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==Discussion==
  
 
==Work Area==
 
==Work Area==
 
===1.3.===
 
 
====1.3.5. Discussion of Formalization : Specific Objects====
 
 
<pre>
 
| "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.
 
</pre>
 
 
=====1.3.5.1. The Will to Form=====
 
 
<pre>
 
| The power of form, the will to give form to oneself.  "Happiness"
 
| admitted as a goal.  Much strength and energy behind the emphasis
 
| on forms.  The delight in looking at a life that seems so easy. --
 
| To the French, the Greeks looked like children.
 
|
 
| (Nietzsche, 'The Will to Power', S 94, 58).
 
 
Let me see if I can summarize as quickly as possible the problem that I see before me.
 
On each occasion that I try to express my experience, to lend it a form that others
 
can recognize, to put it in a shape that I myself can later recall, or to store it
 
in a state that allows me the chance of its re-experience, I generate an image of
 
the way things are, or at least a description of how things seem to me.  I call
 
this process "reflection", since it fabricates an image in a medium of signs
 
that reflects an aspect of experience.  Very often this experience is said
 
to be "of" -- what? -- something that exists or persists at least partly
 
outside the immediate experience, some action, event, or object that is
 
imagined to inform the present experience, or perhaps some conduct of
 
one's own doing that obtrudes for a moment into the world of others
 
and meets with a reaction there.  In all of these cases, where the
 
experience is everted to refer to an object and thus becomes the
 
attribute of something with an external aspect, something that
 
is thus supposed to be a prior cause of the experience, the
 
reflection on experience doubles as a reflection on that
 
conduct, performance, or transaction that the experience
 
is an experience "of".  In short, if the experience has
 
an eversion that makes it an experience of an object,
 
then its reflection is again a reflection that is
 
also of this object.
 
 
Just at the point where one threatens to become lost in the morass of
 
words for describing experience and the nuances of their interpretation,
 
one can adopt a formal perspective, and realize that the relation among
 
objects, experiences, and reflective images is formally analogous to the
 
relation among objects, signs, and interpretant signs that is covered by
 
the pragmatic theory of signs.  One still has the problem:  How are the
 
expressions of experience everted to form the exterior faces of extended
 
objects and exploited to embed them in their external circumstances, and
 
no matter whether this object with an outer face is oneself or another?
 
Here, one needs to understand that expressions of experience include
 
the original experiences themselves, at least, to the extent that
 
they permit themselves to be recognized and reflected in ongoing
 
experience.  But now, from the formal point of view, "how" means
 
only:  To describe the formal conditions of a formal possibility.
 
</pre>
 
 
=====1.3.5.2. The Forms of Reasoning=====
 
 
<pre>
 
| The most valuable insights are arrived at last;
 
| but the most valuable insights are methods.
 
|
 
| (Nietzsche, 'The Will to Power', S 469, 261).
 
 
A certain arbitrariness has to be faced in the terms that one uses
 
to talk about reasoning, to split it up into different parts and
 
to sort it out into different types.  It is like the arbitrary
 
choice that one makes in assigning the midpoint of an interval
 
to the subintervals on its sides.  In setting out the forms of
 
a nomenclature, in fitting the schemes of my terminology to the
 
territory that it disturbs in the process of mapping, I cannot
 
avoid making arbitrary choices, but I can aim for a strategy
 
that is flexible enough to recognize its own alternatives and
 
to accommodate the other options that lie within their scope.
 
 
If I make the mark of deduction the fact that it reduces the
 
number of terms, as it moves from the grounds to the end of
 
an argument, then I am due to devise a name for the process
 
that augments the number of terms, and thus prepares the
 
grounds for any account of experience.
 
 
What name hints at the many ways that signs arise in regard to things?
 
What name covers the manifest ways that a map takes over its territory?
 
What name fits this naming of names, these proceedings that inaugurate
 
a sign in the first place, that duly install it on the office of a term?
 
What name suits all these actions of addition, annexation, incursion, and
 
invention that instigate the initial bearing of signs on an object domain?
 
