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Given an ontological framework that can provide multiple perspectives and moving platforms for dealing with object structure, in other words, that can organize diverse hierarchies and developing orders of objects, attention can now return to the discussion of sign relations as models of intellectual processes.

Given an ontological framework that can provide multiple perspectives and moving platforms for dealing with object structure, in other words, that can organize diverse hierarchies and developing orders of objects, attention can now return to the discussion of sign relations as models of intellectual processes.

A principal aim of using sign relations as formal models is to be capable of analyzing complex activities that arise in nature and human domains.  Proceeding by the opportunistic mode of ''analysis by synthesis'' (ABS), one generates likely constructions from a stock of favored, familiar, and well-understood sign relations, the supply of which hopefully grows with time, constantly matching their formal properties against the structures encountered in the "wilds" of natural phenomena and human conduct.  When salient traits of both the freely generated products and the widely gathered phenomena coincide in enough points, then the details of the constructs one has built for oneself can help to articulate a plausible hypothesis as to how the observable appearances might be explained.

A principal aim of using sign relations as formal models is to be capable of analyzing complex activities that arise in nature and human domains.  Proceeding by the opportunistic mode of ''analysis by synthesis'', one generates likely constructions from a stock of favored, familiar, and well-understood sign relations, the supply of which hopefully grows with time, constantly matching their formal properties against the structures encountered in the "wilds" of natural phenomena and human conduct.  When salient traits of both the freely generated products and the widely gathered phenomena coincide in enough points, then the details of the constructs one has built for oneself can help to articulate a plausible hypothesis as to how the observable appearances might be explained.

A principal difficulty of using sign relations for this purpose arises from the very power of productivity they bring to bear in the process, the capacity of triadic relations to generate a welter of what are bound to be mostly arbitrary structures, with only a scattered few hoping to show any promise, but the massive profusion of which exceeds from the outset any reason's ability to sort them out and test them in practice.  And yet, as the phenomena of interest become more complex, the chances grow slimmer that adequate explanations will be found in any of the thinner haystacks.  In this respect, sign relations inherit the basic proclivities of set theory, which can be so successful and succinct in presenting and clarifying the properties of already found materials and hard won formal insights, and yet so overwhelming to use as a tool of random exploration and discovery.

A principal difficulty of using sign relations for this purpose arises from the very power of productivity they bring to bear in the process, the capacity of triadic relations to generate a welter of what are bound to be mostly arbitrary structures, with only a scattered few hoping to show any promise, but the massive profusion of which exceeds from the outset any reason's ability to sort them out and test them in practice.  And yet, as the phenomena of interest become more complex, the chances grow slimmer that adequate explanations will be found in any of the thinner haystacks.  In this respect, sign relations inherit the basic proclivities of set theory, which can be so successful and succinct in presenting and clarifying the properties of already found materials and hard won formal insights, and yet so overwhelming to use as a tool of random exploration and discovery.

The OG I apply here is called the genre of ''properties and instances''.  One moves through its space, higher and lower in a particular ontology, by means of two dyadic relations, upward by taking a ''property of'' and downward by taking an ''instance of'' whatever object initially enters one's focus of attention.  Each object of this OG is reckoned to be the unique common property of the set of objects that lie one step below it, objects that are in turn reckoned to be instances of the given object.

The OG I apply here is called the genre of ''properties and instances''.  One moves through its space, higher and lower in a particular ontology, by means of two dyadic relations, upward by taking a ''property of'' and downward by taking an ''instance of'' whatever object initially enters one's focus of attention.  Each object of this OG is reckoned to be the unique common property of the set of objects that lie one step below it, objects that are in turn reckoned to be instances of the given object.

Pretty much the same relational structures could be found in the genre or paradigm of ''qualities and examples'', but the use of ''examples'' here is polymorphous enough to include experiential, exegetic, and executable examples (EXE's).  This points the way to a series of related genres, for example, the OG's of ''principles and illustrations'', ''laws and existents'', ''precedents and exercises'', and on to ''lessons and experiences''.  All in all, in their turn, these modulations of the basic OG show a way to shift the foundations of ontological hierarchies toward bases in individual and systematic experience, and thus to put existentially dynamic rollers under the blocks of what seem to be essentially invariant pyramids.

Pretty much the same relational structures could be found in the genre or paradigm of ''qualities and examples'', but the use of ''examples'' here is polymorphous enough to include experiential, exegetic, and executable examples.  This points the way to a series of related genres, for example, the OG's of ''principles and illustrations'', ''laws and existents'', ''precedents and exercises'', and on to ''lessons and experiences''.  All in all, in their turn, these modulations of the basic OG show a way to shift the foundations of ontological hierarchies toward bases in individual and systematic experience, and thus to put existentially dynamic rollers under the blocks of what seem to be essentially invariant pyramids.

Any object of these OG's can be contemplated in the light of two potential relationships, namely, with respect to its chances of being an ''object quality'' (OQ) or an ''object example'' (OE) of something else.  In future references, abbreviated notations like "OG (Prop, Inst)" or "OG = (Prop, Inst)" will be used to specify particular genres, giving the intended interpretations of their generating relations {&nbsp;<math>\lessdot</math>&nbsp;,&nbsp;<math>\gtrdot</math>&nbsp;}.

Any object of these OG's can be contemplated in the light of two potential relationships, namely, with respect to its chances of being an ''object quality'' or an ''object example'' of something else.  In future references, abbreviated notations like <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst})</math> or <math>\operatorname{OG} = (\operatorname{Prop}, \operatorname{Inst})</math> will be used to specify particular genres, giving the intended interpretations of their generating relations <math>\{ \lessdot,\gtrdot \}.</math>

With respect to this OG, I can now characterize icons and indices.  Icons are signs by virtue of being instances of properties of objects.  Indices are signs by virtue of being properties of instances of objects.

With respect to this OG, I can now characterize icons and indices.  Icons are signs by virtue of being instances of properties of objects.  Indices are signs by virtue of being properties of instances of objects.

Because the initial discussion seems to flow more smoothly if I apply dyadic relations on the left, I formulate these definitions as follows:

Because the initial discussion seems to flow more smoothly if I apply dyadic relations on the left, I formulate these definitions as follows:

:{|

{| align="center" cellpadding="8"

| For Icons:

|

| Sign (Obj)

| =

\text{For Icons:} &

| Inst (Prop (Obj)),

\operatorname{Sign} (\operatorname{Obj}) & = &

\operatorname{Inst} (\operatorname{Prop} (\operatorname{Obj})), \\

| For Indices:

| Sign (Obj)

\text{For Indices:} &

| =

\operatorname{Sign} (\operatorname{Obj}) & = &

| Prop (Inst (Obj)).

\operatorname{Prop} (\operatorname{Inst} (\operatorname{Obj})). \\

|}

|}

Imagine starting from the sign and retracing steps to reach the object, in this way finding the converses of these relations to be as follows:

Imagine starting from the sign and retracing steps to reach the object, in this way finding the converses of these relations to be as follows:

:{|

{| align="center" cellpadding="8"

| For Icons:

|

| Obj (Sign)

| =

\text{For Icons:} &

| Inst (Prop (Sign)),

\operatorname{Obj} (\operatorname{Sign}) & = &

\operatorname{Inst} (\operatorname{Prop} (\operatorname{Sign})), \\

| For Indices:

| Obj (Sign)

\text{For Indices:} &

| =

\operatorname{Obj} (\operatorname{Sign}) & = &

| Prop (Inst (Sign)).

\operatorname{Prop} (\operatorname{Inst} (\operatorname{Sign})). \\

|}

|}