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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.16. Recursive Aspects===
===6.16. Recursive Aspects===
<pre>
'''Note.''' This section will most likely be rendered obsolete once all the planned changes in notation are worked through the text, as I will make a point of always distinguishing the interpretive agents <math>\text{A}\!</math> and <math>\text{B}\!</math> from the corresponding sign relations <math>L(\text{A})\!</math> and <math>L(\text{B}).\!</math>
There is a one piece of unfinished business concerning the presentation of this example that deserves further comment.
There is a one piece of unfinished business concerning the presentation of this example that deserves further comment.
Since the objects of reference, A and B, are imagined to be interpretive agents, it is convenient to use their names to denote the corresponding sign relations. Thus, the interpreters A and B are self referent and mutually referent to the extent that they have names for themselves and each other. However, their discussion as a whole fails to contain any term for itself, and it even lacks a full set of grammatical cases for the objects in it. Whether these recursions and omissions cause any problems for my discussion will depend on the level of interpretive sophistication, not of A and B, but of the external systems of interpretation that are brought to bear on it.
Since the objects of reference, <math>\text{A}\!</math> and <math>\text{B},\!</math> are imagined to be interpretive agents, it is convenient to use their names to denote the corresponding sign relations. Thus, the interpreters <math>\text{A}\!</math> and <math>\text{B}\!</math> are self-referent and mutually referent to the extent that they have names for themselves and each other. However, their discussion as a whole fails to contain any term for itself, and it even lacks a full set of grammatical cases for the objects in it. Whether these recursions and omissions cause any problems for my discussion will depend on the level of interpretive sophistication, not of <math>\text{A}\!</math> and <math>\text{B},\!</math> but of the external systems of interpretation that are brought to bear on it.
<pre>
In defining the activities of interpreters A and B as sign relations, I have implicitly specified set theoretic equations of the following form:
In defining the activities of interpreters A and B as sign relations, I have implicitly specified set theoretic equations of the following form: