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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 21:40, 14 August 2012
, 21:40, 14 August 2012→6.14. Issue 3. The Status of Variables: markup
The set <math>\underline{\underline{X}}\!</math> is known in formal settings as the ''literal alphabet'' or the ''literal lexicon'' associated with <math>X,\!</math> but on more familiar grounds it can be called the ''double'' of <math>X.\!</math> Under conditions of careful interpretation, any finite set <math>X\!</math> can be construed as its own double, but for now it is safest to preserve the apparent distinction in roles until the sense of this double usage has become second nature.
The set <math>\underline{\underline{X}}\!</math> is known in formal settings as the ''literal alphabet'' or the ''literal lexicon'' associated with <math>X,\!</math> but on more familiar grounds it can be called the ''double'' of <math>X.\!</math> Under conditions of careful interpretation, any finite set <math>X\!</math> can be construed as its own double, but for now it is safest to preserve the apparent distinction in roles until the sense of this double usage has become second nature.
This construction is often useful in situations where has to deal with a set of signs <math>\{ {}^{\backprime\backprime} s_1 {}^{\prime\prime}, \ldots, {}^{\backprime\backprime} s_n {}^{\prime\prime} \}\!</math> with a fixed or a faulty interpretation. Here one needs a fresh set of signs <math>\{ \underline{\underline{x_1}}, \ldots, \underline{\underline{x_n}} \}\!</math> that can be used in ways analogous to the original, but free enough to be controlled and flexible enough to be repaired. In other words, the interpretation of the new list is subject to experimental variation, freely controllable in such a way that it can follow or assimilate the original interpretation whenever it makes sense to do so, but critically reflected and flexible enough to have its interpretation amended whenever necessary.
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Interpreted on a casual basis, the set X can be treated as a list of "boolean variables", or, according to another reading, as a list of "boolean variable names", but both of these choices are subject to the eventual requirement of saying exactly what a "variable" is.
Interpreted on a casual basis, the set X can be treated as a list of "boolean variables", or, according to another reading, as a list of "boolean variable names", but both of these choices are subject to the eventual requirement of saying exactly what a "variable" is.