## Logical Graphs, Truth Tables, Venn Diagrams • 6

Dear John, Lyle,

See:  Ampheck

Peirce discovered this about 1880 but did not publish it, leaving it to be named after Sheffer at a much later date.  In one discussion Peirce used simple concatenation for the abstract operation which can be interpreted in two ways:  “Both Not” (joint denial, Nnor) or “Not Both” (alternate denial, Nand).  In the passage linked above Peirce used a symbol for Nnor whose nearest facsimiles in HTML are $``\curlywedge"$ (&curlywedge;) and “⥿” (&dfisht;), adding an overbar for Nand.  Peirce used 2 × 2 matrices to represent the truth tables of all 16 boolean operators then converted the matrices into cursive symbols for the operators.  Warren S. McCulloch mentioned Peirce’s discovery and his matrices, referring to Nand and Nnor collectively as “amphecks” on account of their abstract duality.

Regards,

Jon

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