studies (PPG-Fil, PUC-SP) {{ISSN|2316-5278}}
* {{anchor|CDPT}}[http://www.commens.org/ Commens Digital Companion to C.S. Peirce], Mats Bergman, Sami Paavola, & {{lang|pt|João Queiroz}}, formerly [https://web.archive.org/web/20140121203128/http://www.helsinki.fi/science/commens/index.html Commens at Helsinki U]. Includes Commens Dictionary of Peirce's Terms with Peirce's definitions, often many per term across the decades, and the Digital Encyclopedia of Charles S. Peirce ([[#DECSP|old edition still at old website]]).
* {{anchor|CSPI}}[http://www.filosofia.unimi.it/peirce/ {{lang|it|Centro Studi}} Peirce] {{Webarchive |url=https://web.archive.org/web/20130908144039/http://www.filosofia.unimi.it/peirce/ |date=September 8, 2013}}, Carlo Sini, Rossella Fabbrichesi, et al., U. of Milan, Italy. In Italian and English. Part of [http://www.associazionepragma.com/ Pragma].
* [http://www.peirce-foundation.org/ Charles S. Peirce Foundation]. Co-sponsoring the 2014 Peirce International Centennial Congress (100th anniversary of Peirce's death).
* {{anchor|CSPS}}[http://www.peircesociety.org/ Charles S. Peirce Society]<br>''[https://web.archive.org/web/20071011065724/http://peircesociety.org/transactions.html Transactions of the Charles S. Peirce Society]''. Quarterly journal of Peirce studies since spring 1965. [https://web.archive.org/web/20091203103238/http://www.peircesociety.org/contents.html Table of Contents] of all issues.
* [http://www.peirce.org/ Charles S. Peirce Studies], Brian Kariger, ed.
* {{MathGenealogy |id=24099}}
* [http://translate.google.com/translate?hl=en&sl=de&u=http://bildakt-verkoerperung.de/forschungsschwerpunkte/ Collegium for the Advanced Study of Picture Act and Embodiment]: The Peirce Archive. Humboldt U, Berlin, Germany. Cataloguing Peirce's innumerable drawings & graphic materials. [https://web.archive.org/web/20110707185056/http://www.audsisselhoel.com/wordpress/?p=69 More info] (Prof. Aud Sissel Hoel).
* {{anchor|DECSP}}[http://www.digitalpeirce.fee.unicamp.br/ Digital Encyclopedia of Charles S. Peirce], {{lang|pt|João Queiroz}} ([https://ufjf.academia.edu/JoaoQueiroz now at UFJF]) & Ricardo Gudwin ([http://www.dca.fee.unicamp.br/~gudwin/ at Unicamp]), eds., [[Universidade Estadual de Campinas]] (Portuguese), Brazil, in English. 84 authors listed, 51 papers online & more listed, as of January 31, 2009. Newer edition now at [[#CDPT|''Commens Digital Companion to C.S. Peirce'']].
* [https://web.archive.org/web/20050901083355/http://www.existentialgraphs.com/ Existential Graphs], Jay Zeman, ed., U. of Florida. Has 4 Peirce texts.
* {{anchor|GEP}}{{lang|es|[http://www.unav.es/gep/index-en.html Grupo de Estudios Peirceanos (GEP) / Peirce Studies Group], Jaime Nubiola}}, ed., U. of Navarra, Spain. Big study site, Peirce & others in Spanish & English, bibliography, more.
* {{anchor|HPRC}}[http://www.helsinki.fi/peirce/ Helsinki Peirce Research Center] (HPRC), Ahti-Veikko Pietarinen et al., U. of Helsinki.
* [http://www.wyttynys.net/ His Glassy Essence]. Autobiographical Peirce. Kenneth Laine Ketner.
* [http://www.pragmaticism.net/ Institute for Studies in Pragmaticism], Kenneth Laine Ketner, Clyde Hendrick, et al., Texas Tech U. Peirce's life and works.
* {{anchor|IRGAI}}[https://web.archive.org/web/*/http://www.rz.uni-frankfurt.de/~wirth International Research Group on Abductive Inference], {{lang|de|Uwe Wirth}} et al., eds., {{lang|de|Goethe}} U., Frankfurt, Germany. Uses frames. Click on link at bottom of its home page for English. Moved to [[University of Gießen|U. of Gießen]], Germany, [https://web.archive.org/web/20131103211119/http://www.abduktionsforschung.de/abduktionsforschung.html home page] not in English but see Artikel section there.
