Local-global Principle
Generally speaking, the term "local to global" refers to the idea that a global problem is first done at a local level, which tends to simplify the questions. Then, of course, the information gained in the local analysis has to be put together to get back to some global statement. For example, the notion of sheaves reifies that idea in topology and geometry.
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“Circumstances ... give in reality to every political principle its distinguishing colour and discriminating effect. The circumstances are what render every civil and political scheme beneficial or noxious to mankind.”
—Edmund Burke (1729–1797)