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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 16:40, 15 May 2013
, 16:40, 15 May 2013→6.43. Reflective Extensions: markup
Raised angle brackets or ''supercilia'' <math>({}^{\langle} \ldots {}^{\rangle})\!</math> are here being used on a par with ordinary quotation marks <math>({}^{\backprime\backprime} \ldots {}^{\prime\prime})\!</math> to construct a new sign whose object is precisely the sign they enclose.
Raised angle brackets or ''supercilia'' <math>({}^{\langle} \ldots {}^{\rangle})\!</math> are here being used on a par with ordinary quotation marks <math>({}^{\backprime\backprime} \ldots {}^{\prime\prime})\!</math> to construct a new sign whose object is precisely the sign they enclose.
Regarded as sign relations in their own right, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> both have the following relational domains.
Regarded as sign relations in their own right, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> are formed on the following relational domains.
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{ccccl}
O & = & O^{(1)} \cup O^{(2)} & = &
\{ \text{A}, \text{B} \}
~ \cup ~
\{
{}^{\langle} \text{A} {}^{\rangle},
{}^{\langle} \text{B} {}^{\rangle},
{}^{\langle} \text{i} {}^{\rangle},
{}^{\langle} \text{u} {}^{\rangle}
\}
\\[8pt]
S & = & S^{(1)} \cup S^{(2)} & = &
\{
{}^{\langle} \text{A} {}^{\rangle},
{}^{\langle} \text{B} {}^{\rangle},
{}^{\langle} \text{i} {}^{\rangle},
{}^{\langle} \text{u} {}^{\rangle}
\}
~ \cup ~
\{
{}^{\langle\langle} \text{A} {}^{\rangle\rangle},
{}^{\langle\langle} \text{B} {}^{\rangle\rangle},
{}^{\langle\langle} \text{i} {}^{\rangle\rangle},
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\}
\\[8pt]
I & = & I^{(1)} \cup I^{(2)} & = &
\{
{}^{\langle} \text{A} {}^{\rangle},
{}^{\langle} \text{B} {}^{\rangle},
{}^{\langle} \text{i} {}^{\rangle},
{}^{\langle} \text{u} {}^{\rangle}
\}
~ \cup ~
\{
{}^{\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{array}</math>
|}
<pre>
<pre>
Thus, S overlaps with O in the set of first order signs or second order objects S<1> = O<2>, exemplifying the extent to which signs have become objects in the new sign relations.
Thus, S overlaps with O in the set of first order signs or second order objects S<1> = O<2>, exemplifying the extent to which signs have become objects in the new sign relations.