View source for Categories (Peirce)

{{Short description|Philosophical concept}}
{{context|date=July 2017}} <!-- Does anyone still use this theory? Has it been replaced by anything else? -->
{{C. S. Peirce articles}}
On May 14, 1867, the 27–year-old [[Charles Sanders Peirce]], who eventually founded [[pragmatism]], presented a paper entitled "[[s:On a New List of Categories|On a New List of Categories]]" to the [[American Academy of Arts and Sciences]]. Among other things, this paper outlined a theory of predication involving three universal '''categories''' that Peirce continued to apply in philosophy and elsewhere for the rest of his life.<ref name=Burch>[[Burch, Robert W.]] (2001, 2010), "[http://plato.stanford.edu/entries/peirce/ Charles Sanders Peirce]", ''Stanford Encyclopedia of Philosophy''. See §9 "Triadism and the Universal Categories".</ref><ref name=Bergman>Bergman, Michael K. (2018), ''[https://www.springer.com/us/book/9783319980911 A Knowledge Representation Practionary: Guidelines Based on Charles Sanders Peirce]'', Springer Nature Switzerland AG, Cham, Switzerland. See Table 6.2 for about 60 examples throughout Peirce's career.</ref> The categories demonstrate and concentrate the pattern seen in "[[s:How to Make Our Ideas Clear|How to Make Our Ideas Clear]]" (1878, the foundational paper for [[pragmatism]]), and other three-way distinctions in Peirce's work.

==The Categories==
In Aristotle's logic, [[Categories (Aristotle)|categories]] are adjuncts to reasoning that are designed to resolve equivocations, ambiguities that make expressions or signs recalcitrant to being ruled by logic. Categories help the reasoner to render signs ready for the application of logical laws. An equivocation is a variation in meaning—a manifold of sign senses—such that, as Aristotle put it about names in the opening of ''[[Wikisource:Categories|Categories]]'' (1.1<sup>a</sup>1–12), "Things are said to be named 'equivocally' when, though they have a common name, the definition corresponding with the name differs for each." So Peirce's claim that three categories are sufficient amounts to an assertion that all manifolds of meaning can be unified in just three steps.

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

{{blockquote|
I will now say a few words about what you have called Categories, but for which I prefer the designation Predicaments, and which you have explained as predicates of predicates.

That wonderful operation of [[hypostatic abstraction]] by which we seem to create ''entia rationis'' that are, nevertheless, sometimes real, furnishes us the means of turning predicates from being signs that we think or think ''through'', into being subjects thought of. We thus think of the thought-sign itself, making it the object of another thought-sign.

Thereupon, we can repeat the operation of hypostatic abstraction, and from these second intentions derive third intentions. Does this series proceed endlessly? I think not. What then are the characters of its different members?

My thoughts on this subject are not yet harvested. I will only say that the subject concerns Logic, but that the divisions so obtained must not be confounded with the different Modes of Being: Actuality, Possibility, Destiny (or Freedom from Destiny).

On the contrary, the succession of Predicates of Predicates is different in the different Modes of Being. Meantime, it will be proper that in our system of diagrammatization we should provide for the division, whenever needed, of each of our three Universes of modes of reality into Realms for the different Predicaments. (Peirce 1906<ref>p. [https://books.google.com/books?id=3KoLAAAAIAAJ&pg=RA3-PA523&#PRA3-PA522,M1 522], "Prolegomena to an Apology for Pragmaticism", The ''Monist'', [https://books.google.com/books?id=3KoLAAAAIAAJ&pg=RA3-PA523&#PRA3-PA473,M1 vol. XVI, no. 4], Oct. 1906, pp. [https://books.google.com/books?id=3KoLAAAAIAAJ&pg=RA3-PA523&#PRA3-PA492,M1 492]–546, reprinted in the ''Collected Papers'' vol 4, paragraphs 530–572, see [http://www.existentialgraphs.com/peirceoneg/prolegomena.htm#Paragraph549 paragraph 549]. {{Webarchive|url=https://web.archive.org/web/20070905164710/http://www.existentialgraphs.com/peirceoneg/prolegomena.htm#Paragraph549 |date=2007-09-05 }}</ref>).
}}

The first thing to extract from this passage is the fact that Peirce's Categories, or "Predicaments", are predicates of predicates. Meaningful predicates have both ''[[Extension (semantics)|extension]]'' and ''[[intension]]'', so predicates of predicates get their meanings from at least two sources of information, namely, the classes of relations and the qualities of qualities to which they refer. Considerations like these tend to generate hierarchies of subject matters, extending through what is traditionally called the ''logic of second intentions'',<ref>Such "intentions" are more like [[intension]]s than like aims or purposings.</ref> or what is handled very roughly by ''[[second order logic]]'' in contemporary parlance, and continuing onward through higher intensions, or ''[[higher order logic]]'' and ''[[type theory]]''.

