Changes

Accordingly, one of the roles intended for this OF is to provide a set of standard formulations for describing the moment to moment uncertainty of interpretive systems.  The formally definable concepts of the MOI (the objective case of a SOI) and the IM (the momentary state of a SOI) are intended to formalize the intuitive notions of a generic mental constitution and a specific mental disposition that usually serve in discussing states and directions of mind.

Accordingly, one of the roles intended for this OF is to provide a set of standard formulations for describing the moment to moment uncertainty of interpretive systems.  The formally definable concepts of the MOI (the objective case of a SOI) and the IM (the momentary state of a SOI) are intended to formalize the intuitive notions of a generic mental constitution and a specific mental disposition that usually serve in discussing states and directions of mind.

The structures present at each objective level are formulated by means of converse pairs of ''staging relations'', prototypically symbolized by the signs "<" and ">".  At the more generic levels of OF's and OG's the ''staging operations'' associated with the generators "<" and ">" involve the application of dyadic relations analogous to class membership "&isin;" and its converse, but the increasing amounts of parametric information that are needed to determine specific motives and detailed motifs give OM's the full power of triadic relations.  Using the same pair of symbols to denote staging relations at all objective levels helps to prevent an excessive proliferation of symbols, but it means that the meaning of these symbols is always heavily dependent on context.  In particular, even fundamental properties like the effective ''arity'' of the relations signified can vary from level to level.

The structures present at each objective level are formulated by means of converse pairs of ''staging relations'', prototypically symbolized by the signs "<font face="system"><s>&lt;</s></font>" and "<font face="system"><s>&gt;</s></font>".  At the more generic levels of OF's and OG's the ''staging operations'' associated with the generators "<font face="system"><s>&lt;</s></font>" and "<font face="system"><s>&gt;</s></font>" involve the application of dyadic relations analogous to class membership "&isin;" and its converse "&ni;", but the increasing amounts of parametric information that are needed to determine specific motives and detailed motifs give OM's the full power of triadic relations.  Using the same pair of symbols to denote staging relations at all objective levels helps to prevent an excessive proliferation of symbols, but it means that the meaning of these symbols is always heavily dependent on context.  In particular, even fundamental properties like the effective ''arity'' of the relations signified can vary from level to level.

The staging relations divide into two orientations, "<" versus ">", indicating opposing senses of direction with respect to the distinction between analytic and synthetic projects:

The staging relations divide into two orientations, "<" versus ">", indicating opposing senses of direction with respect to the distinction between analytic and synthetic projects: