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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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This entire topic, involving the relationship of reflective interpreters to the realm of higher order sign relations and the available operators for quotation, forms the subject of a recurring investigation that extends throughout the rest of this work. This section introduces only enough of the basic concepts, terminology, and technical machinery that is necessary to get the theory of higher order signs off the ground.
This entire topic, involving the relationship of reflective interpreters to the realm of higher order sign relations and the available operators for quotation, forms the subject of a recurring investigation that extends throughout the rest of this work. This section introduces only enough of the basic concepts, terminology, and technical machinery that is necessary to get the theory of higher order signs off the ground.
By way of a first definition, a '''higher order sign relation''' is a sign relation, some of whose signs are '''higher order signs'''. If an extra degree of precision is needed, higher order signs can be distinguished in a variety of different ''species'' or ''types'', to be taken up next.
By way of a first definition, a ''higher order sign relation'' is a sign relation, some of whose signs are ''higher order signs''. If an extra degree of precision is needed, higher order signs can be distinguished in a variety of different ''species'' or ''types'', to be taken up next.
In devising a nomenclature for the required species of higher order signs, it is a good idea to generalize slightly, designing an analytic terminology that can be adapted to classify the higher order signs of arbitrary relations, not just the higher order signs of sign relations. The work of developing a more powerful vocabulary can be put to good account at a later stage of this project, when it is necessary to discuss the structural constituents of arbitrary relations and to reflect on the language that is used to discuss them. However, by way of making a gradual approach, it nonetheless helps to take up the classification of higher order signs in a couple of passes, first considering the categories of higher order signs as they apply to sign relations and then discussing how the same ideas are relevant to arbitrary relations.
In devising a nomenclature for the required species of higher order signs, it is a good idea to generalize slightly, designing an analytic terminology that can be adapted to classify the higher order signs of arbitrary relations, not just the higher order signs of sign relations. The work of developing a more powerful vocabulary can be put to good account at a later stage of this project, when it is necessary to discuss the structural constituents of arbitrary relations and to reflect on the language that is used to discuss them. However, by way of making a gradual approach, it nonetheless helps to take up the classification of higher order signs in a couple of passes, first considering the categories of higher order signs as they apply to sign relations and then discussing how the same ideas are relevant to arbitrary relations.
Here are the species of higher order signs that can be used to discuss the structural constituents and intensional genera of sign relations:
# Signs that denote signs, that is, signs whose objects are signs in the same sign relation, are called '''higher ascent''' (HA) signs.
# Signs that denote dyadic components of elementary sign relations, that is, signs whose objects are elemental pairs or dyadic actions having any one of the forms <math>(o, s),\!</math> <math>(o, i),\!</math> or <math>(s, i),\!</math> are called '''higher employ''' (HE) signs.
# Signs that denote elementary sign relations, that is, signs whose objects are elemental triples or triadic transactions having the form <math>(o, s, i),\!</math> are called '''higher import''' (HI) signs.
# Signs that denote sign relations, that is, signs whose objects are themselves sign relations, are called '''higher upshot''' (HU) signs.
# Signs that denote intensional genera of sign relations, that is, signs whose objects are properties or classes of sign relations, are called '''higher yclept''' (HY) signs.
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Analogous species of HO signs can be used to discuss the structural constituents and intensional genera of arbitrary relations. In order to describe them, it is necessary to introduce a few extra notions from the theory of relations. This, in turn, occasions a recurring difficulty with the exposition that needs to be noted at this point.
Analogous species of HO signs can be used to discuss the structural constituents and intensional genera of arbitrary relations. In order to describe them, it is necessary to introduce a few extra notions from the theory of relations. This, in turn, occasions a recurring difficulty with the exposition that needs to be noted at this point.