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Are Kant's Several Formulas of the Categorical Imperative Truly Equivalent?

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Kant claimed that his different formulas of the categorical imperative, including the Formula of Universal Law and the Formula of Humanity, were all equivalent, but never explained in what sense. The Stanford Encyclopedia of Philosophy's Kant's Moral Philosophy entry surveys competing readings of that equivalence claim, meaning equivalent, logically interderivable, or equivalent only in the duties each formula generates, without settling on one.

What would resolve this A textual argument accepted across Kant scholarship showing precisely how one formula yields the others, or a demonstration that Kant's equivalence claim fails in every proposed sense, would resolve which reading is correct.
OpenKant scholarship (moral philosophy)Stanford Encyclopedia of Philosophy
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Source Stanford Encyclopedia of Philosophy
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Stanford Encyclopedia of Philosophy
Stanford University, Center for the Study of Language and InformationStanford Encyclopedia of Philosophy, Kant's Moral Philosophy, section 9 The Unity of the FormulasView the Source
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