Changes

In keeping with the spirit of a discussion based on concrete examples, the RIF to be improvised here is restrained to the scale of a minimal IF that can reflect on the scene of A and B, in this case, synthesizing a portion of the OFs and IFs suggested by the sign relations <math>A\!</math> and <math>B\!</math> into an integrated SOI.  While I do not plan to specify the additional constraints that would be needed to determine this RIF uniquely, even to say whether it is finite or infinite, it forms a convenient reference point for the rest of this section to designate the purported ideal as ''the RIF generated by <math>A\!</math> and <math>B\!</math>'' and to notate it as <math>\operatorname{RIF}(A, B).\!</math>

In keeping with the spirit of a discussion based on concrete examples, the RIF to be improvised here is restrained to the scale of a minimal IF that can reflect on the scene of A and B, in this case, synthesizing a portion of the OFs and IFs suggested by the sign relations <math>A\!</math> and <math>B\!</math> into an integrated SOI.  While I do not plan to specify the additional constraints that would be needed to determine this RIF uniquely, even to say whether it is finite or infinite, it forms a convenient reference point for the rest of this section to designate the purported ideal as ''the RIF generated by <math>A\!</math> and <math>B\!</math>'' and to notate it as <math>\operatorname{RIF}(A, B).\!</math>

In accord with the customary figure of speech, a RIF can be personified in the agency of a &ldquo;reflective interpreter&rdquo; that possesses the faculties to carry out its actions, and this agent is in turn characterized as the localized representative of a suitably reflective and situated process of interpretation.

In accord with the customary figure of speech, a RIF can be personified in the agency of a "reflective interpreter" that possesses the faculties to carry out its actions, and this agent is in turn characterized as the localized representative of a suitably reflective and situated process of interpretation.

A reflective interpreter needs a capacity for referring to its own role in the process of interpretation, for conceptualizing each transition from sign to interpretant sign as occurring within a context of alternatives, and for noticing that each option has a potentially distinctive value with respect to a prevailing object or objective.  "Capacity", as used in this connection, is a word with both structural and functional connotations.  It implies the structural capacity that is required to articulate, record, and maintain data about observable forms of interpretive conduct, and it involves the functional capacity that is demanded to create and exploit this data, in effect, constituting a higher order of interpretive activity.

A reflective interpreter needs a capacity for referring to its own role in the process of interpretation, for conceptualizing each transition from sign to interpretant sign as occurring within a context of alternatives, and for noticing that each option has a potentially distinctive value with respect to a prevailing object or objective.  ''Capacity'', as used in this connection, is a word with both structural and functional connotations.  It implies the structural capacity that is required to articulate, record, and maintain data about observable forms of interpretive conduct, and it involves the functional capacity that is demanded to create and exploit this data, in effect, constituting a higher order of interpretive activity.

If one tries to understand the conduct of a reflective interpreter as a process of interpretation there are a number of questions that arise.  How can anything so ongoing as a process of interpretation refer to an object, and how can anything so fleeting as a process of interpretation be referred to as an object?

If one tries to understand the conduct of a reflective interpreter as a process of interpretation there are a number of questions that arise.  How can anything so ongoing as a process of interpretation refer to an object, and how can anything so fleeting as a process of interpretation be referred to as an object?

A process that refers to itself is not like a set that collects itself, or a collection that would enroll itself among its own elements, even if some attempts to process the reference and to lay it out in a literal account do try to dissect and explain it as such.  A sign that is elemental to a universe, perhaps by means of which one seeks to explain the universe, does not in fact collect, dominate, or encase the entire universe simply by referring to it, even if some interpretive interloper, at the risk of vitiating the whole account, is tempted to explain the elementary part in terms of the complex totality.

A process that refers to itself is not like a set that collects itself, or a collection that would enroll itself among its own elements, even if some attempts to process the reference and to lay it out in a literal account do try to dissect and explain it as such.  A sign that is elemental to a universe, perhaps by means of which one seeks to explain the universe, does not in fact collect, dominate, or encase the entire universe simply by referring to it, even if some interpretive interloper, at the risk of vitiating the whole account, is tempted to explain the elementary part in terms of the complex totality.

