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| | <pre> | | <pre> |
| − | | "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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| − | | (Nietzsche, 'The Will to Power', S 575, 309).
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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
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| − | 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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| − | 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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| − | 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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| − | 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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| − | 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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| − | 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 | | If inquiry begins in doubt, then inquiry into inquiry begins in |
| | doubt about doubt. All things considered, the formula "y_0 = y y" | | doubt about doubt. All things considered, the formula "y_0 = y y" |