* {{anchor|HIPHILANGSCI}}[https://hiphilangsci.net/2024/04/01/podcast-episode-38/ Interview with Dan Everett on C.S. Peirce and Peircean linguistics] (2024) – Dan Everett talks to James McElvenny about Peirce in the History and Philosophy of the Language Sciences podcast series.
* {{anchor|LIRSCE}}[https://web.archive.org/web/20070717060233/http://webup.univ-perp.fr/lsh/rch/semiotics/irsce/irsce.html L'I.R.S.C.E.] (1974–2003) – {{lang|fr|Institut de Recherche en Sémiotique, Communication et Éducation, Gérard Deledalle, Joëlle Réthoré}}, U. of {{lang|fr|Perpignan}}, France.
* [https://web.archive.org/web/20131102231348/http://www.minutesemeiotic.org/?lang=en Minute Semeiotic], {{lang|pt|Vinicius Romanini}}, U. of {{lang|pt|São Paulo}}, Brazil. English, Portuguese.
* [https://web.archive.org/web/20120711014221/http://www.signosemio.com/peirce/a_peirce.asp Peirce] at ''Signo: Theoretical Semiotics on the Web'', Louis Hébert, director, supported by U. of Québec. Theory, application, exercises of Peirce's [https://web.archive.org/web/20120711003648/http://www.signosemio.com/peirce/a_semiotique.asp Semiotics] and [https://web.archive.org/web/20120711003340/http://www.signosemio.com/peirce/a_esthetique.asp Esthetics]. English, French.
* {{anchor|PEP}}[http://www.iupui.edu/~peirce/ Peirce Edition Project (PEP)] {{Webarchive|url=https://web.archive.org/web/20191020080934/http://www.iupui.edu/~peirce/ |date=2019-10-20  }}, Indiana U.–Purdue U. Indianapolis (IUPUI). André De Tienne, Nathan Houser, et al. Editors of the ''Writings of Charles S. Peirce'' (W) and ''The Essential Peirce'' (EP) v. 2. Many study aids such as the Robin Catalog of Peirce's manuscripts & letters and:<br>Biographical introductions to [http://www.iupui.edu/~peirce/ep/ep.htm EP&nbsp;1–2] and [http://www.iupui.edu/~peirce/writings/crit.htm W&nbsp;1–6] & [http://www.iupui.edu/~peirce/houserintro.html 8]<br>[http://www.iupui.edu/%7Epeirce/writings/v2/toc2.htm Most of ''Writings of Charles S. Peirce'', 2] readable online.<br>[https://web.archive.org/web/20020328213928/http://www.pep.uqam.ca/ PEP's branch at {{lang|fr|Université du Québec à Montréal (UQÀM)}}]. Working on ''Writings of Charles S. Peirce'', 7: Peirce's work on the ''Century Dictionary''. [https://web.archive.org/web/20160304044756/http://www.pep.uqam.ca/definitionoftheweek.pep Definition of the week].
* [http://www.dr-dau.net/eg_readings.shtml Peirce's Existential Graphs], Frithjof Dau, Germany
* [http://peirce.unimi.it/en Peirce Research Group], Department of Philosophy "Piero Martinetti" – University of Milan, Italy.
* [http://www.pragmatism.org/ Pragmatism Cybrary], David Hildebrand & John Shook.
* {{anchor|RGSEME}}[https://web.archive.org/web/19970519142208/http://www.uni-bielefeld.de/idm/eng/arbeit/agsem.htm Research Group on Semiotic Epistemology and Mathematics Education] (late 1990s), {{lang|de|Institut für Didaktik der Mathematik (Michael Hoffman, Michael Otte, Universität Bielefeld,}} Germany). See ''Peirce Project Newsletter'' v. 3, n. 1, [http://www.iupui.edu/~peirce/news/3_1/3_1pdf/Page13.pdf p. 13].
* [http://perso.numericable.fr/robert.marty/semiotique/anglais.htm Semiotics according to Robert Marty], with [http://perso.numericable.fr/robert.marty/semiotique/access.htm 76 definitions of the sign by C.&nbsp;S. Peirce].
*{{HABS |survey=PA-5198 |id=pa1422 |title=Charles S. Peirce House, U.S. Route 209, Milford, Pike County, PA |dwgs=1}}
* {{Librivox author |id=16492}}
* {{Gutenberg author | id=53264 | name=Charles S. Peirce}}

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