[Inquiry] Re: Dynamics And Logic

[Jon Awbrey]

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DAL.  Note 13

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The above-mentioned fact about the regular representations
of a group is universally known as "Cayley's Theorem".  It
is usually stated in the form:  "Every group is isomorphic
to a subgroup of Aut(X), where X is a suitably chosen set
and Aut(X) is the group of its automorphisms".  There is
in Peirce's early papers a considerable generalization
of the concept of regular representations to a broad
class of relational algebraic systems.  The crux of
the whole idea can be summed up as follows:

   Contemplate the effects of the symbol
   whose meaning you wish to investigate
   as they play out on all the stages of
   conduct on which you have the ability
   to imagine that symbol playing a role.

This idea of definition by way of context transforming operators
is basically the same as Jeremy Bentham's notion of "paraphrasis",
a "method of accounting for fictions by explaining various purported
terms away" (Quine, in Van Heijenoort, 'From Frege to Gödel', p. 216).
Today we'd call these constructions "term models".  This, again, is
the big idea behind Schönfinkel's combinators {S, K, I}, and hence
of lambda calculus, and I reckon you all know where that leads.

Jon Awbrey

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