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axiom of reducibility

Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


L ogic, philosophy of mathematics Russell 's ramified theory of types imposes too many restrictions upon mathematics, with the result that substantial mathematical theorems cannot be formulated and proved. To save them, Russell introduces the axiom of reducibility, which sorts propositional functions into levels and claims that for every propositional function of a higher order there exists a corresponding function of the first order which is extensionally equivalent to it. This axiom meets many difficulties, but Russell himself does not take it as a self-evident truth of logic. “The axioms of reducibility, … could perfectly well be stated as a hypothesis whenever it is used, instead of being assumed to be actually true.” Russell, Introduction to Mathematical Philosophy ... log in or subscribe to read full text

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