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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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, 14:34, 19 September 2012→6.24. Literal Intensional Representations: markup
Even while operating within the general lines of the literal, superficial, or <math>\mathcal{O}(n)\!</math> strategy, there are still a number of choices to be made in the style of coding to be employed. For example, if there is an obvious distinction between different components of the world, like that between the objects in <math>O = \{ \text{A}, \text{B} \}\!</math> and the signs in <math>S = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \},\!</math> then it is common to let this distinction go formally unmarked in the LIR, that is, to omit the requirement of declaring an explicit logical feature to make a note of it in the formal coding. The distinction itself, as a property of reality, is in no danger of being obliterated or permanently erased, but it can be obscured and temporarily ignored. In practice, the distinction is not so much ignored as it is casually observed and informally attended to, usually being marked by incidental indices in the context of the representation.
Even while operating within the general lines of the literal, superficial, or <math>\mathcal{O}(n)\!</math> strategy, there are still a number of choices to be made in the style of coding to be employed. For example, if there is an obvious distinction between different components of the world, like that between the objects in <math>O = \{ \text{A}, \text{B} \}\!</math> and the signs in <math>S = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \},\!</math> then it is common to let this distinction go formally unmarked in the LIR, that is, to omit the requirement of declaring an explicit logical feature to make a note of it in the formal coding. The distinction itself, as a property of reality, is in no danger of being obliterated or permanently erased, but it can be obscured and temporarily ignored. In practice, the distinction is not so much ignored as it is casually observed and informally attended to, usually being marked by incidental indices in the context of the representation.
'''Literal Coding'''
'''Literal Coding'''
For the domain W = {A, B, "A", "B", "i", "u"} of six elements one needs to use six logical features, in effect, elevating each individual object to the status of an exclusive ontological category in its own right. The easiest way to do this is simply to reuse the world syntactic domain O as a logical alphabet W, taking element wise identifications as follows:
For the domain <math>W = \{ \text{A}, \text{B}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> of six elements one needs to use six logical features, in effect, elevating each individual object to the status of an exclusive ontological category in its own right. The easiest way to do this is simply to reuse the world domain <math>W\!</math> as a logical alphabet <math>\underline{\underline{W}},\!</math> taking element-wise identifications as follows:
W = {o1, o2, s1, s2, s3, s4} = {A, B, "A", "B", "i", "u"}.
{| align="center" cellspacing="8" width="90%"
W = {w1, w2, w3, w4, w5, w6} = {A, B, a, b, i, u}.
|
<math>\begin{array}{*{15}{c}}
W
& = &
\{ &
o_1
& , &
o_2
& , &
s_1
& , &
s_2
& , &
s_3
& , &
s_4
& \}
\\
& = &
\{ &
\text{A}
& , &
\text{B}
& , &
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
& , &
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
& , &
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
& , &
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
& \}
\\[10pt]
\underline{\underline{W}}
& = &
\{ &
\underline{\underline{w_1}}
& , &
\underline{\underline{w_2}}
& , &
\underline{\underline{w_3}}
& , &
\underline{\underline{w_4}}
& , &
\underline{\underline{w_5}}
& , &
\underline{\underline{w_6}}
& \}
\\
& = &
\{ &
\underline{\underline{\text{A}}}
& , &
\underline{\underline{\text{B}}}
& , &
\underline{\underline{\text{a}}}
& , &
\underline{\underline{\text{b}}}
& , &
\underline{\underline{\text{i}}}
& , &
\underline{\underline{\text{u}}}
& \}
\end{array}</math>
|}
<pre>
Tables 53.1 and 53.2 show three different ways of coding the elements of an ER and the features of a LIR, respectively, for the world set W = W (A, B), that is, for the set of objects, signs, and interpretants that are common to the sign relations A and B. Successive columns of these Tables give the "mnemonic code", the "pragmatic code", and the "abstract code" for each element.
Tables 53.1 and 53.2 show three different ways of coding the elements of an ER and the features of a LIR, respectively, for the world set W = W (A, B), that is, for the set of objects, signs, and interpretants that are common to the sign relations A and B. Successive columns of these Tables give the "mnemonic code", the "pragmatic code", and the "abstract code" for each element.