Re: Jeffrey Brian Downard
At: http://permalink.gmane.org/gmane.science.philosophy.peirce/14434
Jeff, List,
I had a faint memory of discussing the relation between k-adic and k-tomic with
Tom Gollier in my early days on the Peirce List, and for once my memory serves
me well. I found this link to a later discussion in which I recycled parts of
that discussion, in relation to 2-adic versus 2-tomic thinking and the problem
of integration in Susan Haack's ''Evidence and Inquiry'.
http://stderr.org/pipermail/arisbe/2001-August/000878.html
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Subj: Re: Dyads
Date: Fri, 08 Dec 2000 00:48:18 -0500
From: Jon Awbrey <[email protected]>
To: Stand Up Ontology <[email protected]>
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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Jon Awbrey wrote:
Jeff,
The earliest such discussions go back to the turn of the millennium and the
Texas Tech server and might not be possible to find anymore, but I probably
posted various renditions to other lists and archives that are still around.
Given time and a little thought I could probably reconstruct their substance.
Will get on that in a day or two ...
Jon
Jeffrey Brian Downard wrote:
Hello Jon,
If you have links to the earlier discussions of the distinction between
"triadicities" and "trichotomies", I'd like to take a look. In addition to
being interested in distinction you are making, I'd like to read more
about how you are thinking about the projection of the triadic relations
onto the mutually exclusive and exhaustive partitions of a domain.
In his monograph <Reading Peirce Reading>, Richard Smyth makes much of the
conceptions of the restrictions and limitations that apply to a given
domain of inquiry. I'd like to see how your account of the partitions of
the domain compares to his reconstruction of some arguments Peirce develops
in "How to Make Our Ideas Clear."
Thanks,
Jeff
Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354
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