 
In the interests of a "maximal analytic precision" (MAP), it is fitting
 
that I should try to sharpen this notion to the point where it applies
 
purely to a simple act, that of entering a new term on the lists, in
 
effect, of enlisting a new term to the ongoing account of experience.
 
Thus, let me style this process as "adduction" or "production", in
 
spite of the fact that the aim of precision is partially blunted
 
by the circumstance that these words have well-worn uses in other
 
contexts.  In this way, I can isolate to some degree the singular
 
step of adding a term, leaving it to a later point to distinguish
 
the role that it plays in an argument.
 
 
As it stands, the words "adduction" and "production" could apply to the
 
arbitrary addition of terms to a discussion, whether or not these terms
 
participate in valid forms of argument or contribute to their mediation.
 
Although there are a number of auxiliary terms, like "factorization",
 
"mediation", or "resolution", that can help to pin down these meanings,
 
it is also useful to have a word that can convey the exact sense meant.
 
Therefore, I coin the term "obduction" to suggest the type of reasoning
 
process that is opposite or converse to deduction and that introduces
 
a middle term "in the way" as it passes from a subject to a predicate.
 
 
Consider the adjunction to one's vocabulary that is comprised of these three words:
 
"adduction", "production", "obduction".  In particular, how do they appear in the
 
light of their mutual applications to each other and especially with respect to
 
their own reflexivities?  Notice that the terms "adduction" and "production"
 
apply to the ways that all three terms enter this general discussion, but
 
that "obduction" applies only to their introduction only in specific
 
contexts of argument.
 
 
Another dimension of variation that needs to be noted among these different types
 
of processes is their status with regard to determimism.  Given the ordinary case
 
of a well-formed syllogism, deduction is a fully deterministic process, since the
 
middle term to be eliminated is clearly marked by its appearance in a couple of
 
premisses.  But if one is given nothing but the fact that forms this conclusion,
 
or starts with a fact that is barely suspected to be the conclusion of a possible
 
deduction, then there are many other middle terms and many other premisses that
 
might be construed to result in this fact.  Therefore, adduction and production,
 
for all of their uncontrolled generality, but even obduction, in spite of its
 
specificity, cannot be treated as deterministic processes.  Only in degenerate
 
cases, where the number of terms in a discussion is extremely limited, or where
 
the availability of middle terms is otherwise restricted, can it happen that
 
these processes become deterministic.
 
</pre>
 
 
=====1.3.5.3. A Fork in the Road=====
 
 
<pre>
 
| On "logical semblance" -- The concepts "individual" and "species"
 
| equally false and merely apparent.  "Species" expresses only the
 
| fact that an abundance of similar creatures appear at the same
 
| time and that the tempo of their further growth and change is
 
| for a long time slowed down, so actual small continuations
 
| and increases are not very much noticed (-- a phase of
 
| evolution in which the evolution is not visible, so
 
| an equilibrium seems to have been attained, making
 
| possible the false notion that a goal has been
 
| attained -- and that evolution has a goal --).
 
|
 
| (Nietzsche, 'The Will to Power', S 521, 282).
 
 
It is worth trying to discover, as I currently am, how many properties of inquiry
 
can be derived from the simple fact that it needs to be able to apply to itself.
 
I find three main ways to approach the problem of inquiry's self-application,
 
or the question of inquiry's reflexivity:
 
 
  1.  One way attempts to continue the derivation in the manner of a
 
      necessary deduction, perhaps by reasoning in the following vein:
 
      If self-application is a property of inquiry, then it is sensible
 
      to inquire into the concept of application that could make this
 
      conceivable, and not just conceivable, but potentially fruitful.
 
 
  2.  Another way breaks off the attempt at a deductive development and puts forth
 
      a full-scale model of inquiry, one that has enough plausibility to be probated
 
      in the court of experience and enough specificity to be tested in the context
 
      of self-application.
 
 
  3.  The last way is a bit ambivalent in its indications, seeking as it does
 
      both the original unity and the ultimate synthesis at one and the same
 
      time.  Perhaps it goes toward reversing the steps that lead up to this
 
      juncture, marking it down as an impasse, chalking it up as a learning
 
      experience, or admitting the failure of the imagined distinction to
 
      make a difference in reality.  Whether this form of egress is read
 
      as a backtracking correction or as a leaping forward to the next
 
      level of integration, it serves to erase the distinction between
 
      demonstration and exploration.
 
