Changes

In spite of the apparent duality between these patterns of composition, there is a significant asymmetry to be observed in the way that the insistent theme of realism interrupts the underlying genre.  In order to understand this, it is necessary to note that the strain of pragmatic thinking I am using here takes its definition of ''reality'' from the word's original Scholastic sources, where the adjective ''real'' means ''having properties''.  Taken in this sense, reality is necessary but not sufficient to ''actuality'', where ''actual'' means "existing in act and not merely potentially" (Webster's).  To reiterate, actuality is sufficient but not necessary to reality.  The distinction between the ideas is further pointed up by the fact that a potential can be real, and that its reality can be independent of any particular moment in which the power acts.

In spite of the apparent duality between these patterns of composition, there is a significant asymmetry to be observed in the way that the insistent theme of realism interrupts the underlying genre.  In order to understand this, it is necessary to note that the strain of pragmatic thinking I am using here takes its definition of ''reality'' from the word's original Scholastic sources, where the adjective ''real'' means ''having properties''.  Taken in this sense, reality is necessary but not sufficient to ''actuality'', where ''actual'' means "existing in act and not merely potentially" (Webster's).  To reiterate, actuality is sufficient but not necessary to reality.  The distinction between the ideas is further pointed up by the fact that a potential can be real, and that its reality can be independent of any particular moment in which the power acts.

These ''angelic doctrines'' would probably remain distant from the present concern, were it not for two points of connection:

These abstract considerations would probably remain distant from the present concern, were it not for two points of connection:

# Relative to the present genre, the distinction of reality, that can be granted to certain objects of thought and not to others, fulfills an analogous role to the distinction that singles out ''sets'' among ''classes'' in modern versions of set theory.  Taking the membership relation "∈" as a predecessor relation in a pre-designated hierarchy of classes, a class attains the status of a set, and by dint of this becomes an object of more determinate discussion, simply if it has successors.  Pragmatic reality is distinguished from both the medieval and the modern versions, however, by the fact that its reality is always a reality to somebody.  This is due to the circumstance that it takes both an abstract property and a concrete interpreter to establish the practical reality of an object.

# Relative to the present genre, the distinction of reality, that can be granted to certain objects of thought and not to others, fulfills an analogous role to the distinction that singles out ''sets'' among ''classes'' in modern versions of set theory.  Taking the membership relation "∈" as a predecessor relation in a pre-designated hierarchy of classes, a class attains the status of a set, and by dint of this becomes an object of more determinate discussion, simply if it has successors.  Pragmatic reality is distinguished from both the medieval and the modern versions, however, by the fact that its reality is always a reality to somebody.  This is due to the circumstance that it takes both an abstract property and a concrete interpreter to establish the practical reality of an object.

# Icon → Object.  Taking the iconic sign as an initial instance, try to go up to a property and then down to a different or perhaps the same instance.  This form of ascent does not require a distinct object, since reality of the sign is sufficient to itself.  In other words, if the sign has any properties at all, then it is an icon of a real object, even if that object is only itself.

# Icon → Object.  Taking the iconic sign as an initial instance, try to go up to a property and then down to a different or perhaps the same instance.  This form of ascent does not require a distinct object, since reality of the sign is sufficient to itself.  In other words, if the sign has any properties at all, then it is an icon of a real object, even if that object is only itself.

# Index → Object.  Taking the indexical sign as an initial property, try to go down to an instance and then up to a different or perhaps the same property.  This form of descent requires a real instance to substantiate it, but not necessarily a distinct object.  Consequently, the index always has a real connection to its object, even if that object is only itself.

# Index → Object.  Taking the indexical sign as an initial property, try to go down to an instance and then up to a different or perhaps the same property.  This form of descent requires a real instance to substantiate it, but not necessarily a distinct object.  Consequently, the index always has a real connection to its object, even if that object is only itself.

In sum:  For icons a separate reality is optional, for indices a separate reality is obligatory.  As often happens with a form of analysis, each term under the indicated sum appears to verge on indefinite expansion:

In sum:  For icons a separate reality is optional, for indices a separate reality is obligatory.  As often happens with a form of analysis, each term under the indicated sum appears to verge on indefinite expansion:

# ''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 ''M'' and ''N'' are hypothetical sign relations intended to capture all the iconic and indexical relationships, respectively, that a typical object ''x'' enjoys within its genre ''G''.  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 ''H'' 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 ''H''.

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.

Is this prospect a utopian vision?  Perhaps it is exactly that.  But it is the hope that inquiry discovers resting first and last within itself, quietly guiding every other aim and motive of inquiry.

Is this prospect a utopian vision?  Perhaps it is exactly that.  But it is the hope that inquiry discovers resting first and last within itself, quietly guiding every other aim and motive of inquiry.

Turning to the language of ''objective concerns'', what can now be said about the compositional structures of the iconic sign relation ''M'' and the indexical sign relation ''N''&nbsp;?  In preparation for this topic, a few additional steps must be taken to continue formalizing the concept of an objective genre and to begin developing a calculus for composing objective motifs.

Turning to the language of ''objective concerns'', what can now be said about the compositional structures of the iconic sign relation <math>M\!</math> and the indexical sign relation <math>N\!</math>?  In preparation for this topic, a few additional steps must be taken to continue formalizing the concept of an objective genre and to begin developing a calculus for composing objective motifs.

I recall the OG of ''properties and instances'' and re-introduce the symbols "<math>\lessdot</math>" and "<math>\gtrdot</math>" for the converse pair of dyadic relations that generate it.  Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of ''x''&nbsp;" and "instance of ''x''&nbsp;" by means of a case inflection on ''x'', that is, as "''x''&rsquo;s property" and "''x''&rsquo;s instance", respectively.  Described in this way, OG(Prop,&nbsp;Inst) = ?&nbsp;<math>\lessdot</math>&nbsp;,&nbsp;<math>\gtrdot</math>&nbsp;?, where:

I recall the objective genre of ''properties and instances'' and re-introduce the symbols <math>\lessdot</math> and <math>\gtrdot</math> for the converse pair of dyadic relations that generate it.  Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of <math>x\!</math>" and "instance of <math>x\!</math>" by means of a case inflection on <math>x\!,</math> that is, as "<math>x\!</math>&rsquo;s property" and "<math>x\!</math>&rsquo;s instance", respectively.  Described in this way, <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst}) = \langle \lessdot, \gtrdot \rangle,</math> where:

:{|

:{|