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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>
  −
  −
=====1.3.5.8. A Puckish Ref=====
  −
  −
<pre>
  −
| Our subjective compulsion to believe in logic only reveals that,
  −
| long before logic itself entered our consciousness, we did nothing
  −
| but introduce its postulates into events:  now we discover them in
  −
| events -- we can no longer do otherwise -- and imagine that this
  −
| compulsion guarantees something connected with "truth".
  −
|
  −
| (Nietzsche, 'The Will to Power', S 521, 282-283).
  −
  −
In a formal inquiry of the sort projected here, the less the discussants
  −
need to depend on the compliance of understanding interpreters the more
  −
they will necessarily understand at the end of the formalization step.
  −
  −
It might then be thought that the ultimate zero of understanding expected
  −
on the part of the interpreter would correspond to the ultimate height of
  −
understanding demanded on the part of the formalizer, but this assumption
  −
neglects the negative potential of misunderstanding, the sheer perversity
  −
of interpretation that our human creativity can bring to bear on any text.
  −
  −
But computers are initially just as incapable of misunderstanding as they
  −
are of understanding.  Therefore, it actually forms a moderate compromise
  −
to address the task of interpretation to a computational system, a thing
  −
that is known to begin from a moderately neutral intitial condition.
  −
</pre>
  −
  −
=====1.3.5.9. Partial Formalizations=====
  −
  −
<pre>
  −
| It is we who created the "thing", the "identical thing",
  −
| subject, attribute, activity, object, substance, form,
  −
| after we had long pursued the process of making identical,
  −
| coarse, and simple.  The world seems logical to us because
  −
| we have made it logical.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 521, 283).
  −
  −
In many discussions the source context remains unformalized in itself,
  −
taking form only according to the image it receives in one or another
  −
individual MOI.  In cases like these, the step of formalization does
  −
not amount to a total function but is limited to a partial mapping
  −
from the source to the target.  Such a partial representation is
  −
analogous to a sampling operation.  It is not defined on every
  −
point of the source domain but assigns values only to a proper
  −
selection of source elements.  Thus, a partial formalization
  −
can be regarded as achieving its form of simplification in
  −
a loose way, ignoring elements of the source domain and
  −
collapsing material distinctions in irregular fashions.
  −
</pre>
  −
  −
=====1.3.5.10. A Formal Utility=====
  −
  −
<pre>
  −
| Ultimate solution. -- We believe in reason:
  −
| this, however, is the philosophy of gray concepts.
  −
| Language depends on the most naive prejudices.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 522, 283).
  −
  −
The usefulness of the MOI as the upshot of the formalization arrow is
  −
that it provides discussion with a compact image of the source domain.
  −
In formalization one strives to extract a simpler image of the larger
  −
inquiry, a context of participatory action that one is too embroiled
  −
in carrying out step by step to see as a whole.  Seen in this light,
  −
the purpose of formalization is to identify a simpler version of the
  −
problematic phenomenon or to fashion a simpler image of the difficult
  −
inquiry, one that is well-defined enough and simple enough to assure
  −
its termination in a finite interval of space and time.  As a result,
  −
one of the main benefits of adopting the objective of formalization
  −
is that it equips discussion with a pre-set termination criterion,
  −
or a "stopping rule".
  −
  −
In the context of the recursive inquiry that I have outlined,
  −
the step of formalization is intended to bring discussion
  −
appreciably closer to a solid base for the operational
  −
definition of inquiry.
  −
</pre>
  −
  −
=====1.3.5.11. A Formal Aesthetic=====
  −
  −
<pre>
  −
| Now we read disharmonies and problems into things
  −
| because we think only in the form of language --
  −
| and thus believe in the "eternal truth" of
  −
| "reason" (e.g., subject, attribute, etc.)
  −
|
  −
| (Nietzsche, 'The Will to Power', S 522, 283).
  −
  −
Recognizing that the Latin word "forma" means not just "form"
  −
but also "beauty" supplies a clue that not all formal models
  −
are equally valuable for a purpose of interest.  There is
  −
a certain quality of formal elegance, or select character,
  −
that is essential to the practical utility of the model.
  −
  −
The virtue of a good formal model is to provide discussion with
  −
a fitting image of the whole phenomenon of interest.  The aim of
  −
formalization is to extract from an informal discussion or locate
  −
within a broader inquiry a clearer and simpler image of the whole
  −
activity.  If the formalized image or precis is unusually apt then
  −
it might be prized as a gnomon or a recapitulation and be said to
  −
capture the essence, the gist, of the nub of the whole affair.
