Excerpts of Bruce's response...
>Meaning does not come out of infinite syntactical structures (there are no
>such entities) but depends upon the referents of our language and our
>purposes or ends-in-view.
>Self-reference, in ascending hierarchies of abstraction increasingly remote
>from the direct experience that provides their original meaning, may be a
>way to keep track of variously identified meanings by means of neural
>structures of finite or limited potential variety. The mind may be a
>control system in this sense (cf. Aaron Sloman).
>In the context of this discussion, the concept of infinity is important in
>considering the relationship between (1) any formal or conceptual model, of
>necessarily limited variety, and (2) the real world, infinite in time,
>space and potential to surprise us, and is indicative of an unbridgeable
>gulf between these, a limitation which sets a boundary to what is possible
>for human thought.
thanks...
I have a specific question for either you or Don (or anyone else)
Don has said that many of my comments (possibly including my opening
question for this discussion, although he has not yet commented on that one)
are not consistent with Rosen. Don has implied that his ideas on the
modeling relation (which would have to include dealing with just how
infinity or self-reference or infinite regresses fit in the
picture [or not]) are consistent with Rosen. You have said that your ideas
are in some respects consistent with Don. What is causing me confusion
is some passages by Rosen that I am most likely misinterpreting... It
would help me if these passages could be paraphrased or explained...and
perhaps then I would then see the over-all consistency in the viewpoints of
Bruce/Don/Rosen....
Specifically, in Rosens latest article "The mind-brain problem and
the physics of reductionism" Rosen gives what he calls a specific
example (about as specific as Rosen gets!!). I will give excerpts (and
hopefully won't obscure the meaning by any deletions).
I quote: [brackets are my comments], dots are deleted text
Suppose we want to determine...whether a particular pattern x
manifests a certain feature [P]...The conventional answer is to produce a
meter, or feature-detector; another different system (y which does not
equal x) which recognizes the predicate P, and hence in particular
determines the truth or falsity of P(x). But this recognition constitutes
a property or predicate Q(y) of y. We do not know whether P(x) is
true until we know that Q(y) is true. Accordingly, we need another
system z, different from both x and y, which determines this. That is:
z itself must possess a property R, of being a "feature detector"
detector. So we do not know that P(x) is true until we know whether
Q(y) is true, and now we do not know whether Q(y) is true until we
know whether R(z) is true. And so on. We see an unpleasant incipient
infinite regress in the process of information. At each step, we seem to
be dealing with objective properties, but each of them pulls us to the
next step.
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 cognitively
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 it
cognitively.
[Wouldnt this be the case where the "meaning is compounded from the
needs, life context and problems of the organism (pragmatics), specific
references to experience and the world"? Wouldnt this be the encoding
arm of the modeling relationship?]
Rosen continues:
But where does such "independent knowledge" come from? At least, it
comes from outside the system itself, and thus would violate the basic
tenant of formalization, that there is no such "outside".
[Would it be true that if a person did not absolutely insist on a formalism,
or pure objectivity, then this "from outside" would not be a problem? Is
this basically your point and that what follows is just an academic
exersice to re-focus attention on the above? Or is Rosen putting stock in
what follows?]
Rosen continues:
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 question
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 regress,
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=2, so that in the above notation,
we can put z=x. 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].
If, as we have noted earlier, the states of x and y are defined in terms
of the totality of true propositions P(x) about them, then by virtue of
what we have said, the impredicativity makes these states infinite
objects....They also satisfy no condition of "fractionability", whereby
propositions about x or y can be resolved into independent fractional
subsystems, by breaking some finite number of intrafractional bonds
or constraints...that is, x and y have become complex in my sense.
[Don has defined complexity as occurring whenever you have two or
more formalisms that can not be mapped into each other. Rosen
seems here to be implying that complexity necessitates an infinite
number...and because infinity finitely fragmented still yields infinities,
finite fragmentation can not resolve the infinite regress]
[I obviously still have some confusion in interpreting the consistency
of Bruces, Dons, and Rosens statements on the subject. Any
comments from anybody would be much appreciated!!!]
Jeff Prideaux