Jon,
An interesting post. I remember reading the quote about 5 years ago
somewhere.
The dative verb "give" nicely illustrates an irreducibly triadic relation
(Figure 1) as compared to the sum of two dyadic relations (Figure 2):
(1) Irreducibly triadic: A gives B to C (or A gives C B) which can be
diagrammed as:
f g
A -------> B ------> C
| ^
| |
|_______________|
h
Figure 1. Giving as a category, since f x g = h, where f = A let go of B;
g = B becomes the p[ossesion of D; h = A intended B to be possessed by C
(and not by a stranger).
(2) Sum of two independent dyadic relations: A let go of B which happens
to be possessed by C which can be diagrammed as:
f g
A ------- > B --------> C
Figure 2. Two independent dyadic relations connected only by f and g,
where f = B leaving A, and g = B falling in the hands of C.
With all the best.
Sung
On Wed, Feb 4, 2015 at 2:36 PM, Edwina Taborsky <[email protected]> wrote:
> I'm not sure, Jon, what your point is, in this post. Although there may be
> six 'mechanical' ways of relating three 'logical subjects', the reality of
> Mind as represented in the modal categories differentiates them by function.
>
> Edwina
>
> ----- Original Message ----- From: "Jon Awbrey" <[email protected]>
> To: "Peirce List" <[email protected]>
> Sent: Wednesday, February 04, 2015 1:45 PM
> Subject: [PEIRCE-L] Six Ways Of Looking At A Triadic Relation ⌬ 1
>
>
> Post : Six Ways Of Looking At A Triadic Relation ⌬ 1
>> http://inquiryintoinquiry.com/2015/02/04/six-ways-of-
>> looking-at-a-triadic-relation-%e2%8c%ac-1/
>> Posted : February 4, 2015 at 1:00 pm
>> Author : Jon Awbrey
>>
>> Peircers,
>>
>> Here's a triadic factoid from the 1903 Harvard Lectures on Pragmatism
>> that raises a number of important questions for me. I isolated Peirce's
>> observation about the "ordinary logic of relations" from the context of
>> his
>> remarks that follow, partly in order to render the puzzle more striking.
>> There's better copy on my blog, and I'll copy out more as I get time.
>>
>> ---
>>
>> A triadic relation has 3! = 6 ''converses'', six grammatically and
>> rhetorically different ways of representing what is
>> logically the same information. Peirce illustrates the situation as
>> follows, with six variations on the theme of giving.
>>
>> <blockquote>
>>
>> So in a triadic fact, say, for example
>>
>> A gives B to C
>>
>> we make no distinction in the ordinary logic of relations between the
>> ''subject nominative'', the ''direct object'', and
>> the ''indirect object''. We say that the proposition has three ''logical
>> subjects''. We regard it as a mere affair of
>> English grammar that there are six ways of expressing this:
>>
>> A gives B to C
>> A benefits C with B
>> B enriches C at expense of A
>> C receives B from A
>> C thanks A for B
>> B leaves A for C
>>
>> These six sentences express one and the same indivisible phenomenon.
>>
>> </blockquote>
>>
>> References
>>
>> * Peirce, C.S., “The Categories Defended”, Harvard Lectures on Pragmatism
>> : Lecture 3 (MS 308, delivered on 9 April
>> 1903). Published in Collected Papers (CP 5.66–81, 88–92, in part),
>> Harvard Lectures (HL 167–188), Essential Peirce :
>> Volume 2 (EP 2, 160–178).
>>
>> * Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6,
>> Charles Hartshorne and Paul Weiss (eds.), vols.
>> 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA,
>> 1931–1935, 1958. Volume 5 : Pragmatism and
>> Pragmaticism, 1934. (Cited as CP).
>>
>> * Peirce, C.S., Pragmatism as a Principle and Method of Right Thinking :
>> The 1903 Harvard Lectures on Pragmatism,
>> Patricia Ann Turrisi (ed.), State University of New York Press, Albany,
>> NY, 1997. (Cited as HL).
>>
>> Peirce, C.S., The Essential Peirce : Selected Philosophical Writings,
>> Volume 2 (1893–1913), Peirce Edition Project
>> (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1998.
>> (Cited as EP 2).
>>
>> Add a comment to this post:
>> http://inquiryintoinquiry.com/2015/02/04/six-ways-of-
>> looking-at-a-triadic-relation-%e2%8c%ac-1/#respond
>>
>> ---
>>
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>>
>>
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Sungchul Ji, Ph.D.
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Department of Pharmacology and Toxicology
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