[Inquiry] Re: Doctrine Of Individuals -- Discussion

[Jon Awbrey]

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DOI.  Discussion Note 9

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BB = Bill Bailey
JA = Jon Awbrey

Re: DOI-DIS 7.  http://stderr.org/pipermail/inquiry/2005-February/002346.html
In: DOI-DIS.    http://stderr.org/pipermail/inquiry/2005-February/thread.html#2343

Bill,

Before I forget, I had been meaning to get back
to some residual points in your last communique.

BB: If "an unlimited amount of information" means
    the same as "infinite information", it's an
    oxymoron, which is how I first read the post,
    and, I took it, your wry-sounding reply that
    we don't know.

I meant this rather straight-facedly, and I think
that John Collier's subsequent remarks will serve
as an acceptable ironing out of any further irony.

BB: An infinity of information requires an infinite channel, ...

No, it would only take an infinite amount of time
to transmit through a (necessarily finite) channel.

In the first instance, as in Peirce's examples, we are only thinking
of things like a points on a real line as taking an infinite number
of intersecting open interval constraints to pin down exactly.

BB: which are equally oxymoronic as any particular event in an
    infinite channel would be equally likely with any other event --

This part I did not get.

BB: i.e., it would lack the necessary systemic (stochastic) constraints
    (or systematic covariance with an external system) to be a channel.

Here is where a very interesting issue arises, if I read you right.
Peirce's approach to information theory, however incipient in might
have been in its development, is actually more general in principle
than the restricted ways in which the Hartley-Shannon methodology
usually gets applied.  This is because Peirce's theory is worked
out within a 3-adic sign-relational framework that does not try
to reduce the denotative/external/objective aspect to syntax,
as actually happens when you look at the way that channels
are interpreted in the usual manner today.  It is only in
a sign-relational context that one can actually consider
object systems that are truly external, that is, where
the question of a given channel's representational
adequacy has not been begged from the start.
In other words, the usual application of
information theory does not deal with
externals at all, but only compares
what comes over different channels.

Jon Awbrey

BB: If "unlimited amount of information" means "an unspecifiable amount"
    of "it's green", "solid", "round", etc., but an amount we'll recognize
    when it is sufficient, your reply is still correct, but with less
    wryness.  If it means an infinite amount of "it's green", solid",
    "round", etc., then we are back to an oxymoron again because the
    infinity would surely encompass "not-green", "not-solid", etc.,
    and your reply is back to sounding wry again.

JA: There are many interesting side-tracks here, but before
    we get too far down the scenic railroad on some of them,
    let's recall that this whole question initially rose in
    connection with Peirce's definition of a "logical atom"
    as a "term not capable of logical division", in essence,
    "one of which every predicate may be universally affirmed
    or denied".  The real problem here is with the invocation
    of "every predicate", all of which possible predicates we
    never really invoke in a well-bounded frame of reference,
    but more sensibly limit ourselves to some well-defined
    channel, code set, discursive universe, formal language,
    family of natural kinds, or whatever you want to call it.

JA: In Peirce's original context, it is reasonable to imagine that we can always
    think of one more predicate to divide whatever term we are given, since there
    is no talk yet of realistic practical constraints on our imagination.  In that
    frame of mind, what Peirce says about logical atoms, that they "can be realized
    neither in thought nor in sense", seems true enough.

JA: By way of a slippery slope that I'm still trying to plot the grade of,
    we graduated from this talk of unrealizable logical atoms to talking
    of whole systems, some very different from atoms in their imagery,
    that take overwhelmingly lots and lots of information to specify.
    The question there becomes, not whether we can imagine new ways
    to split the evolutionary heirs of the system, but whether we
    really need to in order to tie the system down sufficiently
    securely.  Whatever the situation with abstract, extreme,
    ideal cases, it seems clear enough that we commonly find
    ourselves pressed in our concrete, middling, practical
    situations to invoke as yet unconsidered distinctions
    in order to describe the situation adequately.  And
    since the use of abstract extreme ideals is mainly
    to illuminate concrete middling practice, we are
    brought to this pass in any case.

JA: One of the interesting issues that arises here is the issue of abduction.
    The problem of abductive inference is the problem of "changing channels",
    that is, a study of the forces that lead us to add a new concept, all the
    better to unify the manifold of sensuous impressions, and the reasons why
    it might be impossible to unify sense in a reasonable fashion without it.

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