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Full Idea
The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction.
Gist of Idea
Mathematical proof by contradiction needs the law of excluded middle
Source
Shaughan Lavine (Understanding the Infinite [1994], VI.1)
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.155
A Reaction
This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku.