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, 01:38, 2 May 2012→6.10. Higher Order Sign Relations : Examples: format table
| <math>\text{Interpretant}\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\ldots
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\ldots
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\text{s}
\text{s}
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\text{s}
\text{s}
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\ldots
\ldots
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\text{t}
\text{t}
\end{matrix}</math>
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<math>\begin{matrix}
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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.
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>
<br>
Table 39.1 Sign Relation for a Succession of HO Signs (1)
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 39.1} ~~ \text{Sign Relation for a Succession of Higher Order Signs (1)}\!</math>
|- style="height:40px; background:#f0f0ff"
| <math>\text{Object}\!</math>
| <math>\text{Sign}\!</math>
</pre>
| <math>\text{Interpretant}\!</math>
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<math>\begin{matrix}
x
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{}^{\langle} x {}^{\rangle}
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{}^{\langle\langle} x {}^{\rangle\rangle}
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\ldots
\end{matrix}</math>
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<math>\begin{matrix}
{}^{\langle} x {}^{\rangle}
\\[2pt]
{}^{\langle\langle} x {}^{\rangle\rangle}
\\[2pt]
{}^{\langle\langle\langle} x {}^{\rangle\rangle\rangle}
\\[2pt]
\ldots
\end{matrix}</math>
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<math>\begin{matrix}
\ldots
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\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\end{matrix}</math>
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<pre>
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