| Line 1: |
Line 1: |
| | <div class="nonumtoc">__TOC__</div> | | <div class="nonumtoc">__TOC__</div> |
| | + | |
| | + | ==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>
| |
