Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 1

Work Area

1.3.

1.3.5. Discussion of Formalization : Specific Objects

| "Knowledge" is a referring back:  in its essence a regressus in infinitum.
| That which comes to a standstill (at a supposed causa prima, at something
| unconditioned, etc.) is laziness, weariness --
|
| (Nietzsche, 'The Will to Power', S 575, 309).

With this preamble, I return to develop my own account of formalization,
with special attention to the kind of step that leads from the inchoate
chaos of casual discourse to a well-founded discussion of formal models.
A formalization step, of the incipient kind being considered here, has
the peculiar property that one can say with some definiteness where it
ends, since it leads precisely to a well-defined formal model, but not
with any definiteness where it begins.  Any attempt to trace the steps
of formalization backward toward their ultimate beginnings can lead to
an interminable multiplicity of open-ended explorations.  In view of
these circumstances, I will limit my attention to the frame of the
present inquiry and try to sum up what brings me to this point.

It begins like this:  I ask whether it is possible to reason about inquiry
in a way that leads to a productive end.  I pose my question as an inquiry
into inquiry, and I use the formula "y_0 = y y" to express the relationship
between the present inquiry, y_0, and a generic inquiry, y.  Then I propose
a couple of components of inquiry, discussion and formalization, that appear
to be worth investigating, expressing this proposal in the form "y >= {d, f}".
Applying these components to each other, as must be done in the present inquiry,
I am led to the current discussion of formalization, y_0 = y y >= f d.

There is already much to question here.  At least,
so many repetitions of the same mysterious formula
are bound to lead the reader to question its meaning.
Some of the more obvious issues that arise are these:

The term "generic inquiry" is ambiguous.  Its meaning in practice
depends on whether the description of an inquiry as being generic
is interpreted literally or merely as a figure of speech.  In the
literal case, the name "y" denotes a particular inquiry, y in Y,
one that is assumed to be plenipotential or prototypical in yet
to be specified ways.  In the figurative case, the name "y" is
simply a variable that ranges over a collection Y of nominally
conceivable inquiries.

First encountered, the recipe "y_0 = y y" seems to specify that
the present inquiry is constituted by taking everything that is
denoted by the most general concept of inquiry that the present
inquirer can imagine and inquiring into it by means of the most
general capacity for inquiry that this same inquirer can muster.

Contemplating the formula "y_0 = y y" in the context of the subordination
y >= {d, f} and the successive containments F c M c D, the y that inquires
into y is not restricted to examining y's immediate subordinates, d and f,
but it can investigate any feature of y's overall context, whether objective,
syntactic, interpretive, and whether definitive or incidental, and finally it
can question any supporting claim of the discussion.  Moreover, the question y
is not limited to the particular claims that are being made here, but applies to
the abstract relations and the general concepts that are invoked in making them.
Among the many additional kinds of inquiry that suggest themselves at this point,
I see at least the following possibilities:

   1.  Inquiry into propositions about application and equality.
       Just by way of a first example, one might well begin by
       considering the forms of application and equality that
       are invoked in the formula "y_0 = y y" itself.

   2.  Inquiry into application, for example, the way that
       the term "y y" indicates the application of y to y
       in the formula "y_0 = y y".  

   3.  Inquiry into equality, for example,
       the meaning of "=" in "y_0 = y y".

   4.  Inquiry into indices, for example,
       the significance of "0" in "y_0".

   5.  Inquiry into terms, specifically, constants and variables.
       What are the functions of "y" and "y_0" in this respect?

   6.  Inquiry into decomposition or subordination, for example,
       as invoked by the sign ">=" in the formula "y >= {d, f}".

   7.  Inquiry into containment or inclusion.  In particular, examine the
       claim "F c M c D" that conditions the chances that a formalization
       has an object, the degree to which a formalization can be carried
       out by means of a discussion, and the extent to which an object
       of formalization can be conveyed by a form of discussion.

If inquiry begins in doubt, then inquiry into inquiry begins in
doubt about doubt.  All things considered, the formula "y_0 = y y"
has to be taken as the first attempt at a description of the problem,
a hypothesis about the nature of inquiry, or an image that is tossed out
by way of getting an initial fix on the object in question.  Everything in
this account so far, and everything else that I am likely to add, can only
be reckoned as hypothesis, whose accuracy, pertinence, and usefulness can
be tested, judged, and redeemed only after the fact of proposing it and
after the facts to which it refers have themselves been gathered up.

A number of problems present themselves due to the context in which
the present inquiry is aimed to present itself.  The hypothesis that
suggests itself to one person, as worth exploring at a particular time,
does not always present itself to another person as worth exploring at
the same time, or even necessarily to the same person at another time.
In a community of inquiry that extends beyond an isolated person and
in a process of inquiry that extends beyond a singular moment in time,
it is therefore necessary to consider the nature of the communication
process that the discussion of inquiry in general and the discussion of
formalization in particular need to invoke for their ultimate utility.

Solitude and solipsism are no solution to the problems of community and
communication, since even an isolated individual, if ever there was, is,
or comes to be such a thing, has to maintain the lines of communication
that are required to integrate past, present, and prospective selves --
in other words, translating everything into present terms, the parts of
one's actually present self that involve actual experiences and present
observations, do present expectations as reflective of actual memories,
and do present intentions as reflective of actual hopes.  Consequently,
the dialogue that one holds with oneself is every bit as problematic
as the dialogue that one enters with others.  Others only surprise
one in other ways than one ordinarily surprises oneself.

I recognize inquiry as beginning with a "surprising phenomenon" or
a "problematic situation", more briefly described as a "surprise"
or a "problem", respectively.  These are the types of moments that
try our souls, the instances of events that instigate inquiry as
an effort to achieve their own resolution.  Surprises and problems
are experienced as afflicted with an irritating uncertainty or a
compelling difficulty, one that calls for a response on the part
of the agent in question:

   1.  A "surprise" calls for an explanation to resolve the
       uncertainty that is present in it.  This uncertainty
       is associated with a difference between observations
       and expectations.

   2.  A "problem" calls for a plan of action to resolve the
       difficulty that is present in it.  This difficulty is
       associated with a difference between observations and
       intentions.

To express this diversity in a unified formula:  Both types of inquiry
begin with a "delta", a compact term that admits of expansion as a debt,
a difference, a difficulty, a discrepancy, a dispersion, a distribution,
a doubt, a duplicity, or a duty.

Expressed another way, inquiry begins with a doubt about one's object,
whether this means what is true of a case, an object, or a world, what
to do about reaching a goal, or whether the hoped-for goal is really
good for oneself -- with all that these questions lead to in essence,
in deed, or in fact.

Perhaps there is an inexhaustible reality that issues in these
apparent mysteries and recurrent crises, but, by the time I say
this much, I am already indulging in a finite image, a hypothesis
about what is going on.  If nothing else, then, one finds again the
familiar pattern, where the formative relation between the informal
and the formal merely serves to remind one anew of the relationship
between the infinite and the finite.