One reason for introducing the distinction between OF's and IF's into the present discussion is to keep track of the complex relationships between object domains and sign domains, between the constitutions of objects and the constitutions of signs.  It is a frequent practice in mathematics to blur this distinction, often saying that an object is constituted as a set of further objects when one really means that the sign or information one has about the object is constituted as a set of further signs or further informations about the object, all of which can refer to further objects, but not always the sorts of objects that are literally intended as elementary constituents of the original object.  Furthermore, each use of the directive "further" in this description marks a place where a suitably reflective interpreter ought to ask whether "further" implies "simpler" or merely "other", and in turn whether "other" means essentially other or only otherwise appearing.

One reason for introducing the distinction between OFs and IFs into the present discussion is to keep track of the complex relationships between object domains and sign domains, between the constitutions of objects and the constitutions of signs.  It is a frequent practice in mathematics to blur this distinction, often saying that an object is constituted as a set of further objects when one really means that the sign or information one has about the object is constituted as a set of further signs or further informations about the object, all of which can refer to further objects, but not always the sorts of objects that are literally intended as elementary constituents of the original object.  Furthermore, each use of the directive ''further'' in this description marks a place where a suitably reflective interpreter ought to ask whether ''further'' implies ''simpler'' or merely ''other'', and in turn whether ''other'' means essentially other or only otherwise appearing.

But the distinction between object and sign, however important, is still a pragmatic distinction, involving a thing's use in a particular role, and not an essential distinction, fixing a thing's prior and eternal nature.  Of course, it can turn out that some objects will never serve as signs and that some signs will never be observed as objects, but these types of eventuality involve empirical questions and contingent facts, and their actualization depends on the kinds of circumstances that have to be discovered after the fact rather than dictated a priori.

But the distinction between object and sign, however important, is still a pragmatic distinction, involving a thing's use in a particular role, and not an essential distinction, fixing a thing's prior and eternal nature.  Of course, it can turn out that some objects will never serve as signs and that some signs will never be observed as objects, but these types of eventuality involve empirical questions and contingent facts, and their actualization depends on the kinds of circumstances that have to be discovered after the fact rather than dictated ''a priori''.

The construction of a RIF forces the discussion to a point where the OF's and IF's and the relationships between them suddenly become much more complex, and where confusion can arise precisely from the fact that the purpose of a RIF is to convert an IF into the sort of thing that can be referred to and reflected on as an object.  Developments like these make it all the more necessary to understand the exact character of the distinction between OF's and IF's.  In a complex IF signs do participate in constitutional relationships, with complex signs being constructed out of simpler signs.  But the relations involved in denotation and connotation are not limited to constitutional linkages of this sort, and thus they cannot be expected to generate by themselves the necessary sorts of analytic and synthetic hierarchies.

The construction of a RIF forces the discussion to a point where the OFs and IFs and the relationships between them suddenly become much more complex, and where confusion can arise precisely from the fact that the purpose of a RIF is to convert an IF into the sort of thing that can be referred to and reflected on as an object.  Developments like these make it all the more necessary to understand the exact character of the distinction between OFs and IFs.  In a complex IF signs do participate in constitutional relationships, with complex signs being constructed out of simpler signs.  But the relations involved in denotation and connotation are not limited to constitutional linkages of this sort, and thus they cannot be expected to generate by themselves the necessary sorts of analytic and synthetic hierarchies.

All in all, a RIF involves the close coordination of an OF and an IF, plus mechanisms for carrying out the so called "reflective operations" (RO's) that go to negotiate between the objective and the interpretive realms.  The work of ROing permits processes of interpretation, initially taking place largely in the IF and impinging on the OF only at isolated points, to be formalized and objectified, thereby becoming segments of the OF.  Taken over time the cumulative effect of this ROing motion gradually turns more and more of the IF into new sectors and layers of the OF.

All in all, a RIF involves the close coordination of an OF and an IF, plus mechanisms for carrying out the so called ''reflective operations'' (ROs) that go to negotiate between the objective and the interpretive realms.  The work of ROing permits processes of interpretation, initially taking place largely in the IF and impinging on the OF only at isolated points, to be formalized and objectified, thereby becoming segments of the OF.  Taken over time the cumulative effect of this ROing motion gradually turns more and more of the IF into new sectors and layers of the OF.

Point 27.

Point 27.