The quality of being dependent on uncertain conditions; the state of being contingent or subject to chance.
From Latin contingentia, from contingere (to happen to, befall), from con- + tangere (to touch). The idea that something touching you by chance makes it contingent.
Medieval philosophers got excited about contingence because it raised the deepest questions: if some things are contingent (dependent on chance), what must be necessary and eternal? Contingence became philosophy's way of thinking about possibility and randomness.
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