Changes

As I understand them, variables are a class of beneficially ambiguous or usefully equivocal signs.  In effect, variables are just signs, but signs possessed of a more adaptive constitution or affected by a more flexible interpretation than signs of the usual, more constant variety.  These forms of employment turn variables into a class of reusable signs, converting them into sustainable resources for meaning that can be used in a plurality of ways and deployed to articulate different choices at different times from among the available points of thematic variation.

As I understand them, variables are a class of beneficially ambiguous or usefully equivocal signs.  In effect, variables are just signs, but signs possessed of a more adaptive constitution or affected by a more flexible interpretation than signs of the usual, more constant variety.  These forms of employment turn variables into a class of reusable signs, converting them into sustainable resources for meaning that can be used in a plurality of ways and deployed to articulate different choices at different times from among the available points of thematic variation.

The next major task of this discussion, while continuing to take its bearings from examples as concrete as <math>L(A)\!</math> and <math>L(B),\!</math> is to develop systematic methods for divining the bearing of such isolated examples on issues of real concern.  This involves two stages:

The next major task of this discussion, while continuing to take its bearings from examples as concrete as A and B, is to develop systematic methods for divining the bearing of such isolated examples on issues of real concern.  This involves two stages:

# One needs to detect the invariant features of the currently known examples, in other words, the dimensions along which their values are, knowingly or unknowingly, held to be constant.

 

# One needs to try varying the features that are presently held to be constant by imagining new examples that are able to realize alternative features.

1. One needs to detect the invariant features of the currently known examples, in other words, the dimensions along which their values are, knowingly or unknowingly, held to be constant.

 

2. One needs to try varying the features that are presently held to be constant by imagining new examples that are able to realize alternative features.

The larger issue at stake throughout these stages is how the agent of inquiry can find ways to express the lessons of individual exercises in ways that persist through and rise above their individual attachments to experience, thereby living through detailed experiences while remaining undiverted by their peculiar distractions.

The larger issue at stake throughout these stages is how the agent of inquiry can find ways to express the lessons of individual exercises in ways that persist through and rise above their individual attachments to experience, thereby living through detailed experiences while remaining undiverted by their peculiar distractions.

I would like to detach, for a moment, from the particular contrast of interest here, the one posed between dynamic and symbolic orientations, to examine the general question of relating contrasting aspects or views.  In this connection, two distinct but correlated efforts at classification and organization arise in tandem with each other.  One concern seeks to classify the attributes, categories, features, properties, or qualities that are used to describe the object observed, while the other project tries to organize the approaches, instruments, methods, perspectives, or views that are used to observe the object described.

I would like to detach, for a moment, from the particular contrast of interest here, the one posed between dynamic and symbolic orientations, to examine the general question of relating contrasting aspects or views.  In this connection, two distinct but correlated efforts at classification and organization arise in tandem with each other.  One concern seeks to classify the attributes, categories, features, properties, or qualities that are used to describe the object observed, while the other project tries to organize the approaches, instruments, methods, perspectives, or views that are used to observe the object described.

To invoke the traditional terminology, natural classes of predicates are referred to as "categories" or "predicaments", making it natural to call the classification and study of predicates by the name of "categoric", while the classification and study of methods is classically referred to as "heuristic" or "methodeutic" (Peirce, CP 2.105 110 & 2.207).

To invoke the traditional terminology, natural classes of predicates are referred to as ''categories'' or ''predicaments'', making it natural to call the classification and study of predicates by the name of ''categoric'', while the classification and study of methods is classically referred to as ''heuristic'' or ''methodeutic'' (Peirce, CP&nbsp;2.105&ndash;110 and 2.207).

Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers:  "Category" from Aristotle and Kant, "Functor" from Carnap ..., and "natural transformation" from then current informal parlance.

(Mac Lane 1971, Cat.Work.Math. 29 30).