 
Without a clear sense of how many properties of inquiry are necessary
 
consequences of its self-application and how many are merely accessory
 
to it, or even whether some contradiction still lies lurking within the
 
notion of reflexivity, I have no choice but to follow all three lines of
 
inquiry wherever they lead, keeping an eye out for the synchronicities,
 
the constructive collusions and the destructive collisions that may
 
happen to occur among them.
 
 
The fictions that one devises to shore up a shaky account of experience
 
can often be discharged at a later stage of development, gradually coming
 
to be replaced with primitive elements of less and less dubious characters.
 
Hypostases and hypotheses, the creative terms and the inventive propositions
 
that one coins to account for otherwise ineffable experiences, are tokens that
 
are subject to a later account.  Under recurring examination, many such tokens
 
are found to be ciphers, marks that no one will miss if they are cancelled out
 
altogether.  The symbolic currencies that tend to survive lend themselves to
 
being exchanged for stronger and more settled constructions, in other words,
 
for concrete definitions and explicit demonstrations, gradually leading to
 
primitive elements of more and more durable utilities.
 
</pre>
 
 
=====1.3.5.4. A Forged Bond=====
 
 
<pre>
 
| The form counts as something enduring and therefore more valuable; 
 
| but the form has merely been invented by us;  and however often
 
| "the same form is attained", it does not mean that it is the
 
| same form -- what appears is always something new, and it
 
| is only we, who are always comparing, who include the new,
 
| to the extent that it is similar to the old, in the unity of
 
| the "form".  As if a type should be attained and, as it were,
 
| was intended by and inherent in the process of formation.
 
|
 
| (Nietzsche, 'The Will to Power', S 521, 282).
 
 
A unity can be forged among the methods by noticing the following
 
connections among them.  All the while that one proceeds deductively,
 
the primitive elements, the definitions and the axioms, must still be
 
introduced hypothetically, notwithstanding the support they get from
 
common sense and widespread assent.  And the whole symbolic system
 
that is constructed through hypothesis and deduction must still be
 
tested in experience to see if it serves any purpose to maintain it.
 
</pre>
 
 
=====1.3.5.5. A Formal Account=====
 
 
<pre>
 
| Form, species, law, idea, purpose -- in all these cases the same error
 
| is made of giving a false reality to a fiction, as if events were in
 
| some way obedient to something -- an artificial distinction is made
 
| in respect of events between that which acts and that toward which
 
| the act is directed (but this "which" and this "toward" are only
 
| posited in obedience to our metaphysical-logical dogmatism:
 
| they are not "facts").
 
|
 
| (Nietzsche, 'The Will to Power', S 521, 282).
 
 
In this Section (1.3.5), I am considering the step of formalization that
 
takes discussion from a large scale informal inquiry to a well-defined
 
formal inquiry, establishing a relation between the implicit context
 
and the explicit text.
 
 
In this project as a whole, formalization is used to produce formal models
 
that represent relevant features of a phenomenon or process of interest.
 
Thus, the formal model is what constitutes the image of formalization.
 
 
The role of formalization splits into two different cases depending on
 
the intended use of the formal model.  When the phenomenon of interest
 
is external to the agent that is carrying out the formalization, then
 
the model of that phenomenon can be developed without doing any great
 
amount of significant reflection on the formalization process itself.
 
This is usually a more straightforward operation, since it can avail
 
itself of automatic competencies that are not themselves in question.
 
But when the phenomenon of interest is entangled with the conduct of
 
the agent in question, then the formal modeling of that conduct will
 
generally involve a more or less difficult component of reflection.
 
 
In a recursive context, a principal benefit of the formalization
 
step is to find constituents of inquiry with reduced complexities,
 
drawing attention from the context of informal inquiry, whose stock
 
of questions may not be grasped well enough to ever be fruitful and
 
the scope of whose questions may not be focused well enough to ever
 
see an answer, and concentrating effort in an arena of formalized
 
inquiry, where the questions are posed well enough to have some
 
hope of bearing productive answers in a finite time.
 
