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===6.10. Higher Order Sign Relations : Examples===
===6.10. Higher Order Sign Relations : Examples===
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.
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Table 36. Semantics for Higher Order Signs
Table 36. Semantics for Higher Order Signs
Object Denoted Equivalent Signs
Object Denoted Equivalent Signs
"i" <<i>> = <"i"> = "<i>"
"i" <<i>> = <"i"> = "<i>"
"u" <<u>> = <"u"> = "<u>"
"u" <<u>> = <"u"> = "<u>"
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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.
<pre>
Table 37.1 Sign Relational Schema C
Table 37.1 Sign Relational Schema C
Object Sign Interpretant
Object Sign Interpretant
x "x" "x"
x "x" "x"
"x" "x" "x"
"x" "x" "x"
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<pre>
Table 37.2 Sign Relational Schema D
Table 37.2 Sign Relational Schema D
Object Sign Interpretant
Object Sign Interpretant
x "x" "x"
x "x" "x"
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<pre>
Table 37.3 Sign Relational Schema E
Table 37.3 Sign Relational Schema E
Object Sign Interpretant
Object Sign Interpretant
"x" "x" "x"
"x" "x" "x"
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<pre>
Table 37.4 Sign Relational Schema D'
Table 37.4 Sign Relational Schema D'
Object Sign Interpretant
Object Sign Interpretant
x <x> "x"
x <x> "x"
x <x> <x>
x <x> <x>
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The invocation of "higher order" (HO) signs raises an important point, having to do with the typical ways that signs can become the objects of further signs, and the relationship that this type of semantic ascent bears to the interpretive agent's capacity for so called "reflection". This is a topic that will recur again as the discussion develops, but a speculative foreshadowing of its character will have to serve for now.
The invocation of higher order signs raises an important point, having to do with the typical ways that signs can become the objects of further signs, and the relationship that this type of semantic ascent bears to the interpretive agent's capacity for so called “reflection”. This is a topic that will recur again as the discussion develops, but a speculative foreshadowing of its character will have to serve for now.
Any object of an interpreter's experience and reasoning, no matter how vaguely and casually it initially appears, up to and including the merest appearance of a sign, is already, by virtue of these very circumstances, on its way to becoming the object of a formalized sign, so long as the signs are made available to denote it. The reason for this is rooted in each agent's capacity for reflection on its own experience and reasoning, and the critical question is only whether these transient reflections can come to constitute signs of a more permanent use.
Any object of an interpreter's experience and reasoning, no matter how vaguely and casually it initially appears, up to and including the merest appearance of a sign, is already, by virtue of these very circumstances, on its way to becoming the object of a formalized sign, so long as the signs are made available to denote it. The reason for this is rooted in each agent's capacity for reflection on its own experience and reasoning, and the critical question is only whether these transient reflections can come to constitute signs of a more permanent use.
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The immediate purpose of the "arch" operation is to equip the text with a syntactic mechanism for constructing "higher order" (HO) signs, that is, signs denoting signs. But the step of reflection that the arch device marks corresponds to a definite change on the part of the interpreter, affecting the "pragmatic stance" or the "intentional attitude" that the interpreter takes up with respect to the affected signs. Accordingly, because of its connection to the interpreter's capacity for critical reflection, the arch operation, whether signified by arches or quotes, opens up a topic of wide importance to the larger question of inquiry. Unfortunately, there is much to do before this issue can be taken up in detail, and immediate concerns make it necessary to break off further discussion for now.
The immediate purpose of the "arch" operation is to equip the text with a syntactic mechanism for constructing "higher order" (HO) signs, that is, signs denoting signs. But the step of reflection that the arch device marks corresponds to a definite change on the part of the interpreter, affecting the "pragmatic stance" or the "intentional attitude" that the interpreter takes up with respect to the affected signs. Accordingly, because of its connection to the interpreter's capacity for critical reflection, the arch operation, whether signified by arches or quotes, opens up a topic of wide importance to the larger question of inquiry. Unfortunately, there is much to do before this issue can be taken up in detail, and immediate concerns make it necessary to break off further discussion for now.
