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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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, 01:04, 15 August 2012→6.14. Issue 3. The Status of Variables: markup
I make one more remark to emphasize the importance of this issue, and then return to the main discussion. Even though there is no great difficulty in conceiving the sign <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> to be interpreted as denoting different types of objects in different contexts, it is more of a problem to imagine that the same object <math>x_i\!</math> can literally be both a value (in <math>\mathbb{B}\!</math>) and a function (from <math>\mathbb{B}^n\!</math> to <math>\mathbb{B}\!</math>).
I make one more remark to emphasize the importance of this issue, and then return to the main discussion. Even though there is no great difficulty in conceiving the sign <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> to be interpreted as denoting different types of objects in different contexts, it is more of a problem to imagine that the same object <math>x_i\!</math> can literally be both a value (in <math>\mathbb{B}\!</math>) and a function (from <math>\mathbb{B}^n\!</math> to <math>\mathbb{B}\!</math>).
In the customary fashion, the name <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> of the variable <math>x_i\!</math> is flexibly interpreted to serve two additional roles. In algebraic and geometric contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> is taken to name the <math>i^\text{th}\!</math> ''coordinate function'' <math>\underline{\underline{x_i}} : \mathbb{B}^n \to \mathbb{B}.\!</math> In logical contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> serves to name the <math>i^\text{th}\!</math> ''basic property'' or ''simple proposition'', also called <math>{}^{\backprime\backprime} \underline{\underline{x_i}} {}^{\prime\prime},\!</math> that goes into the construction of a propositional universe of discourse, in effect, becoming one of the ''sentence letters'' of a truth table and being used to label one of the ''simple enclosures'' of a venn diagram.
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Rationalizing the usage of boolean variables to represent propositional features and functions in this manner, I can now discuss these concepts in greater detail, introducing additional notation along the way.
Rationalizing the usage of boolean variables to represent propositional features and functions in this manner, I can now discuss these concepts in greater detail, introducing additional notation along the way.