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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