[Inquiry] Re: Doctrine Of Individuals -- Discussion

[Jon Awbrey]

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DOI.  Discussion Note 10

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BB = Bill Bailey
JA = Jon Awbrey

Re: DOI-DIS 9.  http://stderr.org/pipermail/inquiry/2005-February/002364.html
In: DOI-DIS.    http://stderr.org/pipermail/inquiry/2005-February/thread.html#2343

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

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

JA: 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: That touches upon my question of what was meant by "amount".
    I think the hypothetical posed is more like an indefinitely
    long sequence of events rather than an infinite amount.
    The conception is similar to Zeno's paradox, isn't it?
    Since every event (or point) is finite, no matter how
    long it goes on, we will never have an infinity of
    information, only discrete bits.

At this first cut, using a simple-minded notion of infinite information --
where I always take "infinite" to mean nothing more than "exceeding any
finite bound that one might name" -- I had in mind the follwoing sort
of statement from Peirce:

CSP: | A logical atom, then, like a point in space, would involve for
     | its precise determination an endless process.  We can only say,
     | in a general way, that a term, however determinate, may be made
     | more determinate still, but not that it can be made absolutely
     | determinate.

Cf: DOI 4.  http://stderr.org/pipermail/inquiry/2005-January/002323.html
In: DOI.    http://stderr.org/pipermail/inquiry/2005-January/thread.html#2320

Now we know that this is not the most sophisticated notion that
might be brought into play, but it suffices to understand what
Peirce was asserting at this particular point in time (1870).

JA, quoting BB:

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

JA: This part I did not get.

JA, quoting BB:

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

BB: I was making the same point as John Collier regarding randomness.
    A channel does not have information, per se, but only events which
    function as signs of something else.  The event in a channel can
    function informationally then only as a covariant of some other
    system, i.e., is by design or nature constrained in the responses
    it can make to the other system.

Perhaps it would be good at this point to establish some shared concepts.
A definition of a "channel" which is general enough for most of my needs
is a probability distribution on a finitely generated set, in other words,
a formal language with a probability distribution defined on it.  We have
then a measure of "entropy" or "uncertainty" on distributions that attains
its maximum on a uniform distribution, and this measure is what we otherwise
call the information capacity of the channel in question.  I personally use
words like "message", "signal", or "sign" to refer to the elements of the
formal language at stake, saving "events" for appropriate subsets of the
sample space.

When you say that "the event [sign] in a channel can function
informationally then only as a covariant of some other system,
i.e., is by design or nature constrained in the responses it
can make to the other system", it is important to recognize
that we do not have any direct, independent, or unmediated
access to this object system, but that the object system
is known only in so far as it comes to be represented in
the signs of the given or some other conceivable channel.
So the covariance that we can evaluate is always that
which is obtained between two alternative channels.

BB: An infinity of possible responses means any response is equally
    likely, and therefore the result is the same as randomness.

I don't see how this follows.

BB: I was not trying to place Peirce in the engineers box.
    But it has to do with human requisites of information
    processing -- which was what Shannon/Weaver/Hartley
    et al were actually elaborating.

Actually, the engineer's box fits quite comfortably
in Peirce's volume, with some dimensions to spare.

Jon Awbrey

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