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  "body": "\n## Summary\n\nIntuitionism is the view, founded by L. E. J. Brouwer, that mathematics is a construction of the human mind.\nA mathematical object exists only when it can be constructed, and a statement is true only when it has a proof.\nAs a result, intuitionists do not accept the law of excluded middle in general.\nIts logic, [[intuitionistic logic|Q11N8X99FK]], is a central example of [[constructivism|G958EQ8CWW]].\n\n## Explanations\n\n### L1 human\n\nFor an intuitionist, saying \"there is a number with this property\" means \"I can show you such a number\".\nProving that \"no such number\" leads to a contradiction is not enough.\nTake a real number $x$ given by an infinite list of digits.\nThe statement \"either $x = 0$ or $x \\ne 0$\" cannot always be settled by a finite check, so an intuitionist does not assert it.\nThis makes intuitionistic mathematics more careful, and every intuitionistic proof contains a method of construction.\n",
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