Changes

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 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?

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.

The formal character of these questions, in the potential complexities that can be forced on contemplation in the pursuit of their answers, is independent of the species of interpreters that are chosen for the termini of comparison, whether person to person, person to computer, or computer to computer.  As always, the truth of this kind of thesis is formal, all too formal.  What it brings is a new refrain of an old motif:  Are there meaningful, if necessarily formal series of analogies that can be strung from the patterns of whizzing electrons and humming protons, whose controlled modes of collective excitation form and inform the conducts of computers, all the way to the rather different patterns of wizened electrons and humbled protons, whose deliberate energies of communal striving substantiate the forms of life known to be intelligible?

The formal character of these questions, in the potential complexities that can be forced on contemplation in the pursuit of their answers, is independent of the species of interpreters that are chosen for the termini of comparison, whether person to person, person to computer, or computer to computer.  As always, the truth of this kind of thesis is formal, all too formal.  What it brings is a new refrain of an old motif:  Are there meaningful, if necessarily formal series of analogies that can be strung from the patterns of whizzing electrons and humming protons, whose controlled modes of collective excitation form and inform the conducts of computers, all the way to the rather different patterns of wizened electrons and humbled protons, whose deliberate energies of communal striving substantiate the forms of life known to be intelligible?

A full consideration of the geometries available for the spaces in which these levels of reflective abstraction are commonly imagined to reside leads to the conclusion that familiar distinctions of "top down" versus "bottom up" are being taken for granted in an arena that has not even been established to be orientable.  Thus, it needs to be recognized that the distinction between objects and signs is relative to a definite SOI.  The pragmatic theory of signs is designed, in part, precisely to deal with the circumstance that thoroughly objective states of systems can be signs of each other, undermining any pretended distinction between objects and signs that one might propose to draw on essential grounds.

A full consideration of the geometries available for the spaces in which these levels of reflective abstraction are commonly imagined to reside leads to the conclusion that familiar distinctions of “top down” versus “bottom up” are being taken for granted in an arena that has not even been established to be orientable.  Thus, it needs to be recognized that the distinction between objects and signs is relative to a definite system of interpretation.  The pragmatic theory of signs is designed, in part, precisely to deal with the circumstance that thoroughly objective states of systems can be signs of each other, undermining any pretended distinction between objects and signs that one might propose to draw on essential grounds.

From now on, I will reuse the ancient term "gnomon" in a technical sense to refer to the godel numbers or code names of formal objects.  In other words, a gnomon is a godel numbering or enumeration function that maps a domain of objects into a domain of signs, Gno : O  > S.  When the syntactic domain S is contained within the object domain O, then the part of the gnomon that maps S into S, providing names for signs and expressions, is usually regarded as a "quoting function".

From now on, I will reuse the ancient term "gnomon" in a technical sense to refer to the godel numbers or code names of formal objects.  In other words, a gnomon is a godel numbering or enumeration function that maps a domain of objects into a domain of signs, Gno : O  > S.  When the syntactic domain S is contained within the object domain O, then the part of the gnomon that maps S into S, providing names for signs and expressions, is usually regarded as a "quoting function".