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 three universal categories that Peirce would apply throughout philosophy and elsewhere for the rest of his life. Most who have studied Peirce will readily agree about their importance in his work. In the categories one will discern, concentrated, the pattern which one finds formed by the three grades of clearness in " [http://www.cspeirce.com/menu/library/bycsp/ideas/id-frame.htm How To Make Our Ideas Clear] " (1878 foundational paper for pragmatism), and in numerous other three-way distinctions in his work.

The Categories

In Aristotle's logic, categories are adjuncts to reasoning that are designed to resolve equivocations and thus to prepare ambiguous signs, that are otherwise recalcitrant to being ruled by logic, for the application of logical laws. An equivocation is a variation in meaning — a manifold of sign senses — such that, as Aristotle put it about names in the opening of "" (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:

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 [p. [http://books.google.com/books?id=3KoLAAAAIAAJ&pg=RA3-PA523&#PRA3-PA522,M1 522] , "Prolegomena to an Apology for Pragmaticism", The "Monist", [http://books.google.com/books?id=3KoLAAAAIAAJ&pg=RA3-PA523&#PRA3-PA473,M1 vol. XVI, no. 4] , Oct. 1906, pp. [http://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] ] ).

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" [Such "intentions" are more like intensions than like aims or purposings.] , 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 [See "The Logic of Relatives," The "Monist", Vol. 7, 1897, p [http://books.google.com/books?id=pa0LAAAAIAAJ&pg=PA554&#PPA161,M1 p. 161] -217, see [http://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.] , (a) triads are necessary because genuinely triadic relations cannot be completely analyzed in terms or 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 have offered proofs of the Reduction Thesis. [The most recent effort is by [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Correia:Joachim_Hereth.html Joachim Hereth Correia] , Reinhard Pöschel: The Teridentity and Peircean Algebraic Logic. ICCS 2006: 229-246.]

Peirce introduces his Categories and their theory in [http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm "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. "*Note:" An interpretant is the product of an interpretive process, or the content of an interpretation. 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.

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), [http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm 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; [http://www.cspeirce.com/menu/library/bycsp/guess/guess.htm Eprint]
* Peirce, C.S. (1888), "Trichotomic", The "Essential Peirce", vol. 1, p. 180.
* Peirce, C.S. (1893), "The Categories", Manuscript 403 PDFlink| [http://www.cspeirce.com/menu/library/bycsp/ms403/ms403.pdf Eprint] |177 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., (c. 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. 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

* [http://www.cspeirce.com/ Arisbe: The Peirce Gateway] , Joseph Ransdell (ed.)
* [http://www.helsinki.fi/science/commens/dictionary.html Commens Dictionary of Peirce Terms] , Mats Bergman & Sami Paavola (eds.)
* List of external links at main Peirce wiki.