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Revision as of 18:12, 20 May 2013
, 18:12, 20 May 2013→6.43. Reflective Extensions: markup
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>
<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===
