[Inquiry] Re: Dynamics And Logic

[Jon Awbrey]

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DAL.  Note 20

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You may be wondering what happened to the announced subject
of "Dynamics And Logic".  What occurred was a bit like this:

We happened to make the observation that the shift operators {E_ij}
form a transformation group that acts on the set of propositions of
the form f : B x B -> B.  Group theory is a very attractive subject,
but it did not draw us so far from our intended course as one might
initially think.  For one thing, groups, especially the groups that
are named after the Norwegian mathematician Marius Sophus Lie, turn
out to be of critical importance in solving differential equations.
For another thing, group operations provide us with an ample supply
of triadic relations that have been extremely well-studied over the
years, and thus they give us no small measure of useful guidance in
the study of sign relations, another brand of 3-adic relations that
have significance for logical studies, and in our acquaintance with
which we have scarcely begun to break the ice.  Finally, I couldn't
resist taking up the links between group representations, amounting
to the very archetypes of logical models, and the pragmatic maxim.

Biographical Data for Marius Sophus Lie (1842-1899):
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lie.html

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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