Although I don't know Rosen's work (shame on me ;-) this whole discussion
reminds me very much of my analysis of the difficulties in modelling
encountered in non-classical domains, such as quantum mechanics. I quote
from a paper of mine (Heylighen F. (1992): "From Complementarity to
Bootstrapping of Distinctions: A Reply to L=F6fgren's Comments on my
Proposed 'Structural Language", International Journal of General Systems
21, no. 1, p. 99. http://pespmc1.vub.ac.be/papers/bootstrapping.html)
"The principle of the linguistic complementarity11,12,14 implies that no
language can completely describe its own interpretation process. In some
cases, there exists a metalanguage that can provide the description, but
the interpretation processes of the metalanguage itself requires yet
another level of description, and, in the best case, this leads to an
infinite regress.
As I have previously argued myself7,8, this problem can be clearly
illustrated by the quantum mechanical observation process. In order to
completely describe the observation process, we need to completely describe
the observation apparatus. But in order to describe the apparatus we need a
second apparatus that would measure the microscopic state of the first one.
That second apparatus on the other hand would still be incompletely
described, and that would incite us to introduce a third apparatus to
measure the second one, and so on. Since the result of the measurement does
not only depend on the state of the system that is to be observed but also
on that of the measuring instrument (unlike measurement in classical
mechanics), the conclusion is that we will never be able to completely
predict that result. This leads to the well-known indeterminacy of quantum
mechanics. "
Rosen:
>There are several [two] ways out of this situation. The first is somehow
>to have "independent knowledge" of what the initial feature is; some kind
>of extraneous list or template which characterizes what is being recognized
>at the first stage of the regress. That makes it unnecessary to cognitivel=
y
>recognize the property Q(y) of y directly, and thus dispenses with all the
>successive systems z and their predicates R. In other words, we must have
>some kind of model of y, built from this "independent knowledge", which
>will enable us to predict or infer the truth of Q(y), without determining i=
t
>cognitively.
My paper:
The situation would be different if distinctions were always conserved, as
classical mechanics assumes6,8. In that case it would suffice to postulate
one set of primitive distinctions, say elementary particles and their basic
properties of position and momentum, and all other distinctions could then
be derived from those primitive elements and their combinations in an
invariant, "distinction-conserving" way, through a mapping or
correspondence.
Rosen:
>The only other possibility is to fold this infinite regress back on itself;
>i.e. to create an impredicativity. [this is what really inspired my questi=
on
>about infinite regresses and the self-referencing act of folding it back on
>itself]. That is, to suppose there is some stage N in this infinite regres=
s,
>which allows us to identify the system we require at that stage with one
>we have already specified at an earlier stage. [this seems like our
>subjectivity, or external referents, are being pulled into the objective
>system]. Suppose, for instance, that N=3D2, so that in the above notation,
>we can put z=3Dx. Then not only P(x) is true, but also R(x) is true, and
>not only R(x), but also the infinite number of other predicates arising
>at all the odd steps in the infinite regress. Likewise, not only Q(y) is
>true, but also all the predicates arising from all the even steps in that
>regress. [it looks like in some form that the infinite regress is retained=
].
My paper:
The essence of the structural language is the idea that distinctions are
determined in a bootstrapping way: in order to determine distinction A, you
need to determine distinction B, which requires the determination of C,
etc., which again requires the determination of distinction A. For example,
in a dictionary, you might find word A defined in terms of word B, whereas
word B would be defined in terms of A. Distinctions always depend on other
distinctions, and there are no primitive distinctions. [... ]The "meaning"
of any given distinctions arise solely from the other distinctions it is
connected with.
In the structural language elementary distinctions are called "arrows",
and each arrow is determined by its set of input arrows and its set of
output arrows. From a certain point of view, the input set of an arrow A
might be seen as its extension (that is to say the set of phenomena that
imply A), and its output set as its intension (the set of phenomena that
are true if A is the case)10.[ ....]
Determining the "meaning" of A occurs in first instance by exploring its
input and output set. This may lead to the identification of A with another
arrow B if both have the same input or output sets (this means that they
cannot be distinguished5,10). However, the elements of input and output
sets are themselves distinguished only by their connections with further
arrows, and so a further exploration of A's meaning will also involve these
"neighbours of neighbours", and further "neighbours of neighbours of
neighbours". The process does not have an end. Yet in practice we are not
interested in completely determining A's meaning: it suffices that we can
situate A with respect to a smaller or larger "context" or "neighbourhood"
of related distinctions.
---------------------
These are just some excerpts from a discussion paper. The work I refer to
is spread over different places including my thesis "Representation and
Change", and the papers "A Structural Language for the Foundations of
Physics", "Classical and Non-Classical Representations ..." and "Knowledge
Structuring ...". See http://pespmc1.vub.ac.be/papers/papersFH.html for a
list of all my publications with abstracts and links to web versions if
available.
Though my approach starts from somewhat different concepts than Rosen's
there is clearly a strong convergence in some respects, but also probably a
fresh approach to some problems that apparently remain obscure in Rosen's
treatment. The thrust of my approach is to replace infinite regresses or
incompatible models by "bootstrapping" models where meaning emerges from
the reciprocal relations between elements, rather than from some outside
observer. These models can to some degree be formalised (through a
formalism having some similarities to category theory, or perhaps hyperset
theory), and run on a computer. But this whole approach still needs a lot
of work in order to become practical.
________________________________________________________________________
Dr. Francis Heylighen, Systems Researcher fheyligh@vnet3.vub.ac.be
PESP, Free University of Brussels, Pleinlaan 2, B-1050 Brussels, Belgium
Tel +32-2-6292525; Fax +32-2-6292489; http://pespmc1.vub.ac.be/HEYL.html