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| | <div class="nonumtoc">__TOC__</div> | | <div class="nonumtoc">__TOC__</div> |
| | + | |
| | + | ==Discussion== |
| | | | |
| | ==Work Area== | | ==Work Area== |
| − |
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| − | ===1.3.===
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| − |
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| − | ====1.3.5. Discussion of Formalization : Specific Objects====
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| − |
| |
| − | <pre>
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| − | | "Knowledge" is a referring back: in its essence a regressus in infinitum.
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| − | | That which comes to a standstill (at a supposed causa prima, at something
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| − | | unconditioned, etc.) is laziness, weariness --
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| − | |
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| − | | (Nietzsche, 'The Will to Power', S 575, 309).
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| − |
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| − | With this preamble, I return to develop my own account of formalization,
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| − | 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.
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| − | A formalization step, of the incipient kind being considered here, has
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| − | the peculiar property that one can say with some definiteness where it
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| − | ends, since it leads precisely to a well-defined formal model, but not
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| − | with any definiteness where it begins. Any attempt to trace the steps
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| − | of formalization backward toward their ultimate beginnings can lead to
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| − | an interminable multiplicity of open-ended explorations. In view of
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| − | these circumstances, I will limit my attention to the frame of the
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| − | present inquiry and try to sum up what brings me to this point.
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| − |
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| − | It begins like this: I ask whether it is possible to reason about inquiry
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| − | in a way that leads to a productive end. I pose my question as an inquiry
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| − | into inquiry, and I use the formula "y_0 = y y" to express the relationship
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| − | between the present inquiry, y_0, and a generic inquiry, y. Then I propose
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| − | a couple of components of inquiry, discussion and formalization, that appear
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| − | to be worth investigating, expressing this proposal in the form "y >= {d, f}".
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| − | Applying these components to each other, as must be done in the present inquiry,
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| − | I am led to the current discussion of formalization, y_0 = y y >= f d.
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| − |
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| − | There is already much to question here. At least,
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| − | so many repetitions of the same mysterious formula
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| − | are bound to lead the reader to question its meaning.
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| − | Some of the more obvious issues that arise are these:
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| − |
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| − | The term "generic inquiry" is ambiguous. Its meaning in practice
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| − | depends on whether the description of an inquiry as being generic
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| − | is interpreted literally or merely as a figure of speech. In the
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| − | literal case, the name "y" denotes a particular inquiry, y in Y,
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| − | one that is assumed to be plenipotential or prototypical in yet
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| − | to be specified ways. In the figurative case, the name "y" is
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| − | simply a variable that ranges over a collection Y of nominally
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| − | conceivable inquiries.
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| − |
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| − | First encountered, the recipe "y_0 = y y" seems to specify that
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| − | the present inquiry is constituted by taking everything that is
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| − | denoted by the most general concept of inquiry that the present
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| − | inquirer can imagine and inquiring into it by means of the most
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| − | general capacity for inquiry that this same inquirer can muster.
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| − |
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| − | Contemplating the formula "y_0 = y y" in the context of the subordination
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| − | y >= {d, f} and the successive containments F c M c D, the y that inquires
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| − | into y is not restricted to examining y's immediate subordinates, d and f,
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| − | but it can investigate any feature of y's overall context, whether objective,
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| − | syntactic, interpretive, and whether definitive or incidental, and finally it
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| − | can question any supporting claim of the discussion. Moreover, the question y
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| − | is not limited to the particular claims that are being made here, but applies to
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| − | the abstract relations and the general concepts that are invoked in making them.
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| − | Among the many additional kinds of inquiry that suggest themselves at this point,
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| − | I see at least the following possibilities:
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| − |
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| − | 1. Inquiry into propositions about application and equality.
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| − | Just by way of a first example, one might well begin by
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| − | considering the forms of application and equality that
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| − | are invoked in the formula "y_0 = y y" itself.
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| − |
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| − | 2. Inquiry into application, for example, the way that
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| − | the term "y y" indicates the application of y to y
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| − | in the formula "y_0 = y y".
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| − |
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| − | 3. Inquiry into equality, for example,
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| − | the meaning of "=" in "y_0 = y y".
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| − |
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| − | 4. Inquiry into indices, for example,
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| − | the significance of "0" in "y_0".
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| − |
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| − | 5. Inquiry into terms, specifically, constants and variables.
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| − | What are the functions of "y" and "y_0" in this respect?
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| − |
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| − | 6. Inquiry into decomposition or subordination, for example,
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| − | as invoked by the sign ">=" in the formula "y >= {d, f}".
