One insight arising from Peirce’s work on the mathematics underlying logic is that the operations on sets known as complementation, intersection, and union, along with the corresponding logical operations of negation, conjunction, and disjunction, are not as fundamental as they first appear.  That is because all of them can be constructed or derived from a smaller set of operations, in fact, taking the logical side of things, from either one of two sole sufficient operators called amphecks by Peirce, strokes by those who re‑discovered them later, and known in computer science as the operators nand and nnor.  Thus by virtue of their precedence in the orders of construction and derivation, the sole sufficient operators have to be regarded as the simplest and most primitive in principle, even if they are scarcely recognized as lying among the more familiar elements of logic.

Resources

• Cactus Language • Pragmatics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

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