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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 04:04, 3 May 2012
, 04:04, 3 May 2012→6.10. Higher Order Sign Relations : Examples: format tables
Notice that the semantic equivalences of nouns and pronouns referring to each interpreter do not extend to semantic equivalences of their higher order signs, exactly as demanded by the literal character of quotations. Also notice that the reflective extensions of the sign relations <math>L(A)\!</math> and <math>L(B)\!</math> coincide in their reflective parts, since exactly the same triples were added to each set.
Notice that the semantic equivalences of nouns and pronouns referring to each interpreter do not extend to semantic equivalences of their higher order signs, exactly as demanded by the literal character of quotations. Also notice that the reflective extensions of the sign relations <math>L(A)\!</math> and <math>L(B)\!</math> coincide in their reflective parts, since exactly the same triples were added to each set.
<pre>
<br>
<pre>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
Table 43. Higher Ascent Sign Relation Ref1(B)
|+ style="height:30px" | <math>\text{Table 42.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(A)\!</math>
|- style="height:40px; background:#f0f0ff"
| <math>\text{Object}\!</math>
| <math>\text{Sign}\!</math>
| <math>\text{Interpretant}\!</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
</pre>
\text{A}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}</math>
|}
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 43.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(B)\!</math>
|- style="height:40px; background:#f0f0ff"
| <math>\text{Object}\!</math>
| <math>\text{Sign}\!</math>
| <math>\text{Interpretant}\!</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}</math>
|}
<br>
<pre>
<pre>