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A new book on Kant's theory of practical knowledge by Stephen Engstrom begins with a reference to a ‘slide’ in Kant's derivation of the universalizability formula of his categorical imperative as it appears in the Groundwork of the Metaphysics of Morals (Engstrom Reference Engstrom2009: 5). Since the universalizability formula is here considered a formula of a requirement of practical reason of a maxim, it will henceforth be abbreviated as ‘UR’.

In this respect, Engstrom's book continues a line of criticism begun by Bruce Aune in his book on Kant's moral theory (Aune Reference Aune1979: 28ff.), subsequently pursued by Allen W. Wood in his book on Hegel's ethical thought (Wood Reference Wood1992: 121–2; cited by Engstrom Reference Engstrom2009: 5) and in his first book on Kant's ethical thought (Wood Reference Wood1999: 81ff), and, for our purposes, concluding with Henry E. Allison's treatment of the presumed omission (Allison Reference Allison1996: 143–54; cited by Engstrom Reference Engstrom2009: 5).

The criticism of all four can be stated as follows. From the incontrovertible proposition that practical reason requires of a maxim that it conform to a universal law (henceforth abbreviated as ‘CR’),

and therefore conform to a universal law in general, Kant derives the stronger proposition that practical reason requires of a maxim that it can be willed as a law for all rational beings, that is, UR. That is, Kant derives UR from grounds that support only CR. Wood in particular has claimed that CR ought to be supplemented with the autonomy and humanity formulas of the categorical imperative for UR to be derived validly (Wood Reference Wood1999: 81ff). He has illustrated the weakness of CR with the counter-example of a rational egoist who could agree to CR but refuse to agree to UR, thus invalidating Kant's derivation of the requirement. The counter-example was subsequently cited by both Allison (Reference Allison1996: 144) and Engstrom (Reference Engstrom2009: 6).

Whereas Aune, Allison, and Wood declare the argument invalid as it stands, with Allison's attempting to make up for it with additional premises, drawn specifically from Kant's Critique of Practical Reason as developed in his interpretation of Kant's theory of freedom and Wood's relying on the second and third formulations of the categorical imperative, Engstrom uses what he terms as a ‘slide’ to launch his new book on Kant's theory of practical knowledge. There Engstrom claims to provide an understanding of Kant's theory that makes the derivation of UR defensible in terms of Kant's understanding of the notion of practical reason.

The two main theses of this paper are, first, that such a ‘slide’ in the Groundwork, as Engstrom characterizes the movement of Kant's thought, or a ‘gap’, as first Aune and then Allison put it, or as simply a ‘fallacy’, as Wood describes it, is illusory, and second, that the illusion is due to a failure to see how UR is actually a valid conclusion from Kant's analysis of his concept of a categorical imperative that precedes the requirement. The discussion of the analysis that follows is intended to dispel the illusion. It will be argued that once the illusion is removed, the derivation of UR can be seen as a completed valid argument, without the need of any additional substantive premise to make its validity explicit, such as are offered by Engstrom, Allison and Wood, but nonetheless acknowledging and allowing two presumably unexceptionable principles of inference as necessary to the derivation.Footnote 2 As for Aune's, Wood's, and Allison's declaration that the argument is invalid as it stands, the discussion of Kant's analysis that removes the illusion of invalidity serves as a rebuttal of their view.

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Our four critics’ objection to Kant's derivation of UR actually amounts to a defence of the requirement against a traditional criticism of it begun by Hegel. This tradition has faulted the requirement as being useless in identifying moral maxims. The requirement is said to be so insubstantial that any maxim can qualify as moral. By pushing back the charge of insubstantiality from UR onto its derivation, and in particular, onto CR, our four critics indirectly confer on UR the very substantiality that both creates the omission they claim to find in its derivation and rebuts the traditional criticism that UR is too insubstantial to identify moral maxims.

Thomas E. Hill, Jr. has staked out a position that falls between that of our four critics and Hegel (Hill Reference Hill1993: 121–2). Hill agrees with our critics that the derivation is faulty, but he also argues, now apparently in disagreement with them and in accord with Hegel, that UR can be read as a valid conclusion from CR, which would make UR, also, too insubstantial to identify moral maxims, and hence, for Hill, determine conduct. Hill maintains, however, that Kant ‘thought’ that UR actually contains the substantiality in question (Hill Reference Hill1993: 121–2). Hence, UR can also be given the stronger reading. So Hill criticizes UR on two grounds: it allows, confusingly, both a stronger and a weaker reading and the stronger does not follow from the grounds offered in its support. Since this paper addresses the arguments of our four critics, it also addresses Hill's second criticism. But since we are not here dealing with the question of whether UR is actually substantial or not, and Hill seems more concerned with that issue, our attention will remain focused on just the four critics and only on Hill to the extent that he agrees with them on that issue.

