Ben, list, It is my understanding that the mathematical category is another name for semiosis. In other words, a category is to mathematicians hat semiosis is to semioticians.
To quote Peirce from http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM: A "sign" is anything, A, which, (1) in addition to other characters of its own, (2) stands in a dyadic relation Þ, to a purely active correlate, B, (3) and is also in a triadic relation to B for a purely passive correlate, C, this triadic relation being such as to determine C to be in a dyadic relation, µ, to B, the relation µ corresponding in a recognized way to the relation Þ." I believe that this definition of a sign is isomorphic with the mathematical definition of a category. With all the best. Sung > Sungchul, list > > I know next to nothing about category theory. > > Most generally a triad is a trio. A predicate is called triadic if it > is predicated of three objects like so: /Pxyz/. In Peirce's system a > genuine triad is one involving irreducibly triadic action, called > semiosis, among three correlates: sign, object, and interpretant. > Trichotomy is three-way division, whether as process or as result. > > Best, Ben > > On 10/3/2014 2:04 PM, Sungchul Ji wrote: > >> Ben, Jeff, Jon, lists, >> >> 1) Can we say that there can be many triads, depending one how one >> defines them, but the Peircean triad is special and identical with a >> mathematical category ? >> >> 2) "Triad" is a system of three entities, while "trichotomy" is the >> process of dividing a system into three parts, either physically or >> mentally, the latter case of which is called "prescinding" by Peirce. >> >> With all the best. >> >> Sung >> __________________________________________________ >> Sungchul Ji, Ph.D. >> Associate Professor of Pharmacology and Toxicology >> Department of Pharmacology and Toxicology >> Ernest Mario School of Pharmacy >> Rutgers University >> Piscataway, N.J. 08855 >> 732-445-4701 >> >> www.conformon.net >> >> >> >>> Jeff D., Jon, >>> >>> I'd just like to note that the questions of triads versus trichotomies >>> is something that we've discussed a number of times at peirce-l over >>> the >>> years. For my part, I like using those words in the way that Jon and >>> others have recommended - 'triad' for the triadically related sign, >>> object, interpretant, which are involved as the correlates in genuinely >>> triadic action, and 'trichotomy' for three-fold classifications, >>> especially categorially correlated ones such as qualisign, sinsign, >>> legisign. However, it should be noted that there are passages in which >>> Peirce calls trichotomies 'triads', and other passages by Peirce that >>> make no sense unless one follows the 'triad'-versus-'trichotomy' >>> distinction. I don't have the quotes handy but we've been over it many >>> times. A separate issue is the one about whether the >>> sign-object-interpretant triad is also categorially correlated >>> trichotomy. >>> >>> Best, Ben >>> >>> On 10/1/2014 11:10 PM, Jeffrey Brian Downard wrote: >>> >>>> Hello Jon, >>>> >>>> If you have links to the earlier discussions of the distinction >>>> between >>>> "triadicities" and "trichotomies", I'd like to take a look. In >>>> addition >>>> to being interested in distinction you are making, I'd like to read >>>> more >>>> about how you are thinking about the projection of the triadic >>>> relations >>>> onto the mutually exclusive and exhaustive partitions of a domain. >>>> >>>> In his monograph <Reading Peirce Reading>, Richard Smyth makes much of >>>> the conceptions of the restrictions and limitations that apply to a >>>> given domain of inquiry. I'd like to see how your account of the >>>> partitions of the domain compares to his reconstruction of some >>>> arguments Peirce develops in "How to Make Our Ideas Clear." >>>> >>>> Thanks, >>>> >>>> Jeff >>>> >>>> Jeff Downard >>>> Associate Professor >>>> Department of Philosophy >>>> NAU >>>> (o) 523-8354 >>>> ________________________________________ >>>> From: Jon Awbrey [jawb...@att.net] >>>> Sent: Wednesday, October 01, 2014 7:44 PM >>>> To: Peirce List 1 >>>> Subject: [PEIRCE-L] Re: Natural Propositions ââ¬Â¢ Selected Passages >> >> > >
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
