## The Difference That Makes A Difference That Peirce Makes : 24

The concepts of closure and idempotence are closely related.

We usually speak of a closure operator in contexts where the objects acted on are the primary interest, as in topology, where the objects of interest are open sets, boundaries, closed sets, etc.  In contexts where we abstract away from the operand space, as in algebra, we tend to say idempotence for the detached application $\mathrm{CC} = \mathrm{C}.$  (If I recall right, it was actually Charles Peirce’s father Benjamin who coined the term idempotence.)

At any rate, I’ll have to mutate the principle a bit to cover the uses Peirce makes of it.

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