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Perhaps, then, if the formulas are not equivalent in meaning, they are nevertheless logically interderivable and hence equivalent in this sense. The universal law formula is not itself derived, as some of Kant’s interpreters have suggested, from the principle of non- contradiction. That would have the consequence that the CI is a logical truth, and Kant insists that it is not or at least that it is not analytic. Since the CI formulas are not logical truths, then, it is possible that they could be logically interderivable. However, despite his claim that each contains the others within it, what we find in the Groundwork seems best interpreted as a derivation of each successive formula from the immediately preceding formula. There are, nonetheless, a few places in which it seems that Kant is trying to work in the opposite direction. One is found in his discussion of the Humanity
Formula. There Kant says that only something “whose existence in itself had an absolute worth” could be the ground of a categorically binding law (G 4:428). He then boldly proclaims that humanity is this absolutely valuable thing, referring to this as a “postulate” that he will argue for in the final chapter of the Groundwork (G 4:429n). One might take this as expressing Kant’s intention to derive thereby theuniversal law formula from the Humanity Formula: If something is absolutely valuable, then we must act only on maxims that can be universal laws. But (he postulates) humanity is absolutely valuable. Thus, we must act only on maxims that can be universal laws. This (we think) anomolous discussion may well get at some deep sense in which Kant thought the formulations were equivalent. Nonetheless, this derivation of the universal law formulation from the Humanity Formulation seems to require a substantive, synthetic claim, namely, that humanity is indeed absolutely valuable. And if it does require this, then, contrary to Kant’s own insistence, the argumentof Groundwork II does not appear to be merely an analytic argument meant simply to establish the content of the moral law. The most straightforward interpretation of the claim that the formulas are equivalent is as the claim that following or applying each formula would generate all and only the same duties (Allison 2011). This seems to be supported by the fact that Kant used the same examples throughthe Law of Nature Formula and the Humanity Formula. Thus, the Universal Law Formulation generates a duty to φ if and only if the Humanity Formula generates a duty to φ,
(and so on for the other formulations). In other words, respect for humanity as an end in itself could never lead you to act on maxims that would generate a contradiction when universalized, and vice versa. This way of understanding Kant’s claim also fits with his statement that there is no “objective practical difference” between the formulations although there are “subjective” differences. The subjective differences between formulas are presumably differences that appeal in different ways to various conceptions of what morality demands of us. But this difference in