Thread:
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15622
ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15623
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15625
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/15626
ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15627
SJ:http://permalink.gmane.org/gmane.science.philosophy.peirce/15628
Sung,
Your commutative triangle represents the decomposition of a function h
(which is a dyadic relation) as the functional composition of two other
functions f and g (which are also dyadic relations). This pictures the
decomposability, factoring, or reducibility of a dyadic relation and has
nothing to do with the irreducibility of any triadic relations. Nor does
it picture a category, it is only one commutative triangle in a category.
Regards,
Jon
On 2/4/2015 4:14 PM, Sungchul Ji wrote:
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 possesion 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).
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