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| − |
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| − | 7. Inquiry into containment or inclusion. In particular, examine the
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| − | claim "F c M c D" that conditions the chances that a formalization
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| − | has an object, the degree to which a formalization can be carried
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| − | out by means of a discussion, and the extent to which an object
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| − | of formalization can be conveyed by a form of discussion.
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| − |
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| − | If inquiry begins in doubt, then inquiry into inquiry begins in
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| − | doubt about doubt. All things considered, the formula "y_0 = y y"
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| − | has to be taken as the first attempt at a description of the problem,
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| − | a hypothesis about the nature of inquiry, or an image that is tossed out
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| − | by way of getting an initial fix on the object in question. Everything in
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| − | this account so far, and everything else that I am likely to add, can only
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| − | be reckoned as hypothesis, whose accuracy, pertinence, and usefulness can
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| − | be tested, judged, and redeemed only after the fact of proposing it and
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| − | after the facts to which it refers have themselves been gathered up.
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| − |
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| − | A number of problems present themselves due to the context in which
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| − | the present inquiry is aimed to present itself. The hypothesis that
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| − | suggests itself to one person, as worth exploring at a particular time,
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| − | does not always present itself to another person as worth exploring at
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| − | the same time, or even necessarily to the same person at another time.
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| − | In a community of inquiry that extends beyond an isolated person and
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| − | in a process of inquiry that extends beyond a singular moment in time,
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| − | it is therefore necessary to consider the nature of the communication
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| − | process that the discussion of inquiry in general and the discussion of
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| − | formalization in particular need to invoke for their ultimate utility.
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| − |
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| − | Solitude and solipsism are no solution to the problems of community and
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| − | communication, since even an isolated individual, if ever there was, is,
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| − | or comes to be such a thing, has to maintain the lines of communication
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| − | that are required to integrate past, present, and prospective selves --
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| − | in other words, translating everything into present terms, the parts of
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| − | one's actually present self that involve actual experiences and present
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| − | observations, do present expectations as reflective of actual memories,
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| − | and do present intentions as reflective of actual hopes. Consequently,
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| − | the dialogue that one holds with oneself is every bit as problematic
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| − | as the dialogue that one enters with others. Others only surprise
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| − | one in other ways than one ordinarily surprises oneself.
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| − |
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| − | I recognize inquiry as beginning with a "surprising phenomenon" or
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| − | a "problematic situation", more briefly described as a "surprise"
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| − | or a "problem", respectively. These are the types of moments that
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| − | try our souls, the instances of events that instigate inquiry as
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| − | an effort to achieve their own resolution. Surprises and problems
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| − | are experienced as afflicted with an irritating uncertainty or a
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| − | compelling difficulty, one that calls for a response on the part
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| − | of the agent in question:
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| − |
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| − | 1. A "surprise" calls for an explanation to resolve the
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| − | uncertainty that is present in it. This uncertainty
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| − | is associated with a difference between observations
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| − | and expectations.
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| − |
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| − | 2. A "problem" calls for a plan of action to resolve the
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| − | difficulty that is present in it. This difficulty is
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| − | associated with a difference between observations and
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| − | intentions.
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| − |
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| − | To express this diversity in a unified formula: Both types of inquiry
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| − | begin with a "delta", a compact term that admits of expansion as a debt,
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| − | a difference, a difficulty, a discrepancy, a dispersion, a distribution,
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| − | a doubt, a duplicity, or a duty.
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| − |
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| − | Expressed another way, inquiry begins with a doubt about one's object,
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| − | whether this means what is true of a case, an object, or a world, what
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| − | to do about reaching a goal, or whether the hoped-for goal is really
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| − | good for oneself -- with all that these questions lead to in essence,
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| − | in deed, or in fact.
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| − |
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| − | Perhaps there is an inexhaustible reality that issues in these
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| − | apparent mysteries and recurrent crises, but, by the time I say
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| − | this much, I am already indulging in a finite image, a hypothesis
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| − | about what is going on. If nothing else, then, one finds again the
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| − | familiar pattern, where the formative relation between the informal
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| − | and the formal merely serves to remind one anew of the relationship
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| − | between the infinite and the finite.
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| − | </pre>
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| − |
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| − | =====1.3.5.1. The Will to Form=====
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| − |
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| − | <pre>
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| − | | The power of form, the will to give form to oneself. "Happiness"
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| − | | admitted as a goal. Much strength and energy behind the emphasis
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| − | | on forms. The delight in looking at a life that seems so easy. --
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| − | | To the French, the Greeks looked like children.
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| − | |
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| − | | (Nietzsche, 'The Will to Power', S 94, 58).
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| − |
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| − | Let me see if I can summarize as quickly as possible the problem that I see before me.
