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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 17:40, 1 August 2012
, 17:40, 1 August 2012→6.11. Higher Order Sign Relations : Application: format table
This results in a higher order sign relation for <math>Q_{\text{AB}},\!</math> that is shown in Table 46.
This results in a higher order sign relation for <math>Q_{\text{AB}},\!</math> that is shown in Table 46.
<pre>
<br>
Table 46. Higher Order Sign Relation for Q(A, B)
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 46.} ~~ \text{Higher Order Sign Relation for} ~ Q(\text{A}, \text{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{B}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} L {}^{\rangle}
\\
{}^{\langle} L {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} L {}^{\rangle}
\\
{}^{\langle} L {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
</pre>
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}</math>
|-
| valign="bottom" width="33%" |
<math>\begin{matrix}
(( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{A} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{B} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{A} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{B} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{A} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{B} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{A} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{B} & ), & \text{A} & )
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\end{matrix}</math>
| valign="bottom" width="33%" |
<math>\begin{matrix}
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\end{matrix}</math>
|}
<br>
Following the manner of construction in this extremely reduced example, it is possible to see how answers to the above questions, concerning the meaning of <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime},\!</math> might be worked out. In the present instance:
Following the manner of construction in this extremely reduced example, it is possible to see how answers to the above questions, concerning the meaning of <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime},\!</math> might be worked out. In the present instance: