Changes

§ 8.   The notion of computation that makes sense in this setting is one of a process that replaces an arbitrary sign with a better sign of the same object.  In other words, computation is an interpretive process that improves the indications of intentions.  To deal with computational processes it is necessary to extend the pragmatic theory of signs in a couple of new but coordinated directions.  To the basic conception of a sign relation is added a notion of progress, which implies a notion of process together with a notion of quality.

§ 8.   The notion of computation that makes sense in this setting is one of a process that replaces an arbitrary sign with a better sign of the same object.  In other words, computation is an interpretive process that improves the indications of intentions.  To deal with computational processes it is necessary to extend the pragmatic theory of signs in a couple of new but coordinated directions.  To the basic conception of a sign relation is added a notion of progress, which implies a notion of process together with a notion of quality.

&sect; 9. &nbsp; This section introduces ''higher order'' sign relations, which are used to formalize the process of reflection on interpretation.  The discussion is approaching a point where multiple levels of signs are becoming necessary, mainly for referring to previous levels of signs as the objects of an extended sign relation, and thereby enabling a process of reflection on interpretive conduct.  To begin dealing with this issue, I take advantage of a second look at <math>A\!</math> and <math>B\!</math> to introduce the use of ''raised angle brackets'' <math>({}^{\langle}~{}^{\rangle}),</math> also called ''supercilia'' or ''arches'', as quotation marks.  Ordinary quotation marks <math>({}^{\backprime\backprime}~{}^{\prime\prime})</math> have the disadvantage, for formal purposes, of being used informally for many different tasks.  To get around this obstacle, I use the "arch" operator to formalize one specific function of quotation marks in a computational context, namely, to create distinctive names for syntactic expressions, or what amounts to the same thing, to signify the generation of their gödel numbers.

&sect; 9. &nbsp; This section introduces ''higher order'' sign relations, which are used to formalize the process of reflection on interpretation.  The discussion is approaching a point where multiple levels of signs are becoming necessary, mainly for referring to previous levels of signs as the objects of an extended sign relation, and thereby enabling a process of reflection on interpretive conduct.  To begin dealing with this issue, I take advantage of a second look at <math>A\!</math> and <math>B\!</math> to introduce the use of ''raised angle brackets'' <math>({}^{\langle}~{}^{\rangle}),</math> also called ''supercilia'' or ''arches'', as quotation marks.  Ordinary quotation marks <math>({}^{\backprime\backprime}~{}^{\prime\prime})</math> have the disadvantage, for formal purposes, of being used informally for many different tasks.  To get around this obstacle, I use the ''arch'' operator to formalize one specific function of quotation marks in a computational context, namely, to create distinctive names for syntactic expressions, or what amounts to the same thing, to signify the generation of their gödel numbers.

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