  −
  −
A pragmatic qualification of this virtue requires that the image be
  −
formed quickly enough to take decisive action on.  So the quality of
  −
being a result often takes precedence over the quality of the result.
  −
A definite result, however partial, is frequently reckoned as better
  −
than having to wait for a definitive picture that may never develop.
  −
  −
But an overly narrow or premature formalization, where the nature of
  −
the phenomenon of interest is too much denatured in the formal image,
  −
may result in destroying all interest in the result that does result.
  −
</pre>
  −
  −
=====1.3.5.12. A Formal Apology=====
  −
  −
<pre>
  −
| We cease to think when we refuse to do so under the constraint of language;
  −
| we barely reach the doubt that sees this limitation as a limitation.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 522, 283).
  −
  −
Seizing the advantage of this formal flexibility makes it possible
  −
to take abstract leaps over a multitude of material obstacles,
  −
to reason about many properties of objects and processes
  −
from a knowledge of their form alone, without having
  −
to know everything about their material content
  −
down to the depths that matter can go.
  −
</pre>
  −
  −
=====1.3.5.13. A Formal Suspicion=====
  −
  −
<pre>
  −
| Rational thought is interpretation according to a scheme that we cannot throw off.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 522, 283).
  −
  −
I hope that the reader has arrived by now at an independent suspicion that the
  −
process of formalization is a microcosm nearly as complex as the whole subject
  −
of inquiry itself.  Indeed, the initial formulation of a problem is tantamount
  −
to a mode of "representational inquiry".  In many ways this very first effort,
  −
that stirs from the torpor of ineffable unease to seek out any sort of unity
  −
in the manifold of fragmented impressions, is the most difficult, subtle,
  −
and crucial kind of inquiry.  It begins in doubt about even so much as
  −
a fair way to represent the problematic situation, but its result can
  −
predestine whether subsequent inquiry has any hope of success.  There
  −
is very little in this brand of formal engagement and participatory
  −
representation that resembles the simple and disinterested act of
  −
holding a mirror, flat and featureless, up to nature.
  −
  −
If formalization really is a form of inquiry in itself, then
  −
its formulations have deductive consequences that can be tested.
  −
In other words, formal models have logical effects that reflect on
  −
their fitness to qualify as representations, and these effects can
  −
cause them to be rejected merely on the grounds of being a defective
  −
picture or a misleading conception of the source phenomenon.  Therefore,
  −
it should be appreciated that software tailored to this task will probably
  −
need to spend more time in the alterations of backtracking than it will have
  −
occasion to trot out parades of ready-to-wear models.
  −
  −
Impelled by the mass of assembled clues from restarts and refits to the
  −
gathering form of a coherent direction, the inkling may have gradually
  −
accumulated in the reader that something of the same description has
  −
been treated in the pragmatic theory of inquiry under the heading
  −
of "abductive reasoning".  This is distinguished from inductive
  −
reasoning, that goes from the particular to the general, in
  −
that abductive reasoning must work from a mixed collection
  −
of generals and particulars toward a middle term, a formal
  −
intermediary that is more specific than the vague allusions
  −
gathered about its subject and more generic than the elusive
  −
instances fashioned to illustrate its prospective predicates.
  −
  −
In a recursive context, the function of formalization is to relate a
  −
difficult problem to a simpler problem, breaking the original inquiry
  −
into two parts, the step of formalization and the rest of the inquiry,
  −
both of which branches it is hoped will be nearer to solid ground and
  −
easier to grasp than the original question.
  −
</pre>
  −
  −
=====1.3.5.14. The Double Aspect of Concepts=====
  −
  −
<pre>
  −
| Nothing is more erroneous than to make of
  −
| psychical and physical phenomena the two faces,
  −
| the two revelations of one and the same substance.
  −
| Nothing is explained thereby:  the concept "substance"
  −
| is perfectly useless as an explanation.  Consciousness in
  −
| a subsidiary role, almost indifferent, superfluous, perhaps
  −
| destined to vanish and give way to a perfect automatism --
  −
|
  −
| (Nietzsche, 'The Will to Power', S 523, 283).
  −
  −
This project is a particular inquiry into the nature of inquiry in general.
  −
As a consequence, every concept that appears in it takes on a double aspect.
