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# Attempting to strike a compromise with common usage, I often allow the word ''proposition'' to exploit the full range of its senses, denoting either object or sign according to context, and resorting to the phrase ''propositional expression'' whenever it is necessary to emphasize the involvement of the sign.

# Attempting to strike a compromise with common usage, I often allow the word ''proposition'' to exploit the full range of its senses, denoting either object or sign according to context, and resorting to the phrase ''propositional expression'' whenever it is necessary to emphasize the involvement of the sign.

The operative distinction in every case, propositional or otherwise, is the difference in roles between objects and signs, not the names they are called by.  To reconcile a logical account with the pragmatic theory of signs, one entity is construed as the ''propositional object'' (PO) and the other entity is recognized as the ''propositional sign'' (PS) at each moment of interpretation in a propositional sign relation.  Once these roles are assigned, all the technology of sign relations applies to the logic of propositions as a special case.  In the context of propositional sign relations, a ''semantic equivalence class'' (SEC) is referred to as a ''logical equivalence class'' (LEC).  Each propositional object can then be associated, or even identified for all informative and practical purposes, with the LEC of its propositional signs.  Accordingly, the proposition is reconstituted from its sentences in the appropriate way, as an abstract object existing in a semantic relation to its signs.

The operative distinction in every case, propositional or otherwise, is the difference in roles between objects and signs, not the names they are called by.  To reconcile a logical account with the pragmatic theory of signs, one entity is construed as the "propositional object" (PO) and the other entity is recognized as the "propositional sign" (PS) at each moment of interpretation in a propositional sign relation.  Once these roles are assigned, all the technology of sign relations applies to the logic of propositions as a special case.  In the context of propositional sign relations, a "semantic equivalence class" (SEC) is referred to as a "logical equivalence class" (LEC).  Each propositional object can then be associated, or even identified for all informative and practical puposes, with the LEC of its propositional signs.  Accordingly, the proposition is reconstituted from its sentences in the appropriate way, as an abstract object existing in a semantic relation to its signs.

Taking this topic, "the representation of sign relations", and seeking a computational formulation of its theory, leads to certain considerations about the best approach to the subject.  Computational formulations are those with no recourse but to finitary resources.  In setting up a computational formulation of any theory, one has to specify the finite set of axioms that are constantly available to subsequent reasoning.  This makes it advisable to approach the topic of representations at a level of generality that will give the resulting theory as much power as possible, the kind of power to which inductive hypotheses can have easy and constant recourse.  In order to furnish these resources with an ample supply of theoretical power ...

Taking this topic, ''the representation of sign relations'', and seeking a computational formulation of its theory, leads to certain considerations about the best approach to the subject.  Computational formulations are those with no recourse but to finitary resources.  In setting up a computational formulation of any theory, one has to specify the finite set of axioms that are constantly available to subsequent reasoning.  This makes it advisable to approach the topic of representations at a level of generality that will give the resulting theory as much power as possible, the kind of power to which inductive hypotheses can have easy and constant recourse.  In order to furnish these resources with an ample supply of theoretical power …

In doing this, it is expeditious, if not absolutely necessary, to broaden the focus on sign relations in two ways:  (1) to expand its extension from a special class of triadic relations to the wider sphere of n place relations, and (2) to diffuse its intension from fully specified and concretely presented relations to incompletly specified and abstractly described relations.

In doing this, it is expeditious, if not absolutely necessary, to broaden the focus on sign relations in two ways:  (1) to expand its extension from a special class of triadic relations to the wider sphere of <math>n\!</math>-place relations, and (2) to diffuse its intension from fully specified and concretely presented relations to incompletely specified and abstractly described relations.

===6.16. Recursive Aspects===

===6.16. Recursive Aspects===