Categories (Peirce)

On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled " 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.Burch, Robert (2001, 2010),
Charles Sanders Peirce
, ''Stanford Encyclopedia of Philosophy''. See §9 "Triadism and the Universal Categories".Bergman, Michael K. (2018),
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. The categories demonstrate and concentrate the pattern seen in " 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 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 '' Categories'' (1.1^a1–12), "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:

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'' 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'', 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 reducibility of ''n''-adic relations. According to Peirce's Reduction Thesis, (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.

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 them to twofolds.For references and discussion, see Burgess, Paul (circa 1988) "Why Triadic?: Challenges to the Structure of Peirce's Semiotic"; posted by Joseph M. Ransdell at
Arisbe
'.

Peirce introduces his Categories and their theory in "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.

(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

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. 1–10), (''Chronological Edition'', vol. 2, pp. 49–59)
Eprint

* 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. 245–279

* Peirce, C.S. (1888), "Trichotomic", The ''Essential Peirce'', vol. 1, p. 180.
* Peirce, C.S. (1893), "The Categories", Manuscript 403   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., (), "The Logic of Mathematics; An Attempt to Develop My Categories from Within", the ''Collected Papers'', vol. 1, paragraphs 417–519

* Peirce, C.S., "Phenomenology" (editors' title for collection of articles), The ''Collected Papers'', vol. 1, paragraphs 284-57

* Peirce, C.S. (1903), "The Categories Defended", the third Harvard Lecture: The ''Harvard Lectures'' pp. 167–188; the ''Essential Peirce'', vol. 1, pp. 160–178; and partly in the ''Collected Papers'', vol. 5, paragraphs 66-81 and 88–92.
* Charles Sanders Peirce bibliography

External links

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 e-forum. Much else.

Center for Applied Semiotics (CAS)
(1998–2003), Donald Cunningham & Jean Umiker-Sebeok, Indiana U.
* and previously et al., Pontifical Catholic U. of (PUC-SP), Brazil. In Portuguese, some English.

Commens Digital Companion to C.S. Peirce
Mats Bergman, Sami Paavola, & , formerl

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 ( old edition still at old website).

Peirce
Carlo Sini, Rossella Fabbrichesi, et al., U. of Milan, Italy. In Italian and English. Part o
Pragma


Charles S. Peirce Foundation
Co-sponsoring the 2014 Peirce International Centennial Congress (100th anniversary of Peirce's death).

Charles S. Peirce Society
br>—

'. Quarterly journal of Peirce studies since spring 1965

of all issues.

Charles S. Peirce Studies
Brian Kariger, ed.
*

Collegium for the Advanced Study of Picture Act and Embodiment
The Peirce Archive. Humboldt U, Berlin, Germany. Cataloguing Peirce's innumerable drawings & graphic materials
More info
(Prof. Aud Sissel Hoel).

Digital Encyclopedia of Charles S. Peirce

now at UFJF
& Ricardo Gudwin
at Unicamp
, eds., U. of , Brazil, in English. 84 authors listed, 51 papers online & more listed, as of January 31, 2009. Newer edition now at Commens.

Existential Graphs
Jay Zeman, ed., U. of Florida. Has 4 Peirce texts.
* , ed., U. of Navarra, Spain. Big study site, Peirce & others in Spanish & English, bibliography, more.

Helsinki Peirce Research Center
(HPRC), Ahti-Veikko Pietarinen et al., U. of Helsinki.

His Glassy Essence
Autobiographical Peirce. Kenneth Laine Ketner.

Institute for Studies in Pragmaticism
Kenneth Laine Ketner, Clyde Hendrick, et al., Texas Tech U. Peirce's life and works.

International Research Group on Abductive Inference
et al., eds., U., Frankfurt, Germany. Uses frames. Click on link at bottom of its home page for English. Moved to U. of , Germany
home page
not in English but see Artikel section there.


(1974–2003)—, U. of , France.

Minute Semeiotic
, U. of , Brazil. English, Portuguese.

Peirce
at ''Signo: Theoretical Semiotics on the Web'', Louis Hébert, director, supported by U. of Québec. Theory, application, exercises of Peirce'
Semiotics
an
Esthetics
English, French.

Peirce Edition Project (PEP)
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:
—Biographical introductions t

an



br>â

readable online.
â
PEP's branch at
Working on W 7: Peirce's work on the ''Century Dictionary''
Definition of the week


Peirce's Existential Graphs
Frithjof Dau, Germany


Joseph Esposito. Free online course.

Pragmatism Cybrary
David Hildebrand & John Shook.


(late 1990s), Germany). See ''Peirce Project Newsletter'' v. 3, n. 1
p. 13



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{{Refend

Philosophical logic
Phenomenology
Charles Sanders Peirce
Philosophical categories