(The undistorted figure is attached.) Ben wrote:
(100414-1)
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.
I thikn there are at least two kinds of triads an irreducible triad,
that may be denoted as A-B-C-A, such as Peirces semiosis, which can be
represented diagrammatically as a mathematical category as shown in Figure
1, and a dyadic triad consisting of a linear combination of two
dyadic relations, denoted as A-B-C, without the third relation
connecting these two relations as in A-B-C-A. In other words, Peirces
irreducible triad is characterized by the tree mappings, f, g and h, that
form a closed loop, whereas a dyadic triad lacks a closure, which is
equivalent to saying that it does not satisfy the composition condition of
the mathematical category.
f g
Object ------ > Sign ------> Intperpteretant
| ^
| |
|_____________________________________|
h
Figure 1. Semiosis as a mathematical category. Sign determines
interpretant (see g) in such a way that interpretant ends up having the
same relation with object (see h) that the sign itself has with the
object (see f). This is equivalent to saying that the composition
condition is satisfied, i.e.,
f x g = h.
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
> 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 [[email protected]]
>>>> Sent: Wednesday, October 01, 2014 7:44 PM
>>>> To: Peirce List 1
>>>> Subject: [PEIRCE-L] Re: Natural Propositions ââ¬Â¢ Selected Passages
>>
>>
>
>
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