Finally, the paper will only note the difference between the traditional criticism and the more recent one concerning the appearance of an omission in the derivation of UR, and it will do so without commenting further on the difference. Nonetheless, given the thesis that UR does indeed follow from CR, the paper must hold that CR is just as substantial as UR, whatever degree of substantiality that may be. In any case, the paper will side with our critics in their dispute with the traditional criticism regarding the substantiality of UR in order to stay focused on our critics’ claim that there is an omission in Kant's derivation of UR. But, again, this is done only for the sake of argument; the paper does not present its own case for the substantiality of UR.

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In his analysis of his concept of a categorical imperative in the Groundwork (420) Kant first states that every such imperative contains a law, that is, a necessary rule that holds unconditionally, that is, without the necessity's being relative to a condition that determines the rule, as is the case of the necessity that belongs to a hypothetical imperative (420–1). In the discussion that precedes the derivation of the imperative, Kant ascribes this property of unconditionality to a law (420). For example, the law requiring honesty is contained in a categorical imperative that acts as a constraint on one's will to indulge one's inclination to be dishonest, but that unlike a hypothetical imperative, it does not require honesty because, say, being dishonest eventually hurts one's business. Second, a categorical imperative requires of a maxim the necessity that it conform to the law that is contained in the imperative (421). Third, the requirement of unconditionality entails that the maxim conform to the universality of a law in general (überhaupt), since its unconditionality entails that there is no condition that can limit the scope, or extent, of the law (421). Kant then sums up the requirements of a categorical imperative with the statement that ‘this conformity alone [i.e. the conformity to the universality of a law in general] is what the imperative properly represents as necessary’ (421).Footnote 3 Since a maxim that conforms to the universality of a law in general is a law, or since only a law can be such a maxim that conforms to the universality of a law in general, or, again, since only a law conforms to the universality of a law in general, a maxim that conforms to a law is a law. The foregoing answers the question of how a maxim can be a law, and since a law has the property of universality, due to its subordination to a law in general, the foregoing answers the question of how a maxim can be a universal law. Each step advances a maxim from its start as a proposition that contains a law (420), if it itself is a categorical imperative, or, equivalently, if it is a substitution instance of the universalizability formula UR of the categorical imperative,Footnote 4 to the stage at which it is a universal law.

The final question is how a maxim can be willed as a universal law. It seems an apparently uncontroversial, if not analytic, ‘principle of volition’ that one can will what one's will, or practical reason, requires of one's maxim. Henceforth, this principle will be employed as a principle of inference in the derivation of UR and designated as ‘PV’.

Since one's maxim contains the relevant determination of the will, it contains that which practical reason requires of itself as so determined. In clarification, a maxim of the will contains the determination of the will to take the action in question. If it is practical reason that requires the determination, it seems evident that it cannot require of itself anything it cannot will. So, if practical reason requires something of its maxim, it can will what is required. Therefore, according to PV,

For example, if practical reason requires of one's maxim that it conform to the law that one should be honest, one can will that one be honest.

Armed with PV, we can deliver the answer to the question of how a maxim can be willed as a universal law. By the just adopted principle PV, if practical reason requires of a maxim that it conform to a universal law, one can will that it conform to a universal law. Since Kant's analysis of his concept of a categorical imperative shows that if a maxim conforms to a universal law, it is a universal law, it follows that if practical reason requires of one's maxim that it conform to a universal law, one can will that it is a universal law. In other words, since a maxim's conforming to a universal law entails its being a universal law, practical reason's requiring the former of one's maxim entails that one can will the latter. In short, CR entails UR.

The crux of the argument lies within Kant's analysis of his concept of a categorical imperative, and within that, his concept of a law. The crux is Kant's subordination of a particular law to a law in general (überhaupt). First, conformity of a maxim to a law subordinates the former to the latter. Second, since a law is an instance of a law in general, by the transitivity of the relation of subordination, a law in general subordinates a maxim that conforms to a law. Therefore, a maxim that conforms to a law is a law, since, more generally, a rule that is subordinate to a law in general is a law. In other words, the maxim itself becomes a law, for it is now, as subordinate to a law in general, an instance of a law in general. Indeed, this is exactly the result that Allison claims would be necessary, if the derivation of UR were valid (Allison Reference Allison1996: 149). In short, the maxim becomes an instance of a law in general and thus itself becomes a law merely by conforming to the law that is contained in the imperative. Indeed, this law – the one contained in the imperative – can be none other than the maxim itself! Otherwise we get an endless series of ever more general laws that subordinate preceding laws without ever reaching a law in general or the categorical imperative itself, either of which can bring the series to an end, a regress that would be the bane of Kant's theory. To stop the regress in its tracks, Kant needs only the maxim, or the particular law, and the practical law in general, or the categorical imperative, to which the maxim conforms and through its conformation becomes a law.

