Peirce’s Categories • 1

Re: Peirce ListJeffrey Brian Downard

Just from my experience, the best first approach to questions of firstness, secondness, thirdness, and so on is to regard k-ness as the property that all k-adic relations possess in common.  There is more to say once this first point is appreciated but it is critical to begin from this understanding.

It is best to view k-adic relations as whole sets of k-tuples rather than fixating on single k-tuples at a time since all the most relevant properties of relations are “holistic” properties of whole sets or whole systems that are not reducible to properties of their individual elements.

A k-adic relation and its converses, numbering k! possibilities in all, each bears essentially the same information about the relation of its domains.  This means that fixating on a particular ordering will tend to distract us with inessential features of a particular presentation rather than highlighting the essential properties of the relation in view.

Peirce demonstrates in several places that he appreciates the significance of these facts.

Just my k bits …

cc: Peirce List

This entry was posted in Abstraction, C.S. Peirce, Category Theory, Dimensionality, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatism, Relation Theory, Semiotics, Triadic Relations, Type Theory and tagged , , , , , , , , , , , , , , . Bookmark the permalink.

5 Responses to Peirce’s Categories • 1

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