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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 20:25, 30 April 2012
, 20:25, 30 April 2012→6.9. Higher Order Sign Relations : Introduction: markup
One further remark on the uses of quotation marks is pertinent here. When using HA signs with high orders of complexity and depth, it is often convenient to revert to the use of ordinary quotes at the outer boundary of a quotational expression, in this way marking a return to the ordinary context of interpretation. For example, one observes the colloquial equivalence: <math>{}^{\langle\langle\langle} x {}^{\rangle\rangle\rangle} ~=~ {}^{\backprime\backprime\langle\langle} x {}^{\rangle\rangle\rangle\prime\prime}.</math>
One further remark on the uses of quotation marks is pertinent here. When using HA signs with high orders of complexity and depth, it is often convenient to revert to the use of ordinary quotes at the outer boundary of a quotational expression, in this way marking a return to the ordinary context of interpretation. For example, one observes the colloquial equivalence: <math>{}^{\langle\langle\langle} x {}^{\rangle\rangle\rangle} ~=~ {}^{\backprime\backprime\langle\langle} x {}^{\rangle\rangle\rangle\prime\prime}.</math>
In general, a good way to specify the meaning of a new notation is by means of a semantic equation, or a system of semantic equations, that expresses the function of the new signs in terms of familiar operations. If it is merely a matter of introducing new signs for old meanings, then this method is sufficient. In this vein, the intention and use of the “supercilious notation” for reflecting on signs could have its definition approximated in the following way.
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Let <x> = "x" as signs for the object x, and let <<x>> = <"x"> = "<x>" as signs for the object "x", an object that incidentally happens to be sign. An alternative way of putting this is to say that the members of the set {<x>, "x"} are equivalent as signs for the object x, while the members of the set {<<x>>, <"x">, "<x>"} are equivalent as signs for the sign "x".
Let <x> = "x" as signs for the object x, and let <<x>> = <"x"> = "<x>" as signs for the object "x", an object that incidentally happens to be sign. An alternative way of putting this is to say that the members of the set {<x>, "x"} are equivalent as signs for the object x, while the members of the set {<<x>>, <"x">, "<x>"} are equivalent as signs for the sign "x".
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