Higher-order Logic

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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    There is no morality by instinct.... There is no social salvation—in the end—without taking thought; without mastery of logic and application of logic to human experience.
    Katharine Fullerton Gerould (1879–1944)