Intuitionism clashed with classical mathematics in so far as Brouwer held that there are no truths beyond experience and hence that the law of the excluded middle could not be applied to all mathematical statements (in particular infinitary parts of mathematics are indeterminate with respect to some properties).

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In mathematical logic, predicate logic is the formal system of universal symbolic terms, such as first order logic, second order logic, many types of logic or infinitary logic ...

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infinitary logic：無窮邏輯

非古典邏輯 non-classical logic | 無窮邏輯 infinitary logic | 古典邏輯 classical logic