ONT Re: Differential Logic -- Series A
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DLOG. Note A10
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| Consider what effects that might 'conceivably'
| have practical bearings you 'conceive' the
| objects of your 'conception' to have. Then,
| your 'conception' of those effects is the
| whole of your 'conception' of the object.
|
| Peirce, "Maxim of Pragmaticism",
| 'Collected Papers', CP 5.438.
The genealogy of this conception of pragmatic representation is very intricate.
I will delineate some details that I presently fancy I remember clearly enough,
subject to later correction. Without checking historical accounts, I will not
be able to pin down anything like a real chronology, but most of these notions
were standard furnishings of the 19th Century mathematical study, and only the
last few items date as late as the 1920's.
The idea about the regular representations of a group is universally known
as "Cayley's Theorem", usually in the form: "Every group is isomorphic to
a subgroup of Aut(X), the group of automorphisms of an appropriate set X".
There is a considerable generalization of these regular representations to
a broad class of relational algebraic systems in Peirce's earliest papers.
The crux of the whole idea is this:
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 contextual definition 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, page 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 know where that leads.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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