  −
  −
To illustrate, let us take the concept of a "sign relation" as an example
  −
of a construct that appears in this work and let me use it to speak about
  −
my own agency in this inquiry.  All I need to say about a sign relation
  −
at this point is that it is a three-place relation, and therefore can
  −
be represented as a relational data-base with three columns, in this
  −
case naming the "object", the "sign", and the "interpretant" of the
  −
relation at each moment in time of the corresponding "sign process".
  −
  −
At any given moment of this inquiry I will be participating in a certain
  −
sign relation that constitutes the informal context of my activity, the
  −
full nature of which I can barely hope to conceptualize in explicitly
  −
formal terms.  At times, the object of this informal sign relation
  −
will itself be a sign relation, typically one that is already
  −
formalized or one that I have a better hope of formalizing,
  −
but it could conceivably be the original sign relation
  −
with which I began.
  −
  −
In such cases, when the object of a sign relation
  −
is also a sign relation, the general concept of
  −
a sign relation takes on a double duty:
  −
  −
  1.  The less formalized sign relation is used to mediate the
  −
      present inquiry.  As a conceptual construct, it is not yet
  −
      fully conceived or not yet fully constructed at the moments
  −
      of inquiry being considered.  Perhaps it is better to regard
  −
      it as a "concept under construction".  Employed as a contextual
  −
      apparatus, this sign relation serves an instrumental role in the
  −
      construal and the study of its designated objective sign relation.
  −
  −
  2.  The more formalized sign relation is mentioned as a substantive object
  −
      to be contemplated and manipulated by the proceedings of this inquiry.
  −
      As a conceptual construct, it exemplifies its intended role best if it
  −
      is already as completely formalized as possible.  It is being engaged
  −
      as a substantive object of inquiry.
  −
  −
I have given this inquiry a reflective or recursive cast, portraying it
  −
as an inquiry into inquiry, and one of the consequences of this picture
  −
is that every concept employed in the work will take on a divided role,
  −
double aspect, or dual purpose.  At any moment, the object inquiry of
  −
the moment is aimed to take on a formal definition, while the active
  −
inquiry need not acknowledge any image that it does not recognize
  −
as reflecting itself, nor is it bound by any horizon that does
  −
not capture its spirit.
  −
</pre>
  −
  −
=====1.3.5.15. A Formal Permission=====
  −
  −
<pre>
  −
NB.  These sections are still too provisional to share,
  −
but I will record the epitexts that I have in my notes.
  −
  −
| If there are to be synthetic a priori judgments, then reason must
  −
| be in a position to make connections:  connection is a form.
  −
| Reason must possess the capacity of giving form.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 530, 288).
  −
</pre>
  −
  −
=====1.3.5.16. A Formal Invention=====
  −
  −
<pre>
  −
| Before there is "thought" (gedacht) there
  −
| must have been "invention" (gedichtet);
  −
| the construction of identical cases,
  −
| of the appearance of sameness,
  −
| is more primitive than the
  −
| knowledge of sameness.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 544, 293).
  −
</pre>
  −
  −
====1.3.6. Recursion in Perpetuity====
  −
  −
<pre>
  −
| Will to truth is a making firm, a making true and durable,
  −
| an abolition of the false character of things,
  −
| a reinterpretation of it into beings.
  −
|
  −
| "Truth" is therefore not something there, that might be found or discovered --
  −
| but something that must be created and that gives a name to a process,
  −
| or rather to a will to overcome that has in itself no end --
  −
| introducing truth, as a processus in infinitum, an active determining --
  −
| not a becoming-conscious of something that is in itself firm and determined.
  −
|
  −
| It is a word for the "will to power".
  −
|
  −
| (Nietzsche, 'The Will to Power', S 552, 298).
  −
  −
| Life is founded upon the premise of a belief in enduring
  −
| and regularly recurring things;  the more powerful life is,
  −
| the wider must be the knowable world to which we, as it were,
  −
| attribute being.  Logicizing, rationalizing, systematizing as
  −
| expedients of life.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 552, 298-299).
  −
  −
| Man projects his drive to truth, his "goal" in a certain sense,
  −
| outside himself as a world that has being, as a metaphysical world,
  −
| as a "thing-in-itself", as a world already in existence.  His needs
  −
| as creator invent the world upon which he works, anticipate it;
  −
| this anticipation (this "belief" in truth) is his support.
  −
|
  −
| (Nietzsche, 'The Will to Power', S 552, 299).
  −
</pre>
 
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