Peirce arrived at his own system of three categories after a thoroughgoing study of his predecessors, with special reference to the categories of Aristotle, Kant, and Hegel. The names that he used for his own categories varied with context and occasion, but ranged from reasonably intuitive terms like ''quality'', ''reaction'', and ''representation'' to maximally abstract terms like ''firstness'', ''secondness'', and ''thirdness'', respectively. Taken in full generality, ''nth''-ness can be understood as referring to those properties that all ''n''-adic relations have in common. Peirce's distinctive claim is that a type hierarchy of three levels is generative of all that we need in logic.

Part of the justification for Peirce's claim that three categories are both necessary and sufficient appears to arise from mathematical ideas about the [[Relation reduction|reducibility]] of ''n''-adic relations. According to Peirce's Reduction Thesis,<ref>See "The Logic of Relatives," The ''Monist'', vol. 7, 1897, pp. [https://books.google.com/books?id=pa0LAAAAIAAJ&pg=PA554&#PPA161,M1 161]-217, see [https://books.google.com/books?id=pa0LAAAAIAAJ&pg=PA554&#PPA183,M1 p. 183] (via Google Books with registration apparently not required). Reprinted in the ''Collected Papers'', vol. 3, paragraphs 456-552, see paragraph 483.</ref> (a) triads are necessary because genuinely triadic relations cannot be completely analyzed in terms of monadic and dyadic predicates, and (b) triads are sufficient because there are no genuinely tetradic or larger polyadic relations—all higher-[[arity]] ''n''-adic relations can be analyzed in terms of triadic and lower-arity relations. Others, notably Robert Burch (1991), Joachim Hereth Correia and Reinhard Pöschel (2006), have offered proofs of the Reduction Thesis.<ref>* Burch, Robert (1991), ''A Peircean Reduction Thesis: The Foundations of Topological Logic'', Texas Tech University Press, Lubbock, TX.
* [[Irving Anellis|Anellis, Irving]] (1993) "Review of ''A Peircean Reduction Thesis: The Foundations of Topological Logic'' by Robert Burch" in ''Modern Logic'' v. 3, n. 4, 401-406, Project Euclid Open Access [http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204835124 PDF 697 KB]. Criticism and some suggestions for improvements.
* Anellis, Irving (1997), "Tarski's Development of Peirce's Logic of Relations" (''Google Book Search'' [https://books.google.com/books?id=pWjOg-zbtMAC&pg=PA271&vq=%22Reduction+thesis%22 Eprint]) in Houser, Nathan, Roberts, Don D., and Van Evra, James (eds., 1997), ''Studies in the Logic of Charles Sanders Peirce''. Anellis gives an account of a Reduction Thesis proof discussed and presented by Peirce in his letter to William James of August 1905 (L224, 40-76, printed in Peirce, C. S. and Eisele, Carolyn, ed. (1976), ''The New Elements of Mathematics by Charles S. Peirce'', v. 3, 809-835).
* [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Correia:Joachim_Hereth.html Hereth Correia, Joachim] and Pöschel, Reinhard (2006), "The Teridentity and Peircean Algebraic Logic" in ''Conceptual Structures: Inspiration and Application'' (ICCS 2006): 229-246, [[doi:10.1007/11787181_17|Springer]]. Frithjof Dau [http://www.nabble.com/Re%3A-Peircean-Reduction-Thesis-Was%3A-CG%3A-typical-distribution-of-arities--p11722802.html calls it]  "the strong version" of proof of Peirce's Reduction Thesis. {{Webarchive|url=https://archive.today/20130104115012/http://www.nabble.com/Re:-Peircean-Reduction-Thesis-Was:-CG:-typical-distribution-of-arities--p11722802.html|date=2013-01-04}}. John F. Sowa in the same discussion [http://www.nabble.com/Re%3A-Peircean-Reduction-Thesis-Was%3A-CG%3A-typical-distribution-of-arities--p11712058.html claimed]  that an explanation in terms of conceptual graphs is sufficiently convincing about the Reduction Thesis for those without the time to understand what Peirce was saying. {{Webarchive|url=https://archive.today/20130104021034/http://www.nabble.com/Re:-Peircean-Reduction-Thesis-Was:-CG:-typical-distribution-of-arities--p11712058.html|date=2013-01-04}}.
* In 1954 [[Willard Van Orman Quine|W. V. O. Quine]] claimed to prove the reducibility of larger predicates to dyadic predicates, in Quine, W.V.O., "Reduction to a Dyadic Predicate", ''Selected Logic Papers''.</ref>

There have been proposals by Donald Mertz, Herbert Schneider, Carl Hausman, and Carl Vaught to augment Peirce's threefolds to fourfolds; and one by Douglas Greenlee to reduce the system of three categories to two.<ref>For references and discussion, see Burgess, Paul (circa 1988) "Why Triadic? Challenges to the Structure of Peirce's Semiotic"; posted by [[Joseph Morton Ransdell|Joseph M. Ransdell]] at ''[http://www.cspeirce.com/menu/library/aboutcsp/pr-main.htm#Burgess Arisbe]''.</ref>

Peirce introduces his Categories and their theory in [[wikisource:On_a_New_List_of_Categories|"On a New List of Categories" (1867)]], a work which is cast as a Kantian deduction and is short but dense and difficult to summarize. The following table is compiled from that and later works.
{{C. S. Peirce categorial table}}
(The context for interpretants is not psychology or sociology, but instead philosophical logic. In a sense, an interpretant is whatever can be understood as a conclusion of an inference. The context for the categories as categories is phenomenology, which Peirce also called phaneroscopy and categorics.)

