Dear Anybody Interested in Rosen,
I have continued to plug away at the task of writing a synopsis of the crucial
chapter 5 of Rosen. As you see if you go look at
http://www.sfcomplex.org/wiki/RosenNoodles#Comments_on_chapter_5.2C_Entailment_Without_States:_Relational_Biology
the chapter is in danger of defeating me.
Is the passage below any clearer to anybody else than it is to me??? Because
of the difficulties of distinguishing my words from Rosen;s, reading of the
passage below will be GREATLY facilitated by reading it in HTML.
Rosen writes,
"Now
let us suppose that
[there is a formalism, F] that describes a set of
formal components, interrelated in a particular way. Any two natural systems
that realize this formalism
can they be said to realize, or manifest, a
common organization. Any material system that shares that organization is by
definition a realization of that organization."
Rosen now precedes build such a formalism.
We have by now said enough to clearly specify what the formal image of a
component must be. It must in fact be a mapping (sic!)
f: A-->B
This formal image clearly possesses the necessary polar structure, embodied in
the differentiation it imposes between the domain A of f and its range B. It
also posses the necessary duality; the identity of the component is embodied
in the mapping f itself, while the influence of larger systems, O, in which the
component is embedded, is embodied in the specific arguments in A on which the
mapping can operate.
In what follows, I shall never use the term function in its mathematical
sense, as a synonym for mapping; I reserve it entirely as an expression of the
relation of components to systems and to each other. p. 123, LI.
I have reproduced, rather than summarize this passage, because its meaning is
opaque to me.
The first two paragraphs seem to be saying that components map but the last
paragraph seems to insist that the function of a component is not to map. What
follows in the text is a two-page orgy of notion in which organization is
expressed as a series of mappings and metamapping in the manner outlined below.
Given the disclaimer in the last sentence above, I havent a clue what he could
be saying.
But when the orgy of notation is over, he is clear about what he THINKS he has
said.
organization
involves a family of sets, a corresponding family of mappings
defined on these sets, and above all, the abstract block diagram that
interrelates them, that gives them functions. p.126, LI.
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
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