Howard,
In the best mathematical terms, a triadic relation is a cartesian product of
three sets together with a specified subset of that cartesian product.
Alternatively, one may think of a triadic relation as a set of 3-tuples
contained in a specified cartesian product.
It is important to recognize that sets have formal properties that their
elements do not. The greatest number of category mistakes that bedevil
untutored discussions of relations and especially triadic sign relations arise
from a failure to grasp this fact.
For example, irreducibility (or indecomposability) of triadic relations is a
property of sets-of-triples, not of individual triples. (At least, not the
kinds of irreducibility that we are usually talking about in these context.)
See the articles under the following subhead for concrete examples and further
discussion:
http://intersci.ss.uci.edu/wiki/index.php/Logic_Live#Relational_concepts
Regards,
Jon
Howard Pattee wrote:
At 02:07 PM 12/16/2014, Gary Fuhrman wrote:
The reason that "people keep saying you [Edwina] support dyads" is
that your three "relations" have only two "members" each, to use
Peirce's term. A triadic relation has three members, not two; and a
complexus of three dyadic (two-member) relations is not, according to
Peirce, "a triadic relation."
All these claims are unclear to me. Why are these two descriptions
inconsistent? Is there a graph theory representation of a triadic
relation that does not have a dyadic subgraph?
Howard
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