Structure and Logic
The phrase "structural logic" in yesterday's entry was applied to
Bach's cello suites. It may equally well be applied to
geometry. In particular:
"The aim of this thesis is to classify certain structures which
are, from a certain point of view, as homogeneous as possible, that is
which have as many symmetries as possible."
-- Alice Devillers, "Classification of Some Homogeneous and Ultrahomogeneous Structures," Ph.D. thesis, Université Libre de Bruxelles, academic year 2001-2002
Related material:
In Devillers's words, the above spaces with 8 and
16 points are among those structures that have "as many symmetries as
possible." For more details on what this means, see Devillers's thesis and Finite Geometry of the Square and Cube.
16 points are among those structures that have "as many symmetries as
possible." For more details on what this means, see Devillers's thesis and Finite Geometry of the Square and Cube.
The above models for the corresponding projective spaces may be regarded as illustrating the phrase "structural logic."
For a possible application of the 16-point space's "many symmetries" to logic proper, see The Geometry of Logic.
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