Sunday, March 18, 2007

Sunday March 18, 2007

Filed under: General,Geometry — m759 @ 2:20 PM

Update to
The Geometry of Logic:

A detailed description of a group of 16 “logical automorphisms” of the 16 binary connectives has been given in the paper “Simetria y Logica: La notacion de Peirce para los 16 conectivos binarios,” by Mireya Garcia, Jhon Fredy Gomez, and Arnold Oostra. (Published in the Memorias del XII Encuentro de Geometria y sus Aplicaciones, Universidad Pedagogica Nacional, Bogota, June 2001; on the Web at http://www.unav.es/gep/Articulos/SimetriaYLogica.pdf.) The authors do not identify this group as a subgroup of the affine group of A (the finite affine geometry of four dimensions over the two-element field); this can serve as an exercise.  Another exercise: determining whether the authors’ order-16 group includes all transformations that might reasonably be called “logical automorphisms” of the 16 binary connectives.

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