[Inquiry] Re: Information = Comprehension x Extension -- Discussion

[Jon Awbrey]

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ICE.  Discussion Note 33

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Up to this point I have been exploiting as much as I could
in the way of familiar logical notions in order to explain
Peirce's statements about information and its relationship
to comprehension and extension.  But that's the end of the
easy pickings, and we have reached the edge of what can be
mapped out and patched together in such a piecemeal manner
without forcing too much of a warp into Peirce's picture.

My strategy from this point on will be exploratory.  I will be seeking
concrete, hopefully intuitive, and maximally simple models of Peirce's
hints toward a theory of qualitative information.  There are two tasks
that face us at the present juncture, at any rate, so far as I can see.

1.  I need to discuss some of the problems that have already arisen
    at this point, and to explore a number of ways to deal with them.

    Most of the ways that suggest themselves for tackling these obstacles,
    at least, that come most naturally to mind from a Peircean standpoint,
    involve moving up from the 2-adic relations of partially ordered sets
    like lattices to the 3-adic relations of parametrically ordered sets,
    also known as "interpretive orders" or "relatively ordered sets".
    
2.  I need to develop some background material on what we may call,
    at any rate, for the time being, by one of the following names:
    (a) higher order propositions, (b) measures on propositions,
    (c) propositions about propositions, (d) qualifiers.

    Under the aspect of measures on propositions, we will find
    logical analogues of the usual measures of quantities like
    entropy and information.

Anyway, that's the plan.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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