Re: Category Theory • Chad Nester

CN:

Recently a few of us have been using the “cartesian bicategories of relations” of Carboni and Walters, in particular their string diagrams, as syntax for relations.  The string diagrams in question are more or less a directed version of Peirce’s lines of identity.  They’re usually described in terms of commutative special frobenius algebras.  I suspect the reason we keep finding commutative special frobenius algebras is that they support lines of identity in this way.

Dear Chad, Henry, …

Chaos rules my niche of the world right now so I’ll just break a bit of the ice by sharing the following links to my ongoing study of Peirce’s 1870 Logic Of Relatives.

• Peirce’s 1870 LOR • Overview • Part 1 • Part 2 • Part 3 • References

See especially the following paragraph.

• Peirce • CP 3.93

To my way of thinking the above paragraph is one of the most radical passages in the history of logic, relativizing traditional assumptions of an absolute distinction between generals (universals) and individuals.  Among other things, it pulls the rug out from under any standing for nominalism as opposed to realism about universals.

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Logical Graphs • Laws of Form • Peirce List