In logic, a theory introduced by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910–13) to deal with logical paradoxes arising from the unrestricted use of propositional functions as variables. The type of a propositional function is determined by the number and type of its arguments (the distinct variables it contains). By not allowing propositional functions to be applied to arguments of equal or higher type, contradictions within the system are avoided.

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