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| − | On each occasion that I try to express my experience, to lend it a form that others
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| − | can recognize, to put it in a shape that I myself can later recall, or to store it
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| − | in a state that allows me the chance of its re-experience, I generate an image of
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| − | the way things are, or at least a description of how things seem to me. I call
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| − | this process "reflection", since it fabricates an image in a medium of signs
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| − | that reflects an aspect of experience. Very often this experience is said
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| − | to be "of" -- what? -- something that exists or persists at least partly
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| − | outside the immediate experience, some action, event, or object that is
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| − | imagined to inform the present experience, or perhaps some conduct of
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| − | one's own doing that obtrudes for a moment into the world of others
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| − | and meets with a reaction there. In all of these cases, where the
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| − | experience is everted to refer to an object and thus becomes the
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| − | attribute of something with an external aspect, something that
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| − | is thus supposed to be a prior cause of the experience, the
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| − | reflection on experience doubles as a reflection on that
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| − | conduct, performance, or transaction that the experience
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| − | is an experience "of". In short, if the experience has
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| − | an eversion that makes it an experience of an object,
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| − | then its reflection is again a reflection that is
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| − | also of this object.
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| − |
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| − | Just at the point where one threatens to become lost in the morass of
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| − | words for describing experience and the nuances of their interpretation,
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| − | one can adopt a formal perspective, and realize that the relation among
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| − | objects, experiences, and reflective images is formally analogous to the
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| − | relation among objects, signs, and interpretant signs that is covered by
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| − | the pragmatic theory of signs. One still has the problem: How are the
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| − | expressions of experience everted to form the exterior faces of extended
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| − | objects and exploited to embed them in their external circumstances, and
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| − | no matter whether this object with an outer face is oneself or another?
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| − | Here, one needs to understand that expressions of experience include
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| − | the original experiences themselves, at least, to the extent that
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| − | they permit themselves to be recognized and reflected in ongoing
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| − | experience. But now, from the formal point of view, "how" means
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| − | only: To describe the formal conditions of a formal possibility.
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| − | </pre>
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| − |
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| − | =====1.3.5.2. The Forms of Reasoning=====
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| − |
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| − | <pre>
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| − | | The most valuable insights are arrived at last;
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| − | | but the most valuable insights are methods.
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| − | |
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| − | | (Nietzsche, 'The Will to Power', S 469, 261).
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| − |
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| − | A certain arbitrariness has to be faced in the terms that one uses
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| − | to talk about reasoning, to split it up into different parts and
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| − | to sort it out into different types. It is like the arbitrary
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| − | choice that one makes in assigning the midpoint of an interval
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| − | to the subintervals on its sides. In setting out the forms of
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| − | a nomenclature, in fitting the schemes of my terminology to the
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| − | territory that it disturbs in the process of mapping, I cannot
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| − | avoid making arbitrary choices, but I can aim for a strategy
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| − | that is flexible enough to recognize its own alternatives and
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| − | to accommodate the other options that lie within their scope.
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| − |
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| − | If I make the mark of deduction the fact that it reduces the
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| − | number of terms, as it moves from the grounds to the end of
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| − | an argument, then I am due to devise a name for the process
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| − | that augments the number of terms, and thus prepares the
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| − | grounds for any account of experience.
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| − |
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| − | What name hints at the many ways that signs arise in regard to things?
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| − | What name covers the manifest ways that a map takes over its territory?
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| − | What name fits this naming of names, these proceedings that inaugurate
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| − | a sign in the first place, that duly install it on the office of a term?
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| − | What name suits all these actions of addition, annexation, incursion, and
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| − | invention that instigate the initial bearing of signs on an object domain?
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| − |
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| − | In the interests of a "maximal analytic precision" (MAP), it is fitting
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| − | that I should try to sharpen this notion to the point where it applies
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| − | purely to a simple act, that of entering a new term on the lists, in
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| − | effect, of enlisting a new term to the ongoing account of experience.
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| − | Thus, let me style this process as "adduction" or "production", in
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| − | spite of the fact that the aim of precision is partially blunted
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| − | by the circumstance that these words have well-worn uses in other
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| − | contexts. In this way, I can isolate to some degree the singular
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| − | step of adding a term, leaving it to a later point to distinguish
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| − | the role that it plays in an argument.
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| − |
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| − | As it stands, the words "adduction" and "production" could apply to the
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| − | arbitrary addition of terms to a discussion, whether or not these terms
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| − | participate in valid forms of argument or contribute to their mediation.
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| − | Although there are a number of auxiliary terms, like "factorization",
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| − | "mediation", or "resolution", that can help to pin down these meanings,
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| − | it is also useful to have a word that can convey the exact sense meant.