<p>Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers:  &ldquo;Category&rdquo; from Aristotle and Kant, &ldquo;Functor&rdquo; from Carnap &hellip;, and &ldquo;natural transformation&rdquo; from then current informal parlance.</p>

| align="right" | Mac Lane, Cat.Work.Math. 29&ndash;30

Categoric. Although this subject is historically referred to as the "theory of categories", in modern times it is necessary to distinguish it from the mathematical subject of "category theory", whose claim to the title is confessedly derived by stealth.  By way of suffering unto the older discipline the freshness of the younger subject, the original study and more general classification of predicates can be referred to as the "doctrine of categories" (DOC).  This is a fair description, given that optional schemes of basic categories are commonly taken up, maintained, and transmitted in decidedly catechismic and rigidly dogmatic fashions.

'''Categoric.''' Although this subject is historically referred to as the "theory of categories", in modern times it is necessary to distinguish it from the mathematical subject of "category theory", whose claim to the title is confessedly derived by stealth.  By way of suffering unto the older discipline the freshness of the younger subject, the original study and more general classification of predicates can be referred to as the "doctrine of categories" (DOC).  This is a fair description, given that optional schemes of basic categories are commonly taken up, maintained, and transmitted in decidedly catechismic and rigidly dogmatic fashions.

Perhaps it is the mind's reluctance to revive the uncertainties and to relive the struggles that these schemes were made to resolve, but once the fundamental categories are settled it is nearly impossible to revise them, however poorly they come to fit the current circumstances of life.  No matter how original the thinking that leads up to a site where a stable foundation can be poured, the foundation itself is typically laid down as if it were cut from inalterable stone.

Perhaps it is the mind's reluctance to revive the uncertainties and to relive the struggles that these schemes were made to resolve, but once the fundamental categories are settled it is nearly impossible to revise them, however poorly they come to fit the current circumstances of life.  No matter how original the thinking that leads up to a site where a stable foundation can be poured, the foundation itself is typically laid down as if it were cut from inalterable stone.

I even hope that what I have done may prove a first step toward the resolution of one of the main problems of logic, that of producing a method for the discovery of methods in mathematics. (Peirce, CP 3.364).

I even hope that what I have done may prove a first step toward the resolution of one of the main problems of logic, that of producing a method for the discovery of methods in mathematics. (Peirce, CP 3.364).

Methodeutic.  This subject, that C.S. Peirce gave the alternate titles of "speculative rhetoric" or "formal rhetoric", because it is a science that "would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants" (CP 1.444 & 1.559), and that he assigned the task to find "a method of discovering methods" (CP 2.108 & 3.364), is one that clearly has a special relevance to the pursuit of an inquiry into inquiry.

'''Methodeutic.''' This subject, that C.S. Peirce gave the alternate titles of "speculative rhetoric" or "formal rhetoric", because it is a science that "would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants" (CP 1.444 & 1.559), and that he assigned the task to find "a method of discovering methods" (CP 2.108 & 3.364), is one that clearly has a special relevance to the pursuit of an inquiry into inquiry.

In an effort to gradually begin formalizing these issues, I introduce the concept of a "point of development" (POD).  This notion is intended to capture a particular moment in the history of a system or its agent, as it is reflected in the systems of propositions associated with each POD.  Relative to a particular POD there can be distinguished, though neither exclusively nor exhaustively, two types of propositions that are said to be "associated" with it.  Roughly speaking, these types of propositions reflect the thoughts that are "applied" to a POD and the thoughts that are "attached" to a POD, respectively.

In an effort to gradually begin formalizing these issues, I introduce the concept of a "point of development" (POD).  This notion is intended to capture a particular moment in the history of a system or its agent, as it is reflected in the systems of propositions associated with each POD.  Relative to a particular POD there can be distinguished, though neither exclusively nor exhaustively, two types of propositions that are said to be "associated" with it.  Roughly speaking, these types of propositions reflect the thoughts that are "applied" to a POD and the thoughts that are "attached" to a POD, respectively.