Kant's Groundwork for the Metaphysics of Morals ‘is the single most written about work in modern moral philosophy’ (3). This truth invites two related questions: Why has Kant's short treatise received so much attention? And: Is yet another commentary worthwhile? The answer to the first is that Kant's Groundwork is on a topic and of a quality that merits sustained attention, but also that Kant left enough unclear or unsaid that interpretation and elaboration are needed. Whether another commentary is worthwhile depends on whether the interpretation and elaboration it offers advances our understanding of Kant's argument beyond that already provided by other commentators. Allison's commentary succeeds by this standard.

In the introduction Allison identifies the main questions that a commentary on the Groundwork should answer. Primary among these are two questions about section II of the Groundwork. First, what is the point of section II of the Groundwork? Kant articulates the categorical imperative already in section I of the Groundwork and restates it early in section II (at 4: 421), which leaves us wondering why Kant needs the rest of section II. The second question is related to the first. Kant presents many versions of the categorical imperative – most prominently the formulas of universal law (FUL), of law of nature (FLN), of humanity (FH), and of autonomy (FA). But Kant also says that there can ‘only be a single categorical imperative’ (4: 421) and states it as the FUL. Yet, he also says that the FH is the ‘supreme practical principle with respect to the human will’ (4: 429), and section II concludes that autonomy is the supreme principle of morality. These and like passages leave readers with some serious conundrums concerning the supreme principle of morality: What is the supreme principle of morality? Is it stated by any or all of the formulations of the categorical imperative? How are the different formulas related? And in what sense, if any, are the different formulas of the categorical imperative equivalent, as it seems they must be, if there is only one categorical imperative?

In part I (chapters 1–2) Allison discusses the context, aims, methods and structure of the Groundwork. In chapter 1 Allison shows how Kant wrote the Groundwork partly from a growing dissatisfaction with the argument for the postulates of the Canon of the first Critique and partly to show the inadequacy of Wolffian rationalism and the popular philosophy of the Berlin Enlightenment. In chapter 2 Allison details how we can understand Kant's Groundwork as an engagement with, and rejection of, on one hand, the universal practical philosophy of Wolff, Baumgarten and Meier, and, on the other, the popular moral philosophy of Garve.

In part II (chapters 3–5) Allison deals with section I of the Groundwork. In chapter 3 Allison argues that the good will consists in having a character ‘that is firmly committed to morally good principles. … to regard the obligatory nature of an act as a sufficient reason to perform it’ (79). Actions from duty have moral worth and, since it is impossible to act from duty without a good will, ‘no volitions of an agent without a good will could have such worth’ (87).

In chapter 4 Allison builds on his analysis of the good will to discuss Kant's notion of maxims and to reply to Schiller's objection that Kantian morality has no place for human sentiments. Allison argues that we need the incorporation thesis to make sense of Kant's theory of action, so that, contra Schiller, sentiments matter, though they determine action only as parts of maxims.

In chapter 5 Allison first argues that the implicit first proposition of Kant's analysis of the good will is that ‘a good will under human conditions is one whose maxims have moral content’, by which we should understand ‘one for which the dutifulness of a course of action is contained in (incorporated into) its maxim as a condition of its adoption’ (125). Next, Allison shows how the charge that there is a gap in Kant's derivation of the categorical imperative from the analysis of the good will relies on a misreading: Kant's inference is not from a vacuous to a substantive prescriptive principle, but rather from an analysis of the principle of a good will under human conditions to the substantive prescriptive principle.

In part III (chapters 6–9) Allison deals with section II of the Groundwork. In chapter 6 Allison articulates the two main questions about section II of the Groundwork concerning why it is there and how the different formulas of the categorical imperative are related. To the first question Allison answers that Kant's argument needs the transition from popular philosophy to the metaphysics of morals, because it is only by grounding the categorical imperative in the concept of rational nature that Kant can complete its construction and establish its absolute necessity (150–1). The answer to the second question is that ‘the various formulas express different stages in the complete construction of [the] concept of the categorical imperative and that these stages correspond to stages in a progressive analysis of the concept of a finite rational agent’ (150–1). Chapters 7–9 unfold and defend these theses.

