[Arisbe] Re: Inquiry Into Isms -- k-adic versus k-tomic

[Jon Awbrey]

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Howard, Stan, ...

Here is an old note I've been looking for since we started on this bit about isms,
as I feel like I managed to express in it somewhere my point of view that the key
to integrating variant persepectives is to treat their contrasting values as axes
or dimensions rather than so many points on a line to be selected among, each in
exclusion of all the others.  To express it briefly, it is the difference between
k-tomic decisions among terminal values and k-adic dimensions of extended variation.

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Subj:  Re: Dyads
Date:  Fri, 08 Dec 2000 00:48:18 -0500
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Stand Up Ontology <standard-upper-ontology@ieee.org>

Jon Awbrey wrote (JA):
Tom Gollier wrote (TG):

JA: I think that we also need to distinguish "dichotomous thinking" (DT)
    from "dyadic thinking" (DT).  In spite of my acronymaniac confusion,
    there is yet a "difference that makes a difference" between the DT's --
    one has to do with the number of values, {0, 1}, {F, T}, {evil, good},
    and so on, that one imposes on the cosmos, the other has to do with
    the number of dimensions that a persona puts on the face of the deep,
    that is to say, the number of independent axes in the frame of reverence
    that one projects on the scene or otherwise puts up to put the cosmos on.

TG: Your transmission [above] kind of faded out after the "number of values",
    but do you mean a difference between, say, two values of truth and falsity
    on the one hand, and all things being divided into subjects and predicates,
    functions and arguments, and such as that on the other?  If so, I'd like
    to second the notion, as not only are the two values much less odious,
    if no less rigorous, in their applications, but they're often maligned
    as naive or simplistic by arguments which actually should be applied
    to the idea, naive and simplistic in the extreme, that there are
    only two kinds of things. 

JA: There may be a connection -- I will have to think about it --
    but "trichotomic", "dichotomic", "monocotyledonic", whatever,
    refer to a number of values, 3, 2, 1, whatever, as in the range
    of a function.  In contrast, "triadic", "dyadic", "monadic",
    as a series, refer to the number of independent dimensions that
    are involved in a relation, which you could represent as axes
    of a coordinate frame or as columns in a data table.  As the
    appearance of the word "independent" should clue you in,
    this will be one of those parti-colored woods in which
    the interpretive paths of mathematicians and normal
    folks are likely to diverge.

JA: There is a typical sort of phenomenon of misunderstanding that often
    arises when people imbued in the different ways of thinking try to
    communicate with each other.  Just to illustrate the situation for
    the case where n = 2, let me draw the following picture:

|     Dyadic Span of Dimensions
|        ^                 ^
|         \               /
|          \             /
|           o           o
|           |\         /|
|           | \       / |
|           |  \     /  |
|           |   \   /   |
|           v    \ /    v
|     <-----o-----o-----o----->
|   Dichotomic Spectrum of Values

JA: This is supposed to show how the "number of values" (NOV) thinker
    will project the indications of the "number of axes" (NOA) thinker
    onto the straight-line spectrum of admitted directions, oppositions,
    or values, tending to reduce the mutually complementing dimensions
    into a tug-of-war of strife-torn exclusions and polarizations.

JA: And even when the "tomic" thinker tries to achieve a balance,
    a form of equilibrium, or a compromising harmony, whatever,
    the distortion that is due to this manner of projection
    will always render the resulting system untenable.

JA: Probably my bias is evident.

JA: But I think that it is safe to say, for whatever else
    it might be good, tomic thinking is of limited use in
    trying to understand Peirce's thought. 

JA: Just to mention one of the settings where this theme
    has arisen in my studies recently, you may enjoy the
    exercise of reading, in the light of this projective
    template, Susan Haack's 'Evidence & Inquiry', where
    she strives to achieve a balance or a compromise
    between foundationalism and coherentism, that is,
    more or less, objectivism and relativism, and
    with some attempt to incorporate the insights
    of Peirce's POV.  But a tomic thinker, per se,
    will not be able to comprehend what the heck
    Peirce was talking about.

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