To summarize the removal of the illusion of an omission in Kant's derivation of the categorical imperative, the apparently uncontroversial PV plus the property of transitivity of the logical relation of subordination – our other principle of inference – have been employed to derive UR from a starting point that Kant's critics agree upon, namely, CR. From this minimal and apparently uncontroversial starting point we have been able to derive UR by employing both PV and the transitivity of subordination of a rule to a law, which, it has been argued, are contained in Kant's own analysis of his concept of a categorical imperative.

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The demonstration of the validity of Kant's derivation of UR would not be complete without a rebuttal of the grounds adduced by his critics for their assertions to the contrary. For the sake of review, Aune's criticism is that UR is too effective in identifying moral maxims to be supported by the actual grounds that Kant provides for it. Whereas Aune claims that UR, which can be used to identify particular maxims as moral, can be distinguished from CR, the latter is said to be useless in that regard, since Kant's grounds supporting UR do not go beyond supporting CR, and hence they fail to support UR. Consequently, for Aune there is a difference in ‘practical import’ between the two requirements, that is, that whereas CR fails to demarcate moral from non-moral maxims, UR does so (Aune Reference Aune1979: 29–30). Since the assertion of such a difference contradicts the dissolution of an apparent omission in the derivation that is the thesis of this paper, it should be dealt with at this point in our discussion.

The entailment in the derivation is indeed quite adequate to dispense with the difference in ‘practical import’ that Aune claims to find between the two requirements. If UR can help to identify moral maxims, then, because of the entailment, so can CR. The failure to see the validity of the inference consists in the failure to sufficiently appreciate the force of the crux of Kant's derivation, namely, PV plus the subordination of a maxim to a universal law in general via the subordination of the maxim to a universal law and the transitivity of subordination, which make the maxim itself a universal law.

The ‘practical import’ objection seems to rely on a subjective phenomenon belonging to critics who follow Aune of finding UR more useful in discriminating among maxims than CR. But though one may be more subjectively useful than the other, the now argued conclusion entails that there is nothing objective about the greater utility of UR, since UR follows from CR, with the aid of PV and the transitivity of subordination.

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Wood's objection that UR must depend on the autonomy and the humanity formulas of the categorical imperative has in effect been rebutted by the argument already presented in section 3. The argument instead consists in Kant's analysis of his concept of a categorical imperative that precedes UR, but which has apparently been neglected or ignored by Wood and our other critics. In brief, our critics have given short shrift to Kant's actual derivation of UR – mistakenly placing the full burden of proof on the requirement that a maxim must be universal. The basic intent of the argument in section 3 is to show that Kant's grounds for UR are much richer and more complex than that.

Wood might reply that since, according to his view of the matter, UR can be derived only from autonomy and humanity, PV must in some way depend on them, if it is to play its assigned role in the derivation of UR.Footnote 5 He might continue that, since the universality of UR cannot of itself be the reason rational beings would will maxims of a certain form, the autonomy formula makes up for the lack with the idea that rational beings are the self-legislators of the moral law and as self-legislators rational beings would will such maxims. Nor, conversely, Wood might go on, does universality of itself tell us why self-legislators must be rational, whereas the humanity formula makes that clear, since, according to humanity, rational beings are the ends that are determined by reason alone.

The response to Wood's supposed defence that PV depends on autonomy is, first, that PV states that the only requirements practical reason can make of itself are requirements it can meet. It would not be rational for reason to make impossible demands of itself. This is what lends PV its air of self-evidence. But there is no reference to law, or the unconditional necessity of a rule, in this statement of PV, as there obviously is in autonomy. Although PV shares with autonomy the abstract logical notion of reflexivity, it does not also share the notion of law, at least not obviously so. It is true that law has already been introduced into the overall argument before it gets to point at which PV is introduced, but that only supports the contention that PV is distinct from autonomy; that is, if PV is doing any actual work in the argument. To suppose otherwise, however, that is, that PV is idle, would be incoherent, since the defence of Wood's view is that PV is playing at least some of the role Wood assigns to autonomy (and humanity).

