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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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, 19:42, 30 April 2012→6.9. Higher Order Sign Relations : Introduction: markup
In the informal context, however, quotation marks are used equivocally for several other purposes. In particular, they are frequently used to call attention to the immediate use of a sign, to stress it or redress it for a definitive, emphatic, or skeptical service, but without necessarily intending to interrupt or seriously alter its ongoing use. Furthermore, ordinary quotation marks are commonly taken so literally that they can inadvertently pose an obstacle to functional abstraction. For instance, if I try to refer to the effect of quotation as a mapping that takes signs to higher order signs, thereby attempting to define its action by means of a lambda abstraction: <math>x \mapsto {}^{\backprime\backprime} x {}^{\prime\prime},</math> then there are modes of IL interpretation that would read this literally as a constant map, one that sends every element of the functional domain into the single code for the letter <math>{}^{\backprime\backprime} x {}^{\prime\prime}.</math>
In the informal context, however, quotation marks are used equivocally for several other purposes. In particular, they are frequently used to call attention to the immediate use of a sign, to stress it or redress it for a definitive, emphatic, or skeptical service, but without necessarily intending to interrupt or seriously alter its ongoing use. Furthermore, ordinary quotation marks are commonly taken so literally that they can inadvertently pose an obstacle to functional abstraction. For instance, if I try to refer to the effect of quotation as a mapping that takes signs to higher order signs, thereby attempting to define its action by means of a lambda abstraction: <math>x \mapsto {}^{\backprime\backprime} x {}^{\prime\prime},</math> then there are modes of IL interpretation that would read this literally as a constant map, one that sends every element of the functional domain into the single code for the letter <math>{}^{\backprime\backprime} x {}^{\prime\prime}.</math>
For these reasons I introduce the use of raised angle brackets <math>( {}^{\langle} ~ {}^{\rangle} ),</math> also called “arches” or “supercilia”, to configure a form of quotation marker, but one that is subject to a more definite set of understandings about its interpretation. Namely, the arch marker denotes a function on signs that takes (the name of) a syntactic element located within it as (the name of) a functional argument and returns as its functional value the name of that syntactic element. The parenthetical operators in this statement reflect the optional readings that prevail in some cases, where the simple act of noticing a syntactic element as a functional argument is already tantamount to having a name for it. As a result, a quoting function that is designed to operate on the signs denoting and not on the objects denoted seems to do nothing at all, but merely uses up a moment of time to do it.
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In IL contexts the arch quotes are construed together with their syntactic contents as forming a certain kind of term, one that achieves a naming function on syntactic elements by taking the enclosed text as a functional argument and giving a directly embedded indication of it. In this type of setting the name of a string of length k is a string of length k+2.
In IL contexts the arch quotes are construed together with their syntactic contents as forming a certain kind of term, one that achieves a naming function on syntactic elements by taking the enclosed text as a functional argument and giving a directly embedded indication of it. In this type of setting the name of a string of length k is a string of length k+2.