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Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)
Revision as of 18:18, 17 January 2009
, 18:18, 17 January 2009→1.3.10.6. Stretching Principles: skip problem piece for now and try to markup the rest
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Because this notation is only used in settings where the imagination <math>\underline{f} : (X \to \underline\mathbb{B})^k</math> and the connection <math>F : \underline\mathbb{B}^k \to \underline\mathbb{B}</math> are distinguished by their types, it does not really matter whether one writes <math>{}^{\backprime\backprime} F ~\$~ \underline{f} {}^{\prime\prime}</math> or <math>{}^{\backprime\backprime} \underline{f} ~\$~ F {}^{\prime\prime}</math> for the initial composition.
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Just as a sentence is a sign that denotes a proposition, which thereby serves to indicate a set, a propositional connective is a provision of syntax whose mediate effect is to denote an operation on propositions, which thereby manages to indicate the result of an operation on sets. In order to see how these compound forms of indication can be defined, it is useful to go through the steps that are needed to construct them. In general terms, the ingredients of the construction are as follows:
Just as a sentence is a sign that denotes a proposition, which thereby serves to indicate a set, a propositional connective is a provision of syntax whose mediate effect is to denote an operation on propositions, which thereby manages to indicate the result of an operation on sets. In order to see how these compound forms of indication can be defined, it is useful to go through the steps that are needed to construct them. In general terms, the ingredients of the construction are as follows: