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===6.11. Higher Order Sign Relations : Application===

===6.11. Higher Order Sign Relations : Application===

Given the language in which a notation like <math>{}^{\backprime\backprime} \operatorname{De}(q, R) {}^{\prime\prime}\!</math> makes sense, or in prospect of being given such a language, it is instructive to ask:  &ldquo;What must be assumed about the context of interpretation in which this language is supposed to make sense?&rdquo;  According to the theory of signs that is being examined here, the relevant formal aspects of that context are embodied in a particular sign relation, call it <math>{}^{\backprime\backprime} Q {}^{\prime\prime}.\!</math>  With respect to the hypothetical sign relation <math>Q,\!</math> commonly personified as the prospective reader or the ideal interpreter of the intended language, the denotation of the expression <math>{}^{\backprime\backprime} \operatorname{De}(q, R) {}^{\prime\prime}\!</math> is given by:

Given the language in which a notation like <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime}\!</math> makes sense, or in prospect of being given such a language, it is instructive to ask:  &ldquo;What must be assumed about the context of interpretation in which this language is supposed to make sense?&rdquo;  According to the theory of signs that is being examined here, the relevant formal aspects of that context are embodied in a particular sign relation, call it <math>{}^{\backprime\backprime} Q {}^{\prime\prime}.\!</math>  With respect to the hypothetical sign relation <math>Q,\!</math> commonly personified as the prospective reader or the ideal interpreter of the intended language, the denotation of the expression <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime}\!</math> is given by:

{| align="center" cellspacing="8" width="90%"

{| align="center" cellspacing="8" width="90%"

| <math>\operatorname{De}( {}^{\backprime\backprime} \operatorname{De}(q, R) {}^{\prime\prime}, Q ).\!</math>

| <math>\operatorname{De}( {}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime}, Q ).\!</math>

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