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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 16:48, 3 May 2012
, 16:48, 3 May 2012→6.10. Higher Order Sign Relations : Examples: markup
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Several important facts about the class of higher order sign relations in general are illustrated by these examples. First, the notations appearing in the object columns of <math>\operatorname{HI}^1 L(A)\!</math> and <math>\operatorname{HI}^1 L(B)\!</math> are not the terms that these newly extended interpreters are depicted as using to describe their objects, but the kinds of language that you and I, or other external observers, would typically make available to distinguish them. The sign relations <math>L(A)\!</math> and <math>L(B),\!</math> as extended by the transactions of <math>\operatorname{HI}^1 L(A)\!</math> and <math>\operatorname{HI}^1 L(B),\!</math> respectively, are still restricted to their original syntactic domain <math>\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \}.\!</math> This means that there need be nothing especially articulate about a HI sign relation just because it qualifies as higher order. Indeed, the sign relations <math>\operatorname{HI}^1 L(A)\!</math> and <math>\operatorname{HI}^1 L(B)\!</math> are not very discriminating in their descriptions of the sign relations <math>L(A)\!</math> and <math>L(B),\!</math> referring to many different things under the very same signs that you and I and others would explicitly distinguish, especially in marking the distinction between an interpretive agent and any one of its individual transactions.
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In practice, it does an interpreter little good to have the HI signs for referring to triples of objects, signs, and interpretants if it does not also have the HA signs for referring to each triple's syntactic portions. Consequently, the HO sign relations that one is likely to observe in practice are typically a mixed bag, having both HA and HI sections. Moreover, the ambiguity involved in having signs that refer equivocally to simple world elements and also to complex structures formed from these ingredients would most likely be resolved by drawing additional information from context and fashioning more distinctive signs.
In practice, it does an interpreter little good to have the HI signs for referring to triples of objects, signs, and interpretants if it does not also have the HA signs for referring to each triple's syntactic portions. Consequently, the HO sign relations that one is likely to observe in practice are typically a mixed bag, having both HA and HI sections. Moreover, the ambiguity involved in having signs that refer equivocally to simple world elements and also to complex structures formed from these ingredients would most likely be resolved by drawing additional information from context and fashioning more distinctive signs.