Changes

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation.  Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation.  Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

==Examples of sign relations==

=={{anchor|Examples}}Examples of sign relations==

Because the examples to follow have been artificially constructed to be as simple as possible, their detailed elaboration can run the risk of trivializing the whole theory of sign relations.  Despite their simplicity, however, these examples have subtleties of their own, and their careful treatment will serve to illustrate many important issues in the general theory of signs.

Despite their simplicity, the examples to follow have subtleties of their own and their careful treatment serves to illustrate important issues in the general theory of signs.

Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their interpretive practice that involves the use of the following nouns and pronouns:  “Ann”, “Bob”, “I”, “you”.

Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their interpretive practice that involves the use of the following nouns and pronouns:  “Ann”, “Bob”, “I”, “you”.

==Dyadic aspects of sign relations==

==Dyadic aspects of sign relations==

For an arbitrary triadic relation <math>L \subseteq O \times S \times I,</math> whether it is a sign relation or not, there are six dyadic relations that can be obtained by <i>projecting</i> <math>L</math> on one of the planes of the <math>OSI</math>-space <math>O \times S \times I.</math>&nbsp; The six dyadic projections of a triadic relation <math>L</math> are defined and notated as follows:

For an arbitrary triadic relation <math>L \subseteq O \times S \times I,</math> whether it happens to be a sign relation or not, there are six dyadic relations obtained by <i>projecting</i> <math>L</math> on one of the planes of the <math>OSI</math>-space <math>O \times S \times I.</math>&nbsp; The six dyadic projections of a triadic relation <math>L</math> are defined and notated as shown in Table&nbsp;2.

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By way of unpacking the set-theoretic notation, here is what the first definition says in ordinary language.

By way of unpacking the set&#8209;theoretic notation, here is what the first definition says in ordinary language.

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<p>The dyadic relation that results from the projection of <math>L</math> on the <math>OS</math>-plane <math>O \times S</math> is written briefly as <math>L_{OS}</math> or written more fully as <math>\mathrm{proj}_{OS}(L),</math> and it is defined as the set of all ordered pairs <math>(o, s)</math> in the cartesian product <math>O \times S</math> for which there exists an ordered triple <math>(o, s, i)</math> in <math>L</math> for some interpretant <math>i</math> in the interpretant domain <math>I.</math></p>

<p>The dyadic relation resulting from the projection of <math>L</math> on the <math>OS</math>-plane <math>O \times S</math> is written briefly as <math>L_{OS}</math> or written more fully as <math>\mathrm{proj}_{OS}(L)</math> and is defined as the set of all ordered pairs <math>(o, s)</math> in the cartesian product <math>O \times S</math> for which there exists an ordered triple <math>(o, s, i)</math> in <math>L</math> for some element <math>i</math> in the set <math>I.</math></p>

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In the case where <math>L</math> is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of <math>L</math> can be recognized as formalizing aspects of sign meaning that have received their share of attention from students of signs over the centuries, and thus they can be associated with&nbsp; traditional concepts and terminology.&nbsp; Of course, traditions may vary as to the precise formation and usage of such concepts and terms.&nbsp; Other aspects of meaning have not received their fair share of attention, and thus remain anonymous on the contemporary scene of sign studies.

In the case where <math>L</math> is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of <math>L</math> can be recognized as formalizing aspects of sign meaning which have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology.&nbsp; Of course, traditions vary with respect to the precise formation and usage of such concepts and terms.&nbsp; Other aspects of meaning have not received their fair share of attention and thus remain innominate in current anatomies of sign relations.

===Denotation===

===Denotation===