Changes

To begin formalizing this brand of supplementation, it is necessary to mark salient aspects of the situational, contextual, and inclusively interpretive features of sign usage that were previously held tacit.  In effect, signs once regarded as primitive objects need to be newly analyzed as categorical abstractions that cover multitudes of existential sign instances or ''signs in use''.

To begin formalizing this brand of supplementation, it is necessary to mark salient aspects of the situational, contextual, and inclusively interpretive features of sign usage that were previously held tacit.  In effect, signs once regarded as primitive objects need to be newly analyzed as categorical abstractions that cover multitudes of existential sign instances or ''signs in use''.

One way to to develop these dimensions of the <math>\text{A}\!</math> and <math>\text{B}\!</math> example is to articulate the interpretive parameters of signs by means of subscripts or superscripts attached to the signs or their quotations, in this way forming a corresponding set of ''situated signs'' or ''attributed remarks''.

To develop these dimensions of the A and B dialogue, I will attempt to articulate these interpretive parameters of signs by means of subscripts or superscripts attached to the signs or their quotations, in this way constituting a brand of "situated signs" or "attributed remarks".

The attribution of signs to their activating interpreters preserves the original object domain but produces an expanded syntactic domain, the set of "attributed signs":

The attribution of signs to their interpreters preserves the original object domain but produces an expanded syntactic domain, a corresponding set of ''attributed signs''.  In the <math>\text{A}\!</math> and <math>\text{B}\!</math> example this gives the following domains.

O =     { A, B },

 

S = I = {"A"A, "B"A, "i"A, "u"A, "A"B, "B"B, "i"B, "u"B}.

O & = &

\{ \text{A}, \text{B} \}

S & = &

{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}

{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}

Table&nbsp;76 displays the results of indexing every sign of the dialogue between A and B with a superscript indicating its source or "exponent", namely, the interpreter who actively communicates or transmits the sign.  Ostensibly, the operation of attribution produces two new sign relations for A and B, but it turns out that both sign relations have the same form and content, so a single Table will do.  The new sign relation generated by this operation will be denoted as "At (A, B)" and called the "attributed sign relation" for A and B.

Table&nbsp;76 displays the results of indexing every sign of the dialogue between A and B with a superscript indicating its source or "exponent", namely, the interpreter who actively communicates or transmits the sign.  Ostensibly, the operation of attribution produces two new sign relations for A and B, but it turns out that both sign relations have the same form and content, so a single Table will do.  The new sign relation generated by this operation will be denoted as "At (A, B)" and called the "attributed sign relation" for A and B.

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