[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 63

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Arisbe List, Cybernetics List,

Still speaking generally, the hermeneutic hedge about reflection
that runs, "it must be possible to interpret certain elements of
the ordered system as making statements about the order in which
they reside", should serve to remind us of the hidden catch that
the forms of interpretation that manifest reflection of an order
on itself may not be obvious at first sight, but will in general
have to be sought out by abductive reason, "by hook or by crook".

But speaking more specifically about orders of systems so simple
as alpha graphs, propositional calculus, zeroth order logic, and
their ilk, we find at least some modes of reflection that strike
the mind's eye right off as being manifestly natural and obvious.

For instance, propositions over a finitary universe of discourse,
of the order that we see illustrated in euler-venn diagrams, are
ordered by the relation of implication, making "=>" analogous to
the generic order relation "less than or equal to", notated "=<".

But those statements about the implicational order relation that
take the form "p => q" are themselves statements that have their
place within that very same implicational order relation.  Hence,
propositional logic has a moderate degree of reflective capacity.

Jon Awbrey

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