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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 13:37, 1 May 2012
, 13:37, 1 May 2012→6.10. Higher Order Sign Relations : Examples: format table
In considering the higher order sign relations that stem from the examples <math>L(A)\!</math> and <math>L(B),\!</math> it appears that annexing the first level of HA signs is tantamount to adjoining or instituting an auxiliary interpretive framework, one that has the semantic equations shown in Table 36.
In considering the higher order sign relations that stem from the examples <math>L(A)\!</math> and <math>L(B),\!</math> it appears that annexing the first level of HA signs is tantamount to adjoining or instituting an auxiliary interpretive framework, one that has the semantic equations shown in Table 36.
<pre>
<br>
Table 36. Semantics for Higher Order Signs
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 36.} ~~ \text{Semantics for Higher Order Signs}\!</math>
|- style="height:40px; background:#f0f0ff"
| <math>\text{Object Denoted}\!</math>
| <math>\text{Equivalent Signs}\!</math>
|-
| width="33%" |
</pre>
<math>\begin{matrix}
\text{A}
\\
\text{B}
\end{matrix}</math>
| width="33%" |
<math>\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
& = &
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\langle} \text{B} {}^{\rangle}
& = &
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\end{matrix}</math>
|-
| width="33%" |
<math>\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}</math>
| width="33%" |
<math>\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{A} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{A} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{B} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{B} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{i} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{i} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{u} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{u} {}^{\rangle\prime\prime}
\end{matrix}</math>
|}
<br>
However, there is an obvious problem with this method of defining new notations. It merely provides alternate signs for the same old uses. But if the original signs are ambiguous, then equating new signs to them cannot remedy the problem. Thus, it is necessary to find ways of selectively reforming the uses of the old notation in the interpretation of the new notation.
However, there is an obvious problem with this method of defining new notations. It merely provides alternate signs for the same old uses. But if the original signs are ambiguous, then equating new signs to them cannot remedy the problem. Thus, it is necessary to find ways of selectively reforming the uses of the old notation in the interpretation of the new notation.