Changes

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Notice that the semiotic equivalences of nouns and pronouns for each interpreter do not extend to equivalences of their second-order signs, exactly as demanded by the literal character of quotations.  Moreover, the new sign relations for interpreters <math>\text{A}\!</math> and <math>\text{B}\!</math> coincide in their reflective parts, since exactly the same triples are added to each set.

Notice that the semantic equivalences of nouns and pronouns for each interpreter do not extend to equivalences of their second order signs, exactly as demanded by the literal character of quotations.  Moreover, the new sign relations for A and B coincide in their reflective parts, since exactly the same triples were added to each set.

There are many ways to extend sign relations in an effort to increase their reflective capacities.  The implicit goal of a reflective project is to achieve "reflective closure", S c O, where every sign is an object.

There are many ways to extend sign relations in an effort to increase their reflective capacities.  The implicit goal of a reflective project is to achieve ''reflective closure'', <math>S \subseteq O,\!</math> where every sign is an object.

Considered as reflective extensions, there is nothing unique about the constructions of Ref1 (A) and Ref1 (B), but their common pattern of development illustrates a typical approach toward reflective closure.  In a sense it epitomizes the project of "free", "naive", or "uncritical" reflection, since continuing this mode of production to its closure would generate an infinite sign relation, passing through infinitely many higher orders of signs, but without examining critically to what purpose the effort is directed or evaluating alternative constraints that might be imposed on the initial generators toward this end.

Considered as reflective extensions, there is nothing unique about the constructions of Ref1 (A) and Ref1 (B), but their common pattern of development illustrates a typical approach toward reflective closure.  In a sense it epitomizes the project of "free", "naive", or "uncritical" reflection, since continuing this mode of production to its closure would generate an infinite sign relation, passing through infinitely many higher orders of signs, but without examining critically to what purpose the effort is directed or evaluating alternative constraints that might be imposed on the initial generators toward this end.