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Consequently, naturally occurring sign relations can be expected to fall into species or natural kinds, and to have special properties that make them keep on occurring in nature.  Moreover, cultivated varieties of sign relations, the kinds that have been converted to social purposes and found to be viable in actual practice, will have identifiable and especially effective properties by virtue of which their signs are rendered significant.

Consequently, naturally occurring sign relations can be expected to fall into species or natural kinds, and to have special properties that make them keep on occurring in nature.  Moreover, cultivated varieties of sign relations, the kinds that have been converted to social purposes and found to be viable in actual practice, will have identifiable and especially effective properties by virtue of which their signs are rendered significant.

In the pragmatic theory of sign relations, three natural kinds of signs are recognized, under the names of ''icons'', ''indices'', and ''symbols''.  Examples of indexical or accessional signs figured significantly in the discussion of <math>A\!</math> and <math>B\!</math>, as illustrated by the pronouns "i" and "u" in <math>S.\!</math>  Examples of iconic or analogical signs were also present, though keeping to the background, in the very form of the sign relation Tables that were used to schematize the whole activity of each interpreter.  Examples of symbolic or conventional signs, of course, abide even more deeply in the background, pervading the whole context and making up the very fabric of this discussion.

In the pragmatic theory of sign relations, three natural kinds of signs are recognized, under the names of ''icons'', ''indices'', and ''symbols''.  Examples of indexical or accessional signs figured significantly in the discussion of <math>A\!</math> and <math>B\!</math>, as illustrated by the pronouns <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}</math> and <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}</math> in <math>S\!</math>. Examples of iconic or analogical signs were also present, though keeping to the background, in the very form of the sign relation Tables that were used to schematize the whole activity of each interpreter.  Examples of symbolic or conventional signs, of course, abide even more deeply in the background, pervading the whole context and making up the very fabric of this discussion.

In order to deal with the array of issues presented so far in this subsection, all of which have to do with controlling the generative power of sign relations to serve the specific purposes of understanding, I apply the previously introduced concept of an ''objective genre'' (OG).  This is intended to be a determinate purpose or a deliberate pattern of analysis and synthesis that one can identify as being active at given moments in a discussion and that affects what one regards as the relevant structural properties of its objects.

In order to deal with the array of issues presented so far in this subsection, all of which have to do with controlling the generative power of sign relations to serve the specific purposes of understanding, I apply the previously introduced concept of an ''objective genre'' (OG).  This is intended to be a determinate purpose or a deliberate pattern of analysis and synthesis that one can identify as being active at given moments in a discussion and that affects what one regards as the relevant structural properties of its objects.

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.  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 OGs 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'' 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>

Any object of these OGs 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.

# ''For indices, the existence of a separate reality is obligatory.''  And yet this reality need not affect the object of the sign.  In essence, indices are satisfied with a basis in reality that need only reside in an actual object instance, one that establishes a real connection between the object and its index with regard to the OG in question.

# ''For indices, the existence of a separate reality is obligatory.''  And yet this reality need not affect the object of the sign.  In essence, indices are satisfied with a basis in reality that need only reside in an actual object instance, one that establishes a real connection between the object and its index with regard to the OG in question.

Finally, suppose that <math>M\!</math> and <math>N\!</math> are hypothetical sign relations intended to capture all the iconic and indexical relationships, respectively, that a typical object <math>x\!</math> enjoys within its genre <math>G.\!</math>  A sign relation in which every sign has the same kind of relation to its object under an assumed form of analysis is appropriately called a ''homogeneous sign relation''.  In particular, if <math>H\!</math> is a homogeneous sign relation in which every sign has either an iconic or an indexical relation to its object, then it is convenient to apply the corresponding adjective to the whole of <math>H\!.</math>

Finally, suppose that <math>M\!</math> and <math>N\!</math> are hypothetical sign relations intended to capture all the iconic and indexical relationships, respectively, that a typical object <math>x\!</math> enjoys within its genre <math>G\!</math>. A sign relation in which every sign has the same kind of relation to its object under an assumed form of analysis is appropriately called a ''homogeneous sign relation''.  In particular, if <math>H\!</math> is a homogeneous sign relation in which every sign has either an iconic or an indexical relation to its object, then it is convenient to apply the corresponding adjective to the whole of <math>H\!</math>.

Typical sign relations of the iconic or indexical kind generate especially simple and remarkably stable sorts of interpretive processes.  In arity, they could almost be classified as ''approximately dyadic'', since most of their interesting structure is wrapped up in their denotative aspects, while their connotative functions are relegated to the tangential role of preserving the directions of their denotative axes.  In a metaphorical but true sense, iconic and indexical sign relations equip objective frameworks with "gyroscopes", helping them maintain their interpretive perspectives in a persistent orientation toward their objective world.

Typical sign relations of the iconic or indexical kind generate especially simple and remarkably stable sorts of interpretive processes.  In arity, they could almost be classified as ''approximately dyadic'', since most of their interesting structure is wrapped up in their denotative aspects, while their connotative functions are relegated to the tangential role of preserving the directions of their denotative axes.  In a metaphorical but true sense, iconic and indexical sign relations equip objective frameworks with "gyroscopes", helping them maintain their interpretive perspectives in a persistent orientation toward their objective world.