Peirce’s 1903 Lowell Lectures • Comment 2

How Logic Got Its Blots

Cf: Laws Of Form DiscussionJA

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.

Re: Peirce List DiscussionGF

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 …

This entry was posted in C.S. Peirce, Diagrammatic Reasoning, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization and tagged , , , , , , , , , , , , . Bookmark the permalink.

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