ONT Re: Differential Logic A -- Discussion
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DLOG A. Discussion Note 12
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I return to my picture of the relation between a reality x
and a representation y whose components are y_1, y_2, y_3.
JA: The way I see it, we have a reality, say x, and then we have a representation
of that reality, say y. If the representation y is "analytic" or "articulate"
in any sense of those words, then it will analyze or articulate the reality x
in terms of y's components, say, for example, y_1, y_2, y_3, just for a start.
So we have a picture like this:
x y
o------------->o
/|\
/ | \
/ | \
/ | \
o o o
y_1 y_2 y_3
Let me now draw what I consider to be a critical distinction with respect
to the question of emergence, that is, to put it in the roughest possible
terms, the issue of whether "the whole is more than the sum of its parts".
If by "whole" we mean the object reality x, and if by "parts" we mean the
parts of speech, so to speak, of the representation y, then the emergence
of x beyond the y_j is hardly surprising, indeed, it's a corollary of the
fact that the representation y is approximate, and thus it proves nothing
about the potential emergence of y beyond its own components on the plane
of the given representation. Of course, this issue will only be confused
even further by the unflective reification of representational components.
On the representational plane, however, the utility of the representation
generally depends on each representation being determined by its components.
What results from this requirement of useful representations is an obligation
to render more explicit what we mean by "parts" and by "sum" in a given setting.
For example, if y is simply the set {y_1, y_2, y_3}, then y is something that can
be said to exist "over and above" its elements, at least, in some sense, even in
the case of a singleton set, say, z = {z_1}. But any claim of "emergence" for
the relationship of a set to its elements would most likely be discounted as
trivial, since the set is defined to be a thing that is fully determined by
its elements.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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