In chapter 7 Allison deals with the FUL and FLN. Allison suggests that most of the problems of false positives and false negatives disappear once we understand the nature of maxims. Yet, one set of problems of false positives remains, namely, those that Herman calls ‘maxims of murder and mayhem’ that issue in seemingly impermissible natural actions (193). For example, the maxim to ‘kill babies whose crying at night prevents sound sleep’ creates no logical or practical contradiction when universalized (193). To solve this problem, Allison introduces a distinction between two types of universalizability: intra- and inter-subjective universalizability. Intra-subjective universalizability is required by the FUL/FLN and ‘concerns the compatibility of an agent's maxim with the same maxim considered as universal law’ (196). The requirement of inter-subjective universalizability, by contrast, is stated by FH and FA each of which ‘requires the endorsability of one's maxim by all other rational agents’ (196). Inter-subjective universalizability implies intra-subjective universalizability, but not vice versa. This asymmetry presents the solution to the false positives of murder and mayhem: such maxims are impermissible by the standard of inter-subjective universalizability presented by the FA and FH, but not by the standard of intra-subjective universalizability presented by the FUL/FLN. Moreover, this splitting of the universalizability test presents a clue to the role and structure of section II of the Groundwork: ‘the great problem in understanding Kant's derivation or complete construction of the concept of the categorical imperative is to see how (or if) he is able to proceed from the former to the latter conception of universalizability’ (196).

In chapter 8 Allison takes a step towards solving this problem by interpreting Kant's derivation of the FH. On Allison's interpretation, Kant claims that ‘the existence of something that could be regarded as an end in itself is both a necessary and sufficient condition of the possibility of a categorical imperative’ (205). It is sufficient since, if such an end exists, it is the source of unconditional commands. It is necessary since the categorical imperative presupposes that there are reasons for acting valid for all rational agents, and this presupposition implies that there is at least one end in itself. Kant maintains that humanity and only humanity is such an end in itself, but it is unclear what humanity is, why it is an end in itself, and how we get to the FH. Allison argues that humanity is the capacity for moral agency (215). We can assume that it is the only end in itself, since no other candidates are, and since something must be, if the categorical imperative is possible, as it is by assumption at this point in the argument (219). Finally, the FH follows from accepting the subjective necessity of viewing humanity in oneself as an end in itself: ‘if this is how rational nature, whether in oneself or others, rightly regards itself, then this is how it ought to be treated’ (228).

In chapter 9 Allison argues that the FUL/FLN and FH together imply the FA/FRE and then uses this claim to finally answer the two main questions about the role and structure of section II of the Groundwork identified above. I return to this argument below.

Part IV (chapters 10–12) is about section III of the Groundwork. In chapter 10 Allison argues that Kant provides separate deductions for the moral law and the categorical imperative. Allison further argues that the main premise of either deduction is the reciprocity thesis, that ‘transcendental freedom and the moral law reciprocally imply each other’ (293) and discusses how this thesis unites freedom and morality in the idea of autonomy.

In chapter 11 Allison uses a two standpoints interpretation of transcendental idealism to understand Kant's argument for the necessity of presupposing freedom and the circularity that apparently threatens the deduction of the categorical imperative. Allison argues that the activity of practical deliberation assumes the normativity of practical reasons and ‘that every rational agent must, from a first-person point of view, regard itself as free’ (308). Allison then suggests that there is no threat of circularity, but of a petitio principii, and that this petitio is avoided by a two standpoints interpretation.

Finally, in chapter 12, Allison discusses Kant's deduction of the normative validity of the categorical imperative. Allison argues that the reciprocity thesis is insufficient for the purpose, if we adopt a two worlds interpretation of transcendental idealism, since metaphysical supremacy does not entail normative supremacy. The two standpoints interpretation avoids this problem, since it does not rely on a distinction between normatively superior and inferior entities, but instead on a standpoint of agency for which the validity of the categorical imperative is given.

As indicated, Allison at times relies on distinctions and claims that Kant only worked out in later writings such as the incorporation thesis, the reciprocity thesis and the distinction between Wille and Willkür. Though this method carries risks – we may misunderstand Kant if we read an argument in light of a distinction unclear to him at the time he wrote it – it is defensible, if we cannot make sense of the text without these resources, and if they are explicitly and carefully used. I was persuaded by the fruitfulness of Allison's use of this method.

I now return to the questions about the role of section II of the Groundwork and the relation between the different formulations of the categorical imperative. Allison's answer to the first question is that section II provides ‘a complete construction of the concept of the categorical imperative on the basis of a progressive analysis of the concept of a finite rational agent’ (237). This construction results in articulation of the requirement of inter-subjective universalizability in the form of FH and FA. But this answer invites the second set of questions. In what sense are these formulas statements of a single principle? And in what sense, if any, are they equivalent?

