SUO: REF: Higher Order Sign Relations

[Jon Awbrey <jawbrey@oakland.edu>]

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Reflection SIG,

Here is a preliminary foray into a Section
of my Dissertation where I begin to take up
the bearing of "higher order sign relations"
on the motley crew of intellectual operations
that we cast together and set in motion under
the heading of "reflection".

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3.4.9  Higher Order Sign Relations:  Introduction

When interpreters reflect on their own use of signs they require an
appropriate technical language in which to pursue these reflections.
For this they need signs that refer to sign relations, signs that
refer to the elements and components of sign relations, and signs
that refer to the properties and classes of sign relations.
All of these additional signs can be placed under the
description of "higher order" (HO) signs, and the
extended sign relations that involve them can be
referred to as "higher order" (HO) sign relations.

Whether any forms of observation and reflection can be conducted
outside the medium of language is not a question I can address here.
It is apparent as a practical matter, however, that stable and sharable
forms of knowledge depend on the availability of an adequate language.
Accordingly, there is a relationship of practical necessity that binds the
conditions for reflective interpretation to the possibility of extending
sign relations through higher orders.  At minimum, in addition to the
signs of objects originally given, there must be signs of signs
and signs of their interpretants, and each of these HO signs
requires a further occurrence of HO interpretants to continue
and complete its meaning within a HO sign relation.  In general,
HO signs can arise in a number of independent fashions, but one
of the most common derivations is through the specialized devices
of quotation.  This establishes a contingent relation between
reflection and quotation.

This entire topic, involving the relationship of reflective interpreters
to the realm of HO 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
HO signs off the ground.

By way of a first definition, a "higher order" (HO) sign relation
is a sign relation, some of whose signs are "higher order" (HO) signs.
If an extra degree of precision is needed, HO 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 HO signs,
it is a good idea to generalize slightly, designing an analytic
terminology that can be adapted to classify the HO signs of
arbitrary relations, not just the HO 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 still helps to take up the
classification of HO signs in a couple of passes,
first considering the categories of HO signs as
they apply to sign relations and then discussing
how the same ideas are relevant to arbitrary
relations.

Here are the species of HO signs that can be used to discuss the
structural constituents and intensional genera of sign relations:

1.  Signs that denote signs, that is, signs whose objects are signs
    in the same sign relation, are called "higher ascent" (HA) signs.

2.  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 <o, s>, <o, i>, <s, i>, are called
    "higher employ" (HE) signs.

3.  Signs that denote elementary sign relations, that is,
    signs whose objects are elemental triples or triadic
    transactions having the form <o, s, i>, are called
    "higher import" (HI) signs.

4.  Signs that denote sign relations, that is, signs whose objects are
    themselves sign relations, are called "higher upshot" (HU) signs.

5.  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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To Be Continued,

Jon Awbrey

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