Not too coincidentally with the mention of Peirce’s existential graphs, a tangent of discussion on another blog brought to mind an old favorite passage from Peirce, where he is using his entitative graphs to exposit the logic of relatives. Here is the observation that I was led to make:
Negative operations (NOs), if not more important than positive operations (POs), are at least more powerful or generative, because the right NOs can generate all POs, but the reverse is not so.
Which brings us to Peirce’s amphecks, NAND and NNOR, either of which is a sole sufficient operator for all boolean operations.
In one of his developments of a graphical syntax for logic, that described in passing an application of the Neither-Nor operator, Peirce referred to the stage of reasoning before the encounter with falsehood as “paradisaical logic, because it represents the state of Man’s cognition before the Fall.”
Here’s a bit of what he wrote there —