Changes

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''?  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 ''M'' and the indexical sign relation ''N'' ?  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 "<font face="system"><s>&lt;</s></font>" and "<font face="system"><s>&gt;</s></font>" 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'' and ''instance of x'' 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;<font face="system"><s>&lt;</s></font>&nbsp;,&nbsp;<font face="system"><s>&gt;</s></font>&nbsp;), where:

I recall the OG of ''properties and instances'' and re-introduce the symbols "<font face="system"><s>&lt;</s></font>" and "<font face="system"><s>&gt;</s></font>" 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;<font face="system"><s>&lt;</s></font>&nbsp;,&nbsp;<font face="system"><s>&gt;</s></font>&nbsp;), where:

"x <" = "x's Property" = "Property of x" = "Object above x",

: "''x'' <font face="system"><s>&lt;</s></font>" = "''x''&rsquo;s Property" = "Property of ''x''&nbsp;" = "Object above ''x''&nbsp;",

"x >" = "x's Instance" = "Instance of x" = "Object below x".

: "''x'' <font face="system"><s>&gt;</s></font>" = "''x''&rsquo;s Instance" = "Instance of ''x''&nbsp;" = "Object below ''x''&nbsp;".

A symbol like "x <" or "x >", with extra spaces or dots being optional, is called a ''catenation'', where "x" is the ''catenand'' and "<" or ">" is the ''catenator''.  Due to the fact that "<" and ">" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:

A symbol like "''x''&nbsp;<font face="system"><s>&lt;</s></font>" or "''x''&nbsp;<font face="system"><s>&gt;</s></font>", with extra spaces or dots being optional, is called a ''catenation'', where "''x''" is the ''catenand'' and "<font face="system"><s>&lt;</s></font>" or "<font face="system"><s>&gt;</s></font>" is the ''catenator''.  Due to the fact that "<font face="system"><s>&lt;</s></font>" and "<font face="system"><s>&gt;</s></font>" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:

"x <" = "x is the Instance of what?" = "x's Property",

: "x <" = "x is the Instance of what?" = "x's Property",

"x >" = "x is the Property of what?" = "x's Instance".

: "x >" = "x is the Property of what?" = "x's Instance".

In this fashion, the definitions of icons and indices can be reformulated:

In this fashion, the definitions of icons and indices can be reformulated:

x's Icon   = x's Property's Instance = x.‹›,

: x's Icon = x's Property's Instance = x.‹›,

x's Index = x's Instance's Property = x.›‹.

: x's Index = x's Instance's Property = x.›‹.

According to the definitions of the homogeneous sign relations M and N:

According to the definitions of the homogeneous sign relations M and N:

x's Icon   = x.MOS,

: x's Icon = x.MOS,

x's Index = x.NOS.

: x's Index = x.NOS.

Equating the results of these equations yields the analysis of M and N as forms of composition within the genre of properties and instances:

Equating the results of these equations yields the analysis of M and N as forms of composition within the genre of properties and instances: