12,089
edits
Changes
Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 00:52, 2 May 2012
, 00:52, 2 May 2012→6.10. Higher Order Sign Relations : Examples: change notation & continue markup
\ldots
\ldots
\\
\\
\underline{\underline{s}}
\text{s}
\end{matrix}</math>
\end{matrix}</math>
| width="33%" |
| width="33%" |
<math>\begin{matrix}
<math>\begin{matrix}
\underline{\underline{s}}
\text{s}
\\
\\
\ldots
\ldots
\\
\\
\underline{\underline{t}}
\text{t}
\end{matrix}</math>
\end{matrix}</math>
| width="33%" |
| width="33%" |
<br>
<br>
This is all it takes to make <math>\underline{\underline{s}}\!</math> a lower order sign and <math>\underline{\underline{t}}\!</math> a higher order sign in relation to each other at the moments in question. Whether a global ordering of a more generally justifiable sort can be constructed from an arbitrary series of such purely local impressions is another matter altogether.
This is all it takes to make <math>\text{s}\!</math> a lower order sign and <math>\text{t}\!</math> a higher order sign in relation to each other at the moments in question. Whether a global ordering of a more generally justifiable sort can be constructed from an arbitrary series of such purely local impressions is another matter altogether.
Nevertheless, the preceding observations do show a way to give a definition of higher order signs that does not depend on the peculiarities of quotational devices. For example, consider the previously described sequence of increasingly higher order signs stemming from the object <math>x.\!</math> Table 39.1 shows how this succession can be transcribed into the form of a sign relation. But this is formally no different from the sign relation suggested in Table 39.2, one whose individual signs are not constructed in any special way. Both of these representations of sign relations, if continued in a consistent manner, would have the same abstract structure. If one of them is higher order then so is the other, at least, if the attributes of order are meant to have any formally invariant meaning.
<pre>
<pre>
Table 39.1 Sign Relation for a Succession of HO Signs (1)
Table 39.1 Sign Relation for a Succession of HO Signs (1)
Object Sign Interpretant
Object Sign Interpretant
<<x>> <<<x>>> ...
<<x>> <<<x>>> ...
... ... ...
... ... ...
</pre>
<pre>
Table 39.2 Sign Relation for a Succession of HO Signs (2)
Table 39.2 Sign Relation for a Succession of HO Signs (2)
Object Sign Interpretant
Object Sign Interpretant
s2 s3 ...
s2 s3 ...
... ... ...
... ... ...
</pre>
<pre>
The rest of this section discusses the relationship between HO signs and a concept called the "reflective extension" of a sign relation. Reflective extensions will be subjected to a more detailed study in a later part of this work. For now, just to see how the process works, the sign relations A and B are taken as starting points to illustrate the more common forms of reflective development.
The rest of this section discusses the relationship between HO signs and a concept called the "reflective extension" of a sign relation. Reflective extensions will be subjected to a more detailed study in a later part of this work. For now, just to see how the process works, the sign relations A and B are taken as starting points to illustrate the more common forms of reflective development.