</pre>
 
 
=====1.3.5.6. Analogs, Icons, Models, Surrogates=====
 
 
<pre>
 
| One should not understand this compulsion to construct concepts, species,
 
| forms, purposes, laws ("a world of identical cases") as if they enabled us
 
| to fix the real world;  but as a compulsion to arrange a world for ourselves
 
| in which our existence is made possible: -- we thereby create a world which is
 
| calculable, simplified, comprehensible, etc., for us.
 
|
 
| (Nietzsche, 'The Will to Power', S 521, 282).
 
 
This project makes pivotal use of certain formal models to represent the
 
conceived structure in a "phenomenon of interest" (POI).  For my purposes,
 
the phenomenon of interest is typically a process of interpretation or a
 
process of inquiry, two nominal species of process that will turn out to
 
evolve from different points of view on the very same form of conduct.
 
 
Commonly, a process of interest presents itself as the trajectory
 
that an agent describes through an extended space of configurations.
 
The work of conceptualization and formalization is to represent this
 
process as a conceptual object in terms of a formal model.  Depending
 
on the point of view that is taken from moment to moment in this work,
 
the "model of interest" (MOI) may be cast as a model of interpretation
 
or as a model of inquiry.  As might be anticipated, it will turn out
 
that both descriptions refer essentially to the same subject, but
 
this will take some development to become clear.
 
 
In this work, the basic structure of each MOI is adopted from the
 
pragmatic theory of signs and the general account of its operation
 
is derived from the pragmatic theory of inquiry.  The indispensable
 
usefulness of these models hinges on the circumstance that each MOI,
 
whether playing its part in interpretation or in inquiry, is always
 
a "model" in two important senses of the word.  First, it is a model
 
in the logical sense that its structure satisfies a formal theory or
 
an abstract specification.  Second, it is a model in the analogical
 
sense that it represents an aspect of the structure that is present
 
in another object or domain.
 
</pre>
 
 
=====1.3.5.7. Steps and Tests of Formalization=====
 
 
<pre>
 
| This same compulsion exists in the sense activities that support reason --
 
| by simplification, coarsening, emphasizing, and elaborating, upon which
 
| all "recognition", all ability to make oneself intelligible rests.  Our
 
| needs have made our senses so precise that the "same apparent world"
 
| always reappears and has thus acquired the semblance of reality.
 
|
 
| (Nietzsche, 'The Will to Power', S 521, 282).
 
 
A step of formalization moves the active focus of discussion from
 
the "presentational object" or the source domain that constitutes
 
the phenomenon of interest to the "representational object" or the
 
target domain that makes up the relevant model of interest.  If the
 
structure in the source context is already formalized then the step
 
of formalization can itself be formalized in an especially elegant
 
and satisfying way as a structure-preserving map, a homomorphism,
 
or an "arrow" in the sense of mathematical category theory.
 
 
The test of a formalization being complete is that a computer program could
 
in principle carry out the steps of the process being formalized exactly as
 
represented in the formal model or image.  It needs to be appreciated that
 
this test is a criterion of sufficiency to formal understanding and not of
 
necessity directed toward a material re-creation or a concrete simulation
 
of the formalized process.  The ordinary agents of informal discussion
 
who address the task of formalization do not disappear in the process
 
of completing it, since it is precisely for their understanding that
 
the step is undertaken.  Only if the phenomenon or process at issue
 
were by its very nature solely a matter of form could its formal
 
analogue constitute an authentic reproduction.  However, this
 
potential consideration is far from the ordinary case that
 
I need to discuss at present.
 
 
In ordinary discussion, agents of inquiry and interpretation depend on
 
the likely interpretations of others to give their common notions and
 
their shared notations a meaning in practice.  This means that a high
 
level of implicit understanding is relied on to ground each informal
 
inquiry in practice.  The entire framework of logical assumptions and
 
interpretive activities that is needed to shore up this platform will
 
itself resist analysis, since it is precisely to save the effort of
 
repeating routine analyses that the whole infrastructure is built.
 
</pre>
 

Latest revision as of 12:54, 19 April 2012

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