Changes

=====1.3.5.12.  A Formal Apology=====

=====1.3.5.12.  A Formal Apology=====

<blockquote>

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 S522, 283).

<p>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.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S522, 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 knowledge of their form alone, without having to know everything about their material content down to the depths that matter can go.

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 knowledge of their form alone, without having to know everything about their material content down to the depths that matter can go.

=====1.3.5.13.  A Formal Suspicion=====

=====1.3.5.13.  A Formal Suspicion=====

<blockquote>

Rational thought is interpretation according to a scheme that we cannot throw off.

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

<p>Rational thought is interpretation according to a scheme that we cannot throw off.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S522, 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 first effort, that stirs from the torpor of ineffable unease to seek 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.

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 first effort, that stirs from the torpor of ineffable unease to seek 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.

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.

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.

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.

=====1.3.5.14.  The Double Aspect of Concepts=====

=====1.3.5.14.  The Double Aspect of Concepts=====

<blockquote>

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 S523, 283).

<p>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 &mdash;</p>

|-

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S523, 283]

This work is a particular inquiry into the nature of inquiry in general.  As a consequence, every conceptual construct that appears in it will take on a double aspect.

This work is a particular inquiry into the nature of inquiry in general.  As a consequence, every conceptual construct that appears in it will take on a double aspect.

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:

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 inquiry.  As a conceptual construct, it is not yet fully conceived or 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 study or construal of its objective sign relation.

# The less formalized sign relation is used to mediate the inquiry.  As a conceptual construct, it is not yet fully conceived or 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 study or construal of its objective sign relation.

# The more formalized sign relation is mentioned as a substantive object to be contemplated and manipulated by the inquiry.  As a conceptual construct, it exemplifies the role intended for it best if it is already as completely formalized as possible.  It is being engaged as a substantive object of inquiry.

I have given this project a reflective or a recursive cast, describing it as inquiry into inquiry, and one of the consequences of this is that every concept employed in the work will take on a double aspect, divided role, or dual purpose.  At any moment, the object inquiry of the moment is aimed to take on a formal definition, whereas the active inquiry &hellip;

I have given this project a reflective or a recursive cast, describing it as inquiry into inquiry, and one of the consequences of this is that every concept employed in the work will take on a double aspect, divided role, or dual purpose.  At any moment, the object inquiry of the moment is aimed to take on a formal definition, whereas the active inquiry ...

=====1.3.5.15.  A Formal Permission=====

=====1.3.5.15.  A Formal Permission=====

<blockquote>

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 S530, 288).

<p>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.</p>

| align="right" | &mdash; Nietzsche, ''The Will to Power'', [Nie, S530, 288]

=====1.3.5.16.  A Formal Invention=====

=====1.3.5.16.  A Formal Invention=====

<blockquote>

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 S544, 293).

<p>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.</p>

| align="right" | Nietzsche, ''The Will to Power'', [Nie, S544, 293]

====1.3.6.  Recursion in Perpetuity====

====1.3.6.  Recursion in Perpetuity====