Cf: Paradisaical Logic and the After Math • Comment 1
Re: Peter Cameron • Cultures, Tribes, or Just an Illusion?
Re: Peirce List
One of many 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 piece 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.
Paradisaical Logic and the After Math
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.
Which brings us to Peirce’s amphecks, NAND and NNOR,
either of which is a sole sufficient operator for
all boolean operations.
Amphecks ( https://oeis.org/wiki/Ampheck
NAND ( https://oeis.org/wiki/Logical_NAND
NNOR ( https://oeis.org/wiki/Logical_NNOR
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 —
C.S. Peirce • Relatives of Second Intention
Logic Syllabus ( https://oeis.org/wiki/Logic_Syllabus
Peirce’s 1870 Logic Of Relatives