How Logic Got Its Blots
Taking positive implication as a basic construct, as Peirce does in the lectures at hand, one has to find a way to rationalize the introduction of negative concepts, in the first instance, logical negation and a logical constant for falsity. Questions about this naturally arose in the Peirce List reading, prompting me to make the following comment on Peirce’s just-so-story, especially as it bears on the link between primary arithmetic and primary algebra.
Peirce’s introduction of the “blot” at this point as a logical constant for absurdity or falsity is one of the places where he touches on the arithmetic of logic underlying the algebra of logic, a development that began with his taking up the empty sheet of assertion, a tabula rasa or uncarved block, as a logical constant for truth.
The radical insight involved in this move would later be emphasized by George Spencer Brown when he revived Peirce’s graphical approach to logic in the late 1960s.
More to follow, as I find the opportunity …