One of those recurring themes — you might call it “The Power of Negative Thinking” — arose this time on the Peirce List and it took me back to a post I wrote nine Aprils ago and that took me even further back to the very doors I first walked through into the wonderland of logic à la Peirce.
I fixed the links broken by the ravages of time and the impings of web developers and I added more links to the original context of discussion. A partial transcript follows.
Not too coincidentally with the mention of Peirce’s existential graphs, a tangent of discussion elsewhere brought to mind an old favorite passage from Peirce, where he is using his entitative graphs to expound the logic of relatives. Here is the observation 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.
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 —