The singularity thesis is that there is a single categorical imperative, so that the three formulas are not distinct principles but ‘variant formulations of the single categorical imperative’ (246). According to Allison, the singularity thesis does not require that the formulas are intensionally equivalent, but it does require that they are extensionally equivalent, that is, they must permit and prohibit the same maxims, even if they do so for different reasons. Denying extensional equivalence ‘effectively denies the singularity thesis in any serious sense, such a view should be accepted only as a last resort’ (256). Allison suggests that we can maintain extensional equivalence, if we understand the different formulas as subjectively, but not objectively different, meaning that they differ in ‘the manner in which they bring an idea of reason (presumably the same idea) nearer to intuition and by this means to feeling’ (247).

Alas, it seems that extensional equivalence is inconsistent with the claim that section II of the Groundwork moves from intra- to inter-subjective universalizability. Recall that Kant's solution to the problem of false positives is that these are permitted by the requirement of intra-subjective universalizability stated by the FUL/FLN but are prohibited by the stronger requirement of inter-subjective universalizability stated by the FH and FA. Thus, there are maxims permitted by the FUL/FLN and prohibited by the FH and FA. So, the formulas are not extensionally equivalent.

Allison recognizes this problem: ‘On the one hand, Kant's ethical theory requires the singularity thesis and the latter seems to require at least the extensional equivalence of the formulas; while, on the other hand, Kant's account of the relationship between the formulas makes it difficult to see how this equivalence can be maintained’ (256). Allison suggests that the problem can be solved if we distinguish between first- and second-order formulas. First-order formulas apply directly to maxims, second-order formulas underlie and are expressed by first-order formulas: ‘FLN, FH, and FA/FRE are first-order formulas, which are applied directly to maxims, whereas FUL is a second-order formula or “meta-formula,” which underlies and is expressed by these first-order formulas’ (253–4). The FUL thus has two distinct appearances in the Groundwork: first, as the unconstructed first-order formula that issues from the analysis of duty and, second, as the constructed second-order formula that issues from the full analysis of rational agency.

Allison's solution is unsatisfying. There is slim textual basis for the distinction between first- and second-order formulas or the claim that the FUL appears as both, so the best argument for this interpretation would be that it solves the problem of extensional equivalence and is the best way to make sense of the relation between the categorical imperatives. But, first, the interpretation does not solve the problem of extensional equivalence, and, second, Allison's argument indicates a better way to make sense of the relation between the categorical imperatives.

First, the solution does not solve the problem: it is still the case that the unconstructed FUL/FLN is not extensionally equivalent to FH and FA. Moreover, doubling the levels at which the formulas operate and adding a distinction between first- and second-order FULs exacerbates rather than solves the problem of how the formulas are statements of the same principle: if the FUL is at a different level than the FLN, FH and FA and as such does not apply directly to maxims, then they are not extensionally equivalent. Indeed, in that case the second-order FUL differs from the other formulas not merely by extension, but by domain.

Second, Allison's argument indicates an alternative interpretation of the relation between the categorical imperatives. Allison argues that the complete construction of the categorical imperative appears only once all three aspects (form, matter, complete determination) are at hand. But instead of claiming that the FLN, FH and FA are three statements of the same principle and, therefore, are extensionally equivalent, this argument suggests that each of these formulas identifies a distinct aspect of one and the same principle, namely, the FUL. In that case, the singularity thesis is upheld, since there is only a single categorical imperative: the FUL. But the singularity thesis does not imply that the various formulations are extensionally equivalent. Think of a triangle: the sides of a triangle form a single triangle, but the sides are neither intensionally nor extensionally equivalent. Likewise, the FLN, FH and FA together constitute the single categorical imperative, the FUL, but are not equivalent. The formulas must, of course, be consistent so that no formula requires what another prohibits. But, as Allison's interpretation rightly suggests, it may be that a formula prohibits what another permits, as in the case where the FH and FA prohibit maxims of murder and mayhem permitted by the FLN. There is no problem in such divergence, insofar as a maxim is permissible only if it is permitted by every formula.

In conclusion, I strongly recommend Allison's commentary on Kant's Groundwork to anyone interested in Kant's ethical theory.