Changes

=====1.3.5.5.  A Formal Account=====

=====1.3.5.5.  A Formal Account=====

<blockquote>

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 S521, 282).

<p>Form, species, law, idea, purpose &mdash; 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 &mdash; 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").</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S521, 282]

In this section I consider 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 section I consider 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, 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.

In this project, 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 significant reflection on the formalization process itself.  This is usually a more straightforward operation, since it avails itself of automatic competencies that are not themselves in question.  However, ...

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 significant reflection on the formalization process itself.  This is usually a more straightforward operation, since it avails itself of automatic competencies that are not themselves in question.  However, &hellip;

 

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.

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.

=====1.3.5.6.  Analogs, Icons, Models, Surrogates=====

=====1.3.5.6.  Analogs, Icons, Models, Surrogates=====

<blockquote>

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 S521, 282).

<p>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: &mdash; we thereby create a world which is calculable, simplified, comprehensible, etc., for us.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power''. [Nie, S521, 282]

This project makes pivotal use of certain formal models to represent the conceived structure in a phenomenon of interest.  For my purposes, the phenomenon of interest is typically a process of interpretation (POI) or a process of inquiry (POI), two nominal species of process that will turn out to evolve from different points of view on the same form of conduct.

This project makes pivotal use of certain formal models to represent the conceived structure in a phenomenon of interest.  For my purposes, the phenomenon of interest is typically a process of interpretation (POI) or a process of inquiry (POI), two nominal species of process that will turn out to evolve from different points of view on the 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 formal model of interest may be cast either as a model of interpretation (MOI) or as a model of inquiry (MOI).  As might be guessed, it will turn out that both descriptions refer essentially to the same subject, but this will take some development to become clear.

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 formal model of interest may be cast either as a model of interpretation (MOI) or as a model of inquiry (MOI).  As might be guessed, 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 indispensible utility of these formal 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.

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 utility of these formal 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.

=====1.3.5.7.  Steps and Tests of Formalization=====

=====1.3.5.7.  Steps and Tests of Formalization=====

<blockquote>

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 S521, 282).

<p>This same compulsion exists in the sense activities that support reason &mdash; 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.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S521, 282]

A step of formalization moves the active focus of discussion from the "presentational object" or source domain to the "representational object" or "target domain" that constitutes the relevant MOI.  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, homomorphism, or "arrow" of category theory.

A step of formalization moves the active focus of discussion from the ''presentational object'' or ''source domain'' to the ''representational object'' or ''target domain'' that constitutes the relevant MOI.  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, homomorphism, or ''arrow'' of category theory.

The test of a formalization being complete is that a computer could in principle carry out the steps of the process exactly as represented in the formal model or image.  It needs to be appreciated that this is a criterion of sufficiency to formal understanding and not of necessity relevant to material re-creation.  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 at issue were by its very nature solely a matter of form could its formal analogue constitute an authentic reproduction.  But this potential consideration is far from the ordinary case I need to discuss at present.

The test of a formalization being complete is that a computer could in principle carry out the steps of the process exactly as represented in the formal model or image.  It needs to be appreciated that this is a criterion of sufficiency to formal understanding and not of necessity relevant to material re-creation.  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 at issue were by its very nature solely a matter of form could its formal analogue constitute an authentic reproduction.  But this potential consideration is far from the ordinary case I need to discuss at present.

=====1.3.5.8.  The Referee=====

=====1.3.5.8.  The Referee=====

<blockquote>

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 S521, 282-283).

<p>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 &mdash; we can no longer do otherwise &mdash; and imagine that this compulsion guarantees something connected with "truth".</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S521, 282&ndash;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.  It might 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 neglects the negative potential of misunderstanding, the sheer perversity of interpretation that true 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, something that is known to begin from a relatively neutral intitial condition.

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.  It might 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 neglects the negative potential of misunderstanding, the sheer perversity of interpretation that true 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, something that is known to begin from a relatively neutral initial condition.

=====1.3.5.9.  Partial Formalizations=====

=====1.3.5.9.  Partial Formalizations=====

<blockquote>

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 S521, 283).

<p>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.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S521, 283]

In many discussions the source context remains unformalized in itself, taking form only according to the image it receives in this or that individual MOI.  In this case, the step of formalization is not a total function but 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, by ignoring elements of the source domain and collapsing material distinctions in an irregular fashion.

In many discussions the source context remains unformalized in itself, taking form only according to the image it receives in this or that individual MOI.  In this case, the step of formalization is not a total function but 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, by ignoring elements of the source domain and collapsing material distinctions in an irregular fashion.

<blockquote>

<blockquote>

Ultimate solution. - We believe in reason:  this, however, is the philosophy of gray concepts.  Language depends on the most naive prejudices.

Ultimate solution. &mdash; We believe in reason:  this, however, is the philosophy of gray concepts.  Language depends on the most naive prejudices.

(Nietzsche, The Will to Power S522, 283).

(Nietzsche, The Will to Power S522, 283).

</blockquote>

</blockquote>

</blockquote>

</blockquote>

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.)

Now we read disharmonies and problems into things because we think only in the form of language &mdash; and thus believe in the "eternal truth" of "reason" (e.g., subject, attribute, etc.)

(Nietzsche, The Will to Power S522, 283).

(Nietzsche, The Will to Power S522, 283).

</blockquote>

</blockquote>