In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic.
Read more about Higher-order Logic: Higher-order Simple Predicate Logic, Examples, Criticism
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“Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.”
—Ludwig Wittgenstein (1889–1951)