3.1 Constitutive components

The topline of the remark is that all maxims have a form and matter. Kant says in a footnote at the end of the first section, ‘A maxim is the subjective principle of willing; the objective principle (i.e. the one that would also subjectively serve all rational beings as the practical principle if reason had complete control over the desiderative faculty) is the practical law’ (G, 4: 400, cf. CPrR 5: 19). Maxims are subjective principles of acting.Footnote ¹⁶ Not all maxims are also objective principles or moral laws. The practical law is the type of principle of volition