==See also==
*[[Trikonic]]

==Notes==
<references />

==Bibliography==
* Peirce, C.S. (1867), "On a New List of Categories", ''Proceedings of the American Academy of Arts and Sciences'' 7 (1868), 287–298. Presented, 14 May 1867. Reprinted (''Collected Papers'', vol. 1, paragraphs 545–559), (''The Essential Peirce'', vol. 1, pp.&nbsp;1–10), (''Chronological Edition'', vol. 2, pp.&nbsp;49–59), [http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm Eprint]. {{Webarchive|url=https://web.archive.org/web/20070928062849/http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm |date=2007-09-28 }}.
* Peirce, C.S. (1885), "One, Two, Three: Fundamental Categories of Thought and of Nature", Manuscript 901; the ''Collected Papers'', vol. 1, paragraphs 369-372 and 376-378 parts; the ''Chronological Edition'', vol. 5, 242-247.
* Peirce, C.S. (1887–1888), "A Guess at the Riddle", Manuscript 909; ''The Essential Peirce'', vol. 1, pp.&nbsp;245–279; [http://www.cspeirce.com/menu/library/bycsp/guess/guess.htm Eprint]. {{Webarchive|url=https://web.archive.org/web/20080709050417/http://www.cspeirce.com/menu/library/bycsp/guess/guess.htm |date=2008-07-09 }}.
* Peirce, C.S. (1888), "Trichotomic", The ''Essential Peirce'', vol. 1, p.&nbsp;180.
* Peirce, C.S. (1893), "The Categories", Manuscript 403 {{cite web |url= http://www.cspeirce.com/menu/library/bycsp/ms403/ms403.pdf |title= Eprint |access-date= 2007-10-02 |archive-date= 2007-09-28 |archive-url= https://web.archive.org/web/20070928062924/http://www.cspeirce.com/menu/library/bycsp/ms403/ms403.pdf |url-status= dead }}&nbsp;{{small|(177&nbsp;[[Kibibyte|KiB]])}} An incomplete rewrite by Peirce of his 1867 paper "On a New List of Categories". Interleaved by Joseph Ransdell (ed.) with the 1867 paper itself for purposes of comparison.
* Peirce, C.S., ({{circa|1896}}), "The Logic of Mathematics; An Attempt to Develop My Categories from Within", the ''Collected Papers'', vol. 1, paragraphs 417–519. [http://www.textlog.de/4267.html Eprint].
* Peirce, C.S., "Phenomenology" (editors' title for collection of articles), The ''Collected Papers'', vol. 1, paragraphs 284-572 [http://www.textlog.de/4254.html Eprint].
* Peirce, C.S. (1903), "The Categories Defended", the third Harvard Lecture: The ''Harvard Lectures'' pp.&nbsp;167–188; the ''Essential Peirce'', vol. 1, pp.&nbsp;160–178; and partly in the ''Collected Papers'', vol. 5, paragraphs 66-81 and 88–92.
* [[Charles Sanders Peirce bibliography]].

==External links==
{{Refbegin|colwidth=25em}}
* [https://arisbe.sitehost.iu.edu/ Arisbe: The Peirce Gateway], Joseph Ransdell, ed. Over 100 online writings by Peirce as of November 24, 2010, with annotations. 100s of online papers on Peirce. The Peirce-L Forum. Much else.
* [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|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=2013-09-08 }}, 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.  of all issues.
* [http://www.peirce.org/ Charles S. Peirce Studies], Brian Kariger, ed.
*{{MathGenealogy|id=24099}}.
* [http://translate.google.com/translate?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|U. of {{lang|pt|Campinas}}]], Brazil, in English. 84 authors listed, 51 papers online & more listed, as of January 31, 2009. Newer edition now at [[#CDPT|Commens]].
* [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 {{lang|de|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|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 W 2] readable online.<br>—[https://web.archive.org/web/20160304044756/http://www.pep.uqam.ca/definitionoftheweek.pep PEP's branch at {{lang|fr|Université du Québec à Montréal (UQÀM)}}]. Working on W 7: Peirce's work on the ''Century Dictionary''. .
* [http://www.dr-dau.net/eg_readings.shtml Peirce's Existential Graphs], Frithjof Dau, Germany.
* [http://www.chass.utoronto.ca/epc/srb/cyber/espout.html Peirce's Theory of Semiosis: Toward a Logic of Mutual Affection], Joseph Esposito. Free online course.
* [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, Universi