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Revision as of 18:12, 20 May 2013
, 18:12, 20 May 2013→6.43. Reflective Extensions: markup
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E1: <<A>> = <A>, <<B>> = <B>, <<i>> = <i>, <<u>> = <u>.+By calling attention to their intended status as "semantic" equations, meaning that signs are being set equal in the SECs they inhabit or the objects they denote, I hope to emphasize that these equations are able to say something significant about objects.
−??? Redo F(S) over W ??? Use WF = O U F ???
−</pre>
A variant pair of reflective extensions, <math>\operatorname{Ref}^1 (\text{A} | E_1)\!</math> and <math>\operatorname{Ref}^1 (\text{B} | E_1),\!</math> are presented in Tables 82 and 83, respectively. These are identical to the corresponding free variants, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B}),\!</math> with the exception of those entries that are constrained by the following system of semantic equations.
A variant pair of reflective extensions, <math>\operatorname{Ref}^1 (\text{A} | E_1)\!</math> and <math>\operatorname{Ref}^1 (\text{B} | E_1),\!</math> are presented in Tables 82 and 83, respectively. These are identical to the corresponding free variants, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B}),\!</math> with the exception of those entries that are constrained by the following system of semantic equations.
−<pre>
+{| align="center" cellspacing="8" width="90%"
−|
+<math>\begin{matrix}
+E_1 :
+&
+{}^{\langle\langle} \text{A} {}^{\rangle\rangle} = {}^{\langle} \text{A} {}^{\rangle},
+&
+{}^{\langle\langle} \text{B} {}^{\rangle\rangle} = {}^{\langle} \text{B} {}^{\rangle},
+&
+{}^{\langle\langle} \text{i} {}^{\rangle\rangle} = {}^{\langle} \text{i} {}^{\rangle},
+&
+{}^{\langle\langle} \text{u} {}^{\rangle\rangle} = {}^{\langle} \text{u} {}^{\rangle}.
+\end{matrix}</math>
+|}
This has the effect of making all levels of quotation equivalent.
This has the effect of making all levels of quotation equivalent.
−<br>
<br>
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<br>
<br>
+
+By calling attention to their intended status as ''semantic'' equations, meaning that signs are being set equal in the semantic equivalence classes they inhabit or the objects they denote, I hope to emphasize that these equations are able to say something significant about objects.
+
+'''Question.''' Redo <math>F(S)\!</math> over <math>W\!</math>? Use <math>W_F = O \cup F\!</math>?
===6.44. Reflections on Closure===
===6.44. Reflections on Closure===
