March 18, 2007

  • The Symmetries of Logic

    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.