>I would be interested in... comments on ...
>A constructive interpretation of the full set theory,
>Journal of Symbolic Logic, 52 pp.172-201, 1987. [and the]
>Epistemological position on which that paper is based:
>V.Turchin, On Cybernetic Epistemology,
>Systems Research, Vol.10, No.1, pp.3-28 (1993).
A previous post to PCT by Marvin McDonald (Mar 14) posed the question:
>. . . WHY do our mathematical systems, however obstruse, find
>"application"? What is the relationship between mathematical insight
>and human understanding in other domains?
On March 15 I responded with the thought that -
>If one supposes that the primary requirement for any thought at all involves
>>the phenomenology of consciousness ... then rationality, including the
>>mathematical variety and its theorems, are necessarily dependent upon
>>consciousness, not the other way around.
I believe this view is not dissimilar to that ascribed by Don Mikulecky and
Jeff Prideaux to Rosen and to John Casti, although of course I cannot
pretend to speak for anyone but myself.
In response to Val Turchin's request for comments, and after rereading his
paper On Cybernetic Epistemology, it is my view that the epistemological
position put forth there is a relatively closed conceptual system.
(Concerned the application to set theory I could probably have no other view.)
In brief, it seems to me, these views take their stand within what Popper
has called World 3 - the world of language and abstract concepts - and do
not give at least equal and coordinate status and reality to Worlds 1 and 2
- except as reflected in World 3. The problem for Turchin is that it would
seem impossible to do otherwise, i.e. to take into account the
nonconceptual in ways that are not essentially conceptual. Yet I do not
think a real world interpretation of the principles of cybernetics requires
an approach restricted in this way.
To be more specific, Turchin states:
>We come to philosophy with the standards and methods of science....we create
>formal versions of our common notions in order to understand better
>how our language and mind work, and to create artificial languages
>and minds, which will imitate our mental processes...
Now in one sense this seems quite unexceptionable, and it is not easy to
put the problems I perceive into words. Yet the assumptions involved appear
to me to
suggest that the concepts are considered primary, and human experience and
action, including that special action which is language behavior, are to be
included within the universe of concepts, rather than that human concepts
are no more than tools of use to man, within an environing universe which
is from a practical standpoint infinite in relation to human knowledge.
In other words in might be said that it is the role of philosophy to define
the place and scope of science, not the role of science to assimilate
philosophy.
>Evolution ... precedes ethics, because our ethics is strongly based on
>the concept of evolution.
As an alternative view, one might hold that evolution is an essentially
theoretical framework, while ethics has to do with practical life and death
questions, the choice of what is good or right to do, etc., and is more
basic to human experience that the more specialized tools of abstract
thought. In this view an ethics that is based upon a particular theoretical
position is not fully equipped to confront existential dilemmas, i.e. is
not a full basis for ethical choices. "There is nothing as practical as a
good theory", but a really good theory should include all the relevant
aspects in their proper dimensions, some of which can only be pointed to,
as it were, and not represented as such.
>Before answering a question, the question must be understood;
>after receiving an answer, the answer must be understood.
An expanded view might also include a prior condition, that before
questions (or answers) can be understood, the problems being addressed must
be clearly identified, and that this is not in the first instance a
conceptual task. Of course we must recognize our dependence at any one time
on certain presuppositions, in the light of which we interpret our
perceptions. However as Popper (e.g. in differentiating World 1, 2 & 3) and
others have pointed out, our awareness of this larger context is essential
if we are to pose the questions most usefully.
>As the first stages of the development of our philosophy we
>establish a certain criterion to decide whether a given text
>is meaningful or meaningless. ...
On the other hand (I think it was Bacon who wrote): men must learn to lay
their notions to one side and begin by familiarizing themselves with facts.
Now, I know that the criteria may be held to include empirical facts, but
the issues here involve also the framework of what count as facts.
>In cybernetic view, thought works because it implements some models
>of the world, not because it somehow statically reflects it. The difficult
>questions of the correspondence between thought and its objects
>simply do not arise.
An alternative view might be that thought works only as it reflects,
organizes and relates the whole organism dynamically within the
environment, and keeps whatever models or representations it has current in
that regard. In this interpretation, correspondence between thought and its
objects that is useful may be seen as of the essence as far as life is
concerned.
Of course, a discussion such as this, in a restricted forum such as this,
cannot really elucicate these fundamental problems. Any of the arguments
above can lead into endless discussions about semantic referents, etc. To
state my own orientation from the point of view of a physician whose
training was a clinical orientation that constantly required that concepts
(i.e. diagnosis) be tentative, it sometimes seems to me that many
mathematically oriented systems thinkers are in somewhat the same
intellectual position as learned physicans in the middle ages who had their
Galenic and Platonic concepts of anatomy and disease, and who too often
left the operational details to the barber-surgeons. In many fields today
(engineering, management) education is of course highly oriented to
problem-solving in relation to specific cases, and properly so, since that
is the experience required to put flesh on ideas that otherwise can only be
abstract conceptual constructs at several removes from the realities they
are supposed to represent.
So in my view an appeal to mathematical arguments is really beside the
point when the problem is the relation of logic and reason to deeper
grounds in more inclusive human experience. That this cannot all be put
into words is not so much grounds for objection or criticims as an
observation of fact which it is well to acknowledge and with which to
begin.
Cheers and best wishes.
Bruce B.