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| − | Therefore, I coin the term "obduction" to suggest the type of reasoning
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| − | process that is opposite or converse to deduction and that introduces
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| − | a middle term "in the way" as it passes from a subject to a predicate.
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| − |
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| − | Consider the adjunction to one's vocabulary that is comprised of these three words:
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| − | "adduction", "production", "obduction". In particular, how do they appear in the
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| − | light of their mutual applications to each other and especially with respect to
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| − | their own reflexivities? Notice that the terms "adduction" and "production"
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| − | apply to the ways that all three terms enter this general discussion, but
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| − | that "obduction" applies only to their introduction only in specific
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| − | contexts of argument.
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| − |
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| − | Another dimension of variation that needs to be noted among these different types
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| − | of processes is their status with regard to determimism. Given the ordinary case
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| − | of a well-formed syllogism, deduction is a fully deterministic process, since the
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| − | middle term to be eliminated is clearly marked by its appearance in a couple of
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| − | premisses. But if one is given nothing but the fact that forms this conclusion,
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| − | or starts with a fact that is barely suspected to be the conclusion of a possible
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| − | deduction, then there are many other middle terms and many other premisses that
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| − | might be construed to result in this fact. Therefore, adduction and production,
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| − | for all of their uncontrolled generality, but even obduction, in spite of its
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| − | specificity, cannot be treated as deterministic processes. Only in degenerate
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| − | cases, where the number of terms in a discussion is extremely limited, or where
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| − | the availability of middle terms is otherwise restricted, can it happen that
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| − | these processes become deterministic.
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| − | </pre>
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| − |
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| − | =====1.3.5.3. A Fork in the Road=====
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| − |
| |
| − | <pre>
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| − | | On "logical semblance" -- The concepts "individual" and "species"
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| − | | equally false and merely apparent. "Species" expresses only the
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| − | | fact that an abundance of similar creatures appear at the same
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| − | | time and that the tempo of their further growth and change is
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| − | | for a long time slowed down, so actual small continuations
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| − | | and increases are not very much noticed (-- a phase of
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| − | | evolution in which the evolution is not visible, so
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| − | | an equilibrium seems to have been attained, making
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| − | | possible the false notion that a goal has been
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| − | | attained -- and that evolution has a goal --).
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| − | |
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| − | | (Nietzsche, 'The Will to Power', S 521, 282).
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| − |
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| − | It is worth trying to discover, as I currently am, how many properties of inquiry
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| − | can be derived from the simple fact that it needs to be able to apply to itself.
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| − | I find three main ways to approach the problem of inquiry's self-application,
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| − | or the question of inquiry's reflexivity:
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| − |
| |
| − | 1. One way attempts to continue the derivation in the manner of a
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| − | necessary deduction, perhaps by reasoning in the following vein:
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| − | If self-application is a property of inquiry, then it is sensible
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| − | to inquire into the concept of application that could make this
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| − | conceivable, and not just conceivable, but potentially fruitful.
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| − |
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| − | 2. Another way breaks off the attempt at a deductive development and puts forth
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| − | 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
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| − | of self-application.
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| − |
| |
| − | 3. The last way is a bit ambivalent in its indications, seeking as it does
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| − | both the original unity and the ultimate synthesis at one and the same
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| − | time. Perhaps it goes toward reversing the steps that lead up to this
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| − | juncture, marking it down as an impasse, chalking it up as a learning
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| − | experience, or admitting the failure of the imagined distinction to
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| − | make a difference in reality. Whether this form of egress is read
| |
| − | as a backtracking correction or as a leaping forward to the next
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| − | level of integration, it serves to erase the distinction between
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| − | demonstration and exploration.
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| − |
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| − | Without a clear sense of how many properties of inquiry are necessary
| |
| − | consequences of its self-application and how many are merely accessory
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| − | 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
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| − | inquiry wherever they lead, keeping an eye out for the synchronicities,
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| − | the constructive collusions and the destructive collisions that may
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| − | happen to occur among them.
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| − |
| |
| − | 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
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| − | 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
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| − | primitive elements of more and more durable utilities.
| |
| − | </pre>
| |
| − |
| |
| − | =====1.3.5.4. A Forged Bond=====
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| − |
| |
| − | <pre>
| |
| − | | The form counts as something enduring and therefore more valuable;
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| − | | but the form has merely been invented by us; and however often
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| − | | "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,
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| − | | to the extent that it is similar to the old, in the unity of
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| − | | the "form". As if a type should be attained and, as it were,
| |
| − | | was intended by and inherent in the process of formation.
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| − | |
| |
| − | | (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>
| |
