Changes

# To continue to illustrate the salient properties of sign relations in the medium of selected examples.

# To continue to illustrate the salient properties of sign relations in the medium of selected examples.

# To demonstrate the use of sign relations to analyze and to clarify a particular order of difficult symbols and complex texts, namely, those that involve recursive, reflective, or reflexive features.

# To demonstrate the use of sign relations to analyze and clarify a particular order of difficult symbols and complex texts, namely, those that involve recursive, reflective, or reflexive features.

# To begin to suggest the implausibility of understanding this order of phenomena without using sign relations or something like them, namely, concepts with the power of triadic relations.

# To begin to suggest the implausibility of understanding this order of phenomena without using sign relations or something like them, namely, concepts with the power of triadic relations.

The prospective lines of an inquiry into inquiry cannot help but meet at various points, where a certain entanglement of the subjects of interest repeatedly has to be faced.  The present discussion of sign relations is currently approaching one of these points.  As the work progresses, the formal tools of logic and set theory become more and more indispensable to say anything significant or to produce any meaningful results in the study of sign relations.  And yet it appears, at least from the vantage of the pragmatic perspective, that the best way to formalize, to justify, and to sharpen the use of these tools is by means of the sign relations that they involve.  And so the investigation shuffles forward on two or more feet, shifting from a stance that fixes on a certain level of logic and set theory, using it to advance the understanding of sign relations, and then exploits the leverage of this new pivot to consider variations, and hopefully improvements, in the very language of concepts and terms that one uses to express questions about logic and sets, in all of its aspects, from syntax, to semantics, to the pragmatics of both human and computational interpreters.

The prospective lines of an inquiry into inquiry cannot help but meet at various points, where a certain entanglement of the subjects of interest repeatedly has to be faced.  The present discussion of sign relations is currently approaching one of these points.  As the work progresses, the formal tools of logic and set theory become more and more indispensable to say anything significant or to produce any meaningful results in the study of sign relations.  And yet it appears, at least from the vantage of the pragmatic perspective, that the best way to formalize, to justify, and to sharpen the use of these tools is by means of the sign relations that they involve.  And so the investigation shuffles forward on two or more feet, shifting from a stance that fixes on a certain level of logic and set theory, using it to advance the understanding of sign relations, and then exploits the leverage of this new pivot to consider variations, and hopefully improvements, in the very language of concepts and terms that one uses to express questions about logic and sets, in all of its aspects, from syntax, to semantics, to the pragmatics of both human and computational interpreters.

The main goals of this section are as follows:

The main goals of the present section are as follows:

# To introduce a basic logical notation and a naive theory of sets, just enough to treat sign relations as the set�theoretic extensions of logically expressible concepts.

# To introduce a basic logical notation and a naive theory of sets, just enough to treat sign relations as the set-theoretic extensions of logically expressible concepts.

# To use this modicum of formalism to define a number of conceptual constructs, useful in the analysis of more general sign relations.

# To use this modicum of formalism to define a number of conceptual constructs, useful in the analysis of more general sign relations.

# To develop a proof format that is suitable for deriving facts about these constructs in a careful and potentially computational manner.

# To develop a proof format that is suitable for deriving facts about these constructs in a careful and potentially computational manner.