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==Note 22==

==Quick Review==

Let us summarize, in rough but intuitive terms, the outlook on differential logic that we have reached so far.  We've been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse, <math>X^\circ,</math> to considering a larger universe of discourse, <math>\operatorname{E}X^\circ.</math>  An operator <math>\operatorname{W}</math> of this general type, namely,<math>\operatorname{W} : X^\circ \to \operatorname{E}X^\circ,</math> acts on each proposition <math>f : X \to \mathbb{B}</math> of the source universe <math>X^\circ</math> to produce a proposition <math>\operatorname{W}f : \operatorname{E}X \to \mathbb{B}</math> of the target universe <math>\operatorname{E}X^\circ.</math>

Let us summarize, in rough but intuitive terms, the outlook on differential logic that we have reached so far.  We've been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse, <math>X^\circ,</math> to considering a larger universe of discourse, <math>\operatorname{E}X^\circ.</math>  An operator <math>\operatorname{W}</math> of this general type, namely,<math>\operatorname{W} : X^\circ \to \operatorname{E}X^\circ,</math> acts on each proposition <math>f : X \to \mathbb{B}</math> of the source universe <math>X^\circ</math> to produce a proposition <math>\operatorname{W}f : \operatorname{E}X \to \mathbb{B}</math> of the target universe <math>\operatorname{E}X^\circ.</math>