Changes

In the pluralistic contexts that go with pragmatic theories of signs, it is no longer entirely appropriate to refer to ''the'' gnomon of any object.  At any moment of discussion, I can only have so-and-so's gnomon or code word for each thing under the sun.  Thus, apparent references to a uniquely determined gnomon only make sense if taken as enthymemic invocations of the ordinary context and all that is comprehended to be implied in it, promising to convert tacit common sense into definite articulations of what is understood.  Actually achieving this requires each elliptic reference to the gnomon to be explicitly grounded in the context of informal discussion, interpreted with respect to the conventional basis of understanding assumed in it, and relayed to the indexing function taken for granted by all parties to it.

In the pluralistic contexts that go with pragmatic theories of signs, it is no longer entirely appropriate to refer to ''the'' gnomon of any object.  At any moment of discussion, I can only have so-and-so's gnomon or code word for each thing under the sun.  Thus, apparent references to a uniquely determined gnomon only make sense if taken as enthymemic invocations of the ordinary context and all that is comprehended to be implied in it, promising to convert tacit common sense into definite articulations of what is understood.  Actually achieving this requires each elliptic reference to the gnomon to be explicitly grounded in the context of informal discussion, interpreted with respect to the conventional basis of understanding assumed in it, and relayed to the indexing function taken for granted by all parties to it.

In computational terms, this brand of pluralism means that neither the gnomon nor the quoting function that forms a part of it can be viewed as well-defined unless it is indexed, explicitly or implicitly, by the name of a particular interpreter.  I will use either one of the equivalent notations <math>{}^{\backprime\backprime} \operatorname{Gno}_i (x) {}^{\prime\prime}\!</math> or <math>{}^{\backprime\backprime\langle} x, i {}^{\rangle\prime\prime}\!</math> to indicate the gnomon of the object <math>x\!</math> with respect to the interpreter <math>i.\!</math>  The value <math>\operatorname{Gno}_i (x) = {}^{\langle} x, i {}^{\rangle} \in S\!</math> is the ''nominal sign in use'' or the ''name in use'' (NIU) of the object <math>x\!</math> with respect to the interpreter <math>i,\!</math> and thus it is a component of <math>i\!</math>'s state.

In computational terms, this brand of pluralism means that neither the gnomon nor the quoting function that forms a part of it can be viewed as well-defined unless it is indexed, explicitly or implicitly, by the name of a particular interpreter.  I will use either one of the equivalent notations <math>{}^{\backprime\backprime} \operatorname{Gno}_i (x) {}^{\prime\prime}\!</math> or <math>{}^{\backprime\backprime\langle} x, i {}^{\rangle\prime\prime}\!</math> to indicate the gnomon of the object <math>x\!</math> with respect to the interpreter <math>i.\!</math>  The value <math>\operatorname{Gno}_i (x) = {}^{\langle} x, i {}^{\rangle} \in S\!</math> is the ''nominal sign in use'' or the ''name in use'' (NIU) of the object <math>x\!</math> with respect to the interpreter <math>i,\!</math> and thus it constitutes a component of <math>i\!</math>'s state.

 

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If it is now asked what measure of invariant understanding can be enjoyed by diverse parties of interpretive agents, then the discussion has come upon an issue with a familiar echo in mathematical analysis.  The organization of many local coordinate frames into systems capable of supporting communicative references to relatively "objective" objects is usually handled by means of the concept of a "manifold".  Therefore, the analogous task that is suggested for this project is to arrive at a workable definition of "sign relational manifolds".

If it is now asked what measure of invariant understanding can be enjoyed by diverse parties of interpretive agents, then the discussion has come upon an issue with a familiar echo in mathematical analysis.  The organization of many local coordinate frames into systems capable of supporting communicative references to relatively "objective" objects is usually handled by means of the concept of a "manifold".  Therefore, the analogous task that is suggested for this project is to arrive at a workable definition of "sign relational manifolds".