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 ''systems of interpretation'' (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 ''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.

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 <math>\text{A}\!</math> and <math>\text{B}\!</math> there happens to be an exact coincidence between signs and states.  That is, the states of the interpretive systems <math>\text{A}\!</math> and <math>\text{B}\!</math> are not distinguished from the signs in <math>S\!</math> that are imagined to be mediating, moment by moment, the attentions of the interpretive agents <math>\text{A}\!</math> and <math>\text{B}\!</math> toward their respective objects in <math>O.\!</math> 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?

To move toward a resolution of this question I reason as follows.  In one direction, it seems obvious that a "sign in use" (SIU) by a particular interpreter constitutes a component of that agent's state.  In other words, the very notion of an identifiable SIU refers to numerous instances of a particular interpreter's state that share in the abstract property of being such instances, whether or not anyone can give a more concise or illuminating characterization of the concept under which these momentary states are gathered.  Conversely, it is at least conceivable that the whole state of a system, constituting its transitory response to the entirety of its environment, history, and goals, can be interpreted as a sign of something to someone.  In sum, there remains an outside chance of signs and states being precisely the same things, since nothing precludes the existence of an IF that could make it so.

To move toward a resolution of this question I reason as follows.  In one direction, it seems obvious that a ''sign in use'' (SIU) by a particular interpreter constitutes a component of that agent's state.  In other words, the very notion of an identifiable SIU refers to numerous instances of a particular interpreter's state that share in the abstract property of being such instances, whether or not anyone can give a more concise or illuminating characterization of the concept under which these momentary states are gathered.  Conversely, it is at least conceivable that the whole state of a system, constituting its transitory response to the entirety of its environment, history, and goals, can be interpreted as a sign of something to someone.  In sum, there remains an outside chance of signs and states being precisely the same things, since nothing precludes the existence of an ''interpretive framework'' (IF) that could make it so.

Still, if the question about the distinction or coincidence between signs and states is restricted to the domains where existential realizations are conceivable, no matter whether in biological or computational media, then the prerequisites of the task become more severe, due to the narrower scope of materials that are admitted to answer them.  In focussing on this arena the problem is threefold:

Still, if the question about the distinction or coincidence between signs and states is restricted to the domains where existential realizations are conceivable, no matter whether in biological or computational media, then the prerequisites of the task become more severe, due to the narrower scope of materials that are admitted to answer them.  In focusing on this arena the problem is threefold:

1. The crucial point is not just whether it is possible to imagine an ideal SOI, an external perspective or an independent POV, for which all states are signs, but whether this is so for the prospective SOI of the very agent that passes through these states.

# The crucial point is not just whether it is possible to imagine an ideal SOI, an external perspective or an independent POV, for which all states are signs, but whether this is so for the prospective SOI of the very agent that passes through these states.

 

The special task of a nuanced hermeneutic approach to computational interpretation is to realize the relativity of all formal codes to their formal coders, and to seek ways of facilitating mutual intelligibility among interpreters whose internal codes can be thoroughly private, synchronistically keyed to external events, and even a bit idiosyncratic.

 

The special task of a nuanced hermeneutic approach to computational interpretation is to realize the relativity of all formal codes to their formal coders, and to seek ways of facilitating mutual intelligibility among interpreters whose internal codes can be thoroughly private, synchronistically keyed to external events, and even a bit idiosyncratic.

Ultimately, working through this maze of "meta" questions, as posed on the tentative grounds of the present project, leads to a question about the "logical reference frames" or "metamathematical coordinate systems" that are supposed to distinguish "objective" from "symbolic" entities and are imagined to discriminate a range of gradations along their lines.  The question is:  Whether any gague of objectivity or scale of virtuality has invariant properties discoverable by all independent interpreters, or whether all is vanity and inane relativism, and everything concerning a subjective point of view is sheer caprice?

Ultimately, working through this maze of "meta" questions, as posed on the tentative grounds of the present project, leads to a question about the "logical reference frames" or "metamathematical coordinate systems" that are supposed to distinguish "objective" from "symbolic" entities and are imagined to discriminate a range of gradations along their lines.  The question is:  Whether any gauge of objectivity or scale of virtuality has invariant properties discoverable by all independent interpreters, or whether all is vanity and inane relativism, and everything concerning a subjective point of view is sheer caprice?

Thus, the problem of mutual intelligibility turns on the question of "common significance":  How can there be signs that are truly public, when the most natural signs that distinct agents can know, their own internal states, have no guarantee and very little likelihood of being related in systematically fathomable ways?  As a partial answer to this, I am willing to contemplate certain forms of pre established harmony, like the common evolution of a biological species or the shared culture of an interpretive community, but my experience has been that harmony, once established, quickly corrupts unless active means are available to maintain it.  So there still remains the task of identifying these means.  With or without the benefit of a prior consensus, or the assumption of an initial, but possibly fragile equilibrium, an explanation of robust harmony must detail the modes of maintaining communication that enable coordinated action to persist in the meanest of times.

Thus, the problem of mutual intelligibility turns on the question of "common significance":  How can there be signs that are truly public, when the most natural signs that distinct agents can know, their own internal states, have no guarantee and very little likelihood of being related in systematically fathomable ways?  As a partial answer to this, I am willing to contemplate certain forms of pre established harmony, like the common evolution of a biological species or the shared culture of an interpretive community, but my experience has been that harmony, once established, quickly corrupts unless active means are available to maintain it.  So there still remains the task of identifying these means.  With or without the benefit of a prior consensus, or the assumption of an initial, but possibly fragile equilibrium, an explanation of robust harmony must detail the modes of maintaining communication that enable coordinated action to persist in the meanest of times.