Changes

===6.47. Mutually Intelligible Codes===

===6.47. Mutually Intelligible Codes===

Before this complex of relationships can be formalized in much detail, I must introduce linguistic devices for generating ''higher order signs'', used to indicate other signs, and ''situated signs'', indexed by the names of their users, their contexts of use, and other types of information incidental to their usage in general.  This leads to the consideration of systems of interpretation that maintain recursive mechanisms for naming everything within their purview.  This “nominal generosity” gives them a new order of generative capacity, producing a sufficient number of distinctive signs to name all the objects and then name the names that are needed in a given discussion.

Before this complex of relationships can be formalized in much detail, I must introduce linguistic devices for generating "higher order signs", used to indicate other signs, and "situated signs", indexed by the names of their users, their contexts of use, and other types of information incidental to their usage in general.  This leads to the consideration of SOIs that maintain recursive mechanisms for naming everything within their purview.  This "nominal generosity" gives them a new order of generative capacity, producing a sufficient number of distinctive signs to name all the objects and then name the names that are needed in a given discussion.

Symbolic systems for quoting inscriptions and ascribing quotations are associated in metamathematics with "godel numberings" of formal objects, enumerative functions that provide systematic but ostensibly arbitrary reference numbers for the signs and expressions in a formal language.  Assuming these signs and expressions denote anything at all, their formal enumerations become the "codes" of formal objects, just as programs taken literally are code names for certain mathematical objects known as computable functions.  Partial forms of specification not withstanding, these codes are the only complete modes of representation that formal objects can have in the medium of mechanical activity.

Symbolic systems for quoting inscriptions and ascribing quotations are associated in metamathematics with ''gödel numberings'' of formal objects, enumerative functions that provide systematic but ostensibly arbitrary reference numbers for the signs and expressions in a formal language.  Assuming these signs and expressions denote anything at all, their formal enumerations become the ''codes'' of formal objects, just as programs taken literally are code names for certain mathematical objects known as computable functions.  Partial forms of specification notwithstanding, these codes are the only complete modes of representation that formal objects can have in the medium of mechanical activity.

In the dialogue of A and B there happens to be an exact coincidence between signs and states.  That is, the states of the interpretive systems A and B are not distinguished from the signs in S that are imagined to be mediating, moment by moment, the attentions of the interpretive agents A and B toward their respective objects in O.  So the question arises:  Is this identity bound to be a general property of all useful sign relations, or is it only a degenerate feature occurring by chance or unconscious design in the immediate example?

In the dialogue of A and B there happens to be an exact coincidence between signs and states.  That is, the states of the interpretive systems A and B are not distinguished from the signs in S that are imagined to be mediating, moment by moment, the attentions of the interpretive agents A and B toward their respective objects in O.  So the question arises:  Is this identity bound to be a general property of all useful sign relations, or is it only a degenerate feature occurring by chance or unconscious design in the immediate example?