Tangent and Remainder Maps If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way. The next venn diagram shows the differential proposition we get by extracting the linear approximation to the difference map at each cell […]
Enlargement and Difference Maps Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension A very important conceptual transition has just occurred here, almost tacitly, as it were. Generally speaking, having a set of mathematical objects of compatible […]
Propositions and Tacit Extensions Now that we’ve introduced the field picture as an aid to visualizing propositions and their analytic series, a pleasing way to picture the relationship of a proposition to its enlargement or shift map and its difference map can now be drawn. To illustrate the possibilities, let’s return to the differential analysis […]
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chosen path 