SUO: *Date 14 Jan 2002
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JA's summary for 14 Jan 2002
Re_1: Auto Da Re, "Adic & Tomic Thinking"
Re_2: Matthew West, "Adic & Tomic Compatibility"
JA = Jon Awbrey
JS = John Sowa
MW = Matthew West
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Re_1: Auto Da Re, "Adic & Tomic Thinking"
i post here some links to background material
on the adic & tomic issue, as it is pertinent
to the discussion of many colliding paradigms:
http://suo.ieee.org/ontology/msg03158.html
http://suo.ieee.org/ontology/msg03162.html
http://suo.ieee.org/ontology/msg03522.html
i append some relevant excerpts. since these are written
in a 'deprecated' style, i will translate them and try to
clear them up as best i can from my present frame of mind.
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.
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.
these issues come up a lot whenever one attempts to integrate, or even just to
clarify the disgruities among different 'frameworks of interpretation' (foi's).
for example, the agon between extreme versions of:
1. foundationalism, fundamentalism, objectivism, realism, etc.
2. coherentism, constructivism, relativism, solidaritism, etc.
there are always attempts to get beyond the conflict and to create
a unified view of what's really going on beneath these contrasting
pictures of the world. a number of explorations that come to mind:
| Richard J. Bernstein,
|'Beyond Objectivism and Relativism:
| Science, Hermeneutics, and Praxis',
| University of Pennsylvania Press, Philadelphia, PA, 1983.
| Susan Haack,
|'Evidence and Inquiry:
| Toward Reconstruction in Epistemology',
| Blackwell, Oxford, UK, 1993.
| Marcus G. Raskin & Herbert J. Bernstein,
|'New Ways of Knowing: The Sciences,
| Society, & Reconstructive Knowledge',
| Rowman & Littlefield, Totowa, NJ, 1987.
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Re_2: Matthew West, "Adic & Tomic Compatibility"
Subj: JA's Bit 13 Jan 2002
Date: Mon, 14 Jan 2002 14:38:56 +0100
From: West, Matthew R <Matthew.R.West@IS.shell.com>
To: Jon Awbrey <jawbrey@oakland.edu>,
Stand Up Ontology <standard-upper-ontology@ieee.org>
MW: I think I missed the point of what you were trying to say below.
MW: The critical point behind what I was trying to convey
is that different ways of looking at the world will
actually discriminate different objects in it.
I think it is a useful lesson to ponder on
how arbitrarily different the way we see
the world can be.
JA: let me try another example: particles versus waves.
you can say that there is a particle-view and a wave-view.
what there really is -- the real object of nature's ontology --
that is likely beyond our comprehension, but we have to work
with the glimpses that we have in the process of seeing more.
but if you go ahead and write down an axiom for "wave" that
says "not a particle", then you have rendered the concepts
logically incompatible -- in your own mind -- whereas
nature may not care a fig what you write or think.
MW: Indeed. Historically I come from the datamodelling arena, and
I have spent much time reviewing over constrained data models
that prevented the business from doing what it really needed to.
So I have tended to be conservative (or perhaps I mean liberal)
when it comes to defining axioms (constraints to everyone else).
JA: i am not a person who says that all reality is constructed by us --
even if there are definitely some realities that we do construct --
but i am a 'constructive thinker' in the sense that i would say that
we construct our knowledge of things, and the raw materials of that
construction are called 'signs', which for me includes concepts and
the data of experience. and we organize our thoughts in such a way
that we might as well go ahead and say that we are often talking
about this or that abstract, formal, hypostatic, or ideal object,
like numbers, propositions, spaces, etc. and then the question
becomes: how do these formal, logical, mathematical objects
compare with the real objects and problems that nature,
including our own nature, keeps tossing our way?
MW: Yup me too.
JA: now, with regard to viewpoints, john sowa was
careful to say in his knowledge rep book that:
JA, quoting JS:
| The physical/abstract distinction is independent of the observer's viewpoint,
| but the continuant/occurrent distinction depends on the choice of time scale.
|
| John Sowa, KR, p. 71
JA: i would probably agree with the latter half of that,
and worry a while what the former half depends on,
but a relative distinction is a different sort
of thing from an absolute distinction, twisi,
at least from my current pov.
MW: Hmmm. Well maybe, but you can still construct the
two world viewpoints that Pat identifies, and they
are still logically incompatible (i.e. at least
some objects of one cannot be in the other).
the question is: are these real objects or imaginary objects?
put another way: are the objects of these opposed predicates
real beings that have their own properties independent of the
theoretical model, or nothing more than constructed entities
and ideal fictions that live but for the grace of the model
space and thus have only those properties that we grant to
them, to the extent that our gratuities are consistent?
another example: the three post-classical geometries:
elliptic, hyperbolic, parabolic. three relatively
consistent geometries -- as we gather from being
able to build a model of each geometry inside
each one of the other two geometries -- but
there can be at most one that holds true
of 'the' physical geometry of space.
which is it? probably none of them!
physical space is turning out to be
much weirder than anybody dreamed
just a few years ago. so the
utility of each geometry has
to be evaulated on another
basis than the very idea
of its being suopreme.
MW: This may just mean that at least one of them is sufficiently far off the mark
that it should be considered a "bad" model (e.g. earth fire and water as the
elements). Alternatively you can do what we do with waves and particles, and
say that they are both useful models, and there is a relationship between some
waves and some particles, whilst not pretending that waves are particles, and
that there may be some underlying reality that we have yet to discover that
will reconcile them.
and what is the method for comparing models with realities,
and by this comparison telling the good from the bad model?
JA: i am not especially onterested in the versus between
trimeters & tetrameters, as i think it's a mistake to
get trapped in such diminished dimensionalities, but
the problems to which you point here do illustrate
a vastly more generic issue that affects the whole
way some people seem to make use of ontological
forms of thought.
JA: i have discussed this before under the heading of the contrast
between k-adic and k-tomic thinking, the difference between
thinking in k axes and thinking in k parts of a partition
of the universe, that is, parts that are thought to be
mutually exclusive and possibly exhaustive sets or
classes or categories or whatever.
JA: for a maximally generic example, let's say you have divided
the world along the lines of "abstract" versus "physical"
or "logos" & "physis" -- what then? doing this, the way
some people do it, anyway, completely misses the utility
of mathematics in talking about objective reality, which
is bound up in the recognition of the synthetic unities
of form and matter, in which thinkers as early as
aristotle were sufficiently well-versed not to
be saying the silly things that we hear
hereabouts on a daily basis.
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