Re: Triadic Relations

Re: Howard Pattee
At: http://permalink.gmane.org/gmane.science.philosophy.peirce/15155

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

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