The response concerning rationality is different. Obviously, PV shares the notion of rationality with humanity. After all, PV is the principle of volition and volition is the will, which is practical reason. But practical reason appears in the two principles – PV and humanity – in different ways. In PV it restricts rules of action to what it can require itself to follow, whereas in humanity it restricts ends of action to beings such as itself, that is, rational beings. The first way does not depend on the second, again, not obviously so, anyhow. Kant argues, of course, that the rules to which reason is restricted by PV must contain the ends of the actions in question in such a way that there is a logical connection between actions and their ends. After all, the rules must be categorical, not hypothetical, imperatives. But that crucial distinction is not part of PV, nor does it appear to be entailed by PV.

Since Wood's rational egoist counter-example is supposed to illustrate his basic objection that Kant's faulty derivation of UR from CR depends on universality alone, it can fare no better than the basic objection itself. The illustration, again, is that someone could be completely rational if she both acknowledges that everyone should obey a universal law (CR) and yet at the same time balks at willing that everyone do so (UR). The rational egoist objection supposes that an egoist could rationally balk at willing for everyone despite the universality that reason requires of her egoistical maxim.

But Wood, and thus Allison and Engstrom in giving Wood's objection a prima facie endorsement, slip up here. For Kant, law entails the unconditional necessity of a rule. However, the rule to which an egoistical maxim would conform would not be unconditionally necessary, because, according to rational egoism itself, it allows that someone – even the rational egoist herself – might act or might have acted in similar circumstances on an altruistic maxim. That is, the very possibility of an altruistic maxim entails that a rationally egoistical maxim would not be unconditionally necessary. Consequently, a maxim that conforms to rational egoism would not conform to a practical law, regardless of how rational the maxim might otherwise be. It therefore does not constitute a valid objection to the derivation of UR, for it is not even an instance of CR.

In addition, one should not be misled by Kant's formulation of UR as requiring of a maxim that it can be willed as a universal law of nature, as if this allows rational egoism to determine a law to which a maxim is to conform, as required by CR. It makes no sense to say of practical reason that it requires of a maxim that the maxim conform to a law of nature, where for the sake of practical reason a law is taken to hold unconditionally with respect to the will, as it is in UR. Practical reason can require of a maxim that it conform to a law of nature only conditionally. If the prior object of one's action is the gratification of one's desire for happiness, a constraint on one's will, in the form of a hypothetical imperative, will of course be affected by one's physical and psychological capacity to achieve the object desired, and thus in that sense CR would entail that a maxim conform to a law of nature. But that is not the sense in which CR belongs to Kant's analysis of a categorical imperative.

In summary, any maxim appearing as a counter-example to Kant's derivation of UR must fail. A maxim that cannot be willed as a universal law cannot conform to a universal law, and since any putative counter-example could not be willed as a universal law, yet ex hypothesi would conform to a universal law, nothing could actually be a counter-example that would demonstrate an omission in Kant's derivation of UR such as is alleged by our five critics of Kant, again including Hill.

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Though this paper has not addressed the traditional question of the effectiveness of the categorical imperative in identifying moral maxims, it has attempted to rebut the objection of the five critics, now including Hill, that the derivation of UR contains an omission introduced into the literature by Aune. With respect to the traditional question just mentioned, it has sided with our four original critics, but only in the form of making an assumption for the sake of argument. The bases of the rebuttal of the objection of the critics have been: Kant's analysis of his concepts of the categorical imperative and of law, the use of PV, and the transitive relation of subordination.

Since the success of the rebuttal partly depends on siding with Beck against Allison on the issue of whether a maxim can be (a case of) a categorical imperative, and since the rebuttal is a consequence of the defence of Kant's derivation of the UR formula of the categorical imperative, our discussion of the validity of the derivation of UR would seem to enhance the philosophical significance of the issue between Beck and Allison. The fact that Beck's interpretation leads to a demonstration of the validity of the Kant's derivation of the imperative – something we have already noted Allison himself acknowledges – seems to be an important point in Beck's favour against Allison.

Finally, the notion of law as the unconditional necessity of a rule, which started the argument in section 3 has for Kant a much wider application than moral theory, of course. It is also essential to his theory of our knowledge of nature. Since it is comprehended in his concept of the a priori, whether it be representation or knowledge, including now knowledge of either nature or morality, neglecting or even minimizing the role of the a priori in Kant's thought in general, say for the purpose of giving greater significance to the role of experience can, from the perspective of our present considerations, only distort his deepest philosophical commitments, whether they pertain to the laws of nature or the laws of freedom, and therefore, the moral law.