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This work is a particular inquiry into the nature of inquiry in general.  As a consequence, every conceptual construct that appears in it will take on a double aspect.

This project is a particular inquiry into the nature of inquiry in general.  As a consequence, every concept that appears in it takes on a double aspect.

To illustrate, let us take the concept of a ''sign relation'' as an example and let me use it to speak about my own agency in this inquiry.  All I need to say about a sign relation at this point is that it is a three-place relation, and therefore can be imagined as a relational data-base with three columns, in this case naming the ''object'', the ''sign'', and the ''interpretant'' of the relation at each moment in time of the corresponding ''sign process''.

To illustrate, let us take the concept of a sign relation as an example of a construct that appears in this work and let me use it to speak about my own agency in this inquiry.  All I need to say about a sign relation at this point is that it is a three-place relation, and therefore can be represented as a relational data-base with three columns, in this case naming the object, the sign, and the interpretant of the relation at each moment in time of the corresponding sign process.

At any given moment of this inquiry I will be participating in a certain sign relation that constitutes the informal context of my activity, the full nature of which I can barely hope to conceptualize in explicitly formal terms.  At times, the object of this informal sign relation will itself be a sign relation, typically one that is already formalized or one that I have a better hope of formalizing, but it could conceivably be the original sign relation with which I began.

At any given moment of this inquiry I will be participating in a certain sign relation that constitutes the informal context of my activity, the full nature of which I can barely hope to conceptualize in explicitly formal terms.  At times, the object of this informal sign relation will itself be a sign relation, typically one that is already formalized or one that I have a better hope of formalizing, but it could conceivably be the original sign relation with which I began.

In such cases, when the object of a sign relation is also a sign relation, the general concept of a sign relation takes on a double duty:

In such cases, when the object of a sign relation is also a sign relation, the general concept of a sign relation takes on a double duty:

# The less formalized sign relation is used to mediate the inquiry.  As a conceptual construct, it is not yet fully conceived or constructed at the moments of inquiry being considered.  Perhaps it is better to regard it as a "concept under construction".  Employed as a contextual apparatus, this sign relation serves an instrumental role in the study or construal of its objective sign relation.

# The less formalized sign relation is used to mediate the present inquiry.  As a conceptual construct, it is not yet fully conceived or not yet fully constructed at the moments of inquiry being considered.  Perhaps it is better to regard it as a concept under construction.  Employed as a contextual apparatus, this sign relation serves an instrumental role in the construal and the study of its designated objective sign relation.

# The more formalized sign relation is mentioned as a substantive object to be contemplated and manipulated by the inquiry.  As a conceptual construct, it exemplifies the role intended for it best if it is already as completely formalized as possible.  It is being engaged as a substantive object of inquiry.

# The more formalized sign relation is mentioned as a substantive object to be contemplated and manipulated by the proceedings of this inquiry.  As a conceptual construct, it exemplifies its intended role best if it is already as completely formalized as possible.  It is being engaged as a substantive object of inquiry.

I have given this project a reflective or a recursive cast, describing it as inquiry into inquiry, and one of the consequences of this is that every concept employed in the work will take on a double aspect, divided role, or dual purpose.  At any moment, the object inquiry of the moment is aimed to take on a formal definition, whereas the active inquiry …

I have given this inquiry a reflective or recursive cast, portraying it as an inquiry into inquiry, and one of the consequences of this picture is that every concept employed in the work will take on a divided role, double aspect, or dual purpose.  At any moment, the object inquiry of the moment is aimed to take on a formal definition, while the active inquiry need not acknowledge any image that it does not recognize as reflecting itself, nor is it bound by any horizon that does not capture its spirit.

=====1.3.5.15. A Formal Permission=====

=====1.3.5.15. A Formal Permission=====