Cf: Sign Relations • Dyadic Aspects
At:
http://inquiryintoinquiry.com/2020/06/21/sign-relations-%e2%80%a2-dyadic-aspects/
We take up the dyadic aspects of triadic relations ...
For an arbitrary triadic relation L ⊆ O × S × I, whether it is a sign relation or not, there are six dyadic relations
obtained by projecting L on one of the planes of the OSI-space O × S × I. The six dyadic projections of a triadic
relation L are defined and notated as shown in Table 2.
Table 2. Dyadic Aspects of Triadic Relations
https://inquiryintoinquiry.files.wordpress.com/2020/06/dyadic-projections-of-triadic-relations.png
By way of unpacking the set-theoretic notation, here is what the first
definition says in ordinary language.
The dyadic relation resulting from the projection of L on the OS-plane O × S is written briefly as L_OS or written more
fully as proj_OS (L) and is defined as the set of all ordered pairs (o, s) in the cartesian product O × S for which
there exists an ordered triple (o, s, i) in L for some interpretant i in the interpretant domain I.
In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some
of the dyadic aspects of L can be recognized as formalizing aspects of sign meaning which have received their share of
attention from students of signs over the centuries, and thus they can be associated with traditional concepts and
terminology. Of course, traditions may vary as to the precise formation and usage of such concepts and terms. Other
aspects of meaning have not received their fair share of attention, and thus remain anonymous on the contemporary scene
of sign studies.
References
==========
• Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75),
in Carolyn Eisele (ed., 1976), The New Elements of Mathematics
by Charles S. Peirce, vol. 4, 13–73.
https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm
• Awbrey, J.L., and Awbrey, S.M. (1995),
“Interpretation as Action : The Risk of Inquiry”,
Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.
https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html
https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
Resources
=========
• Semeiotic ( https://oeis.org/wiki/Semeiotic )
• Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
• Sign Relations ( https://oeis.org/wiki/Sign_relation )
• Triadic Relations ( https://oeis.org/wiki/Triadic_relation )
* Relation Theory ( https://oeis.org/wiki/Relation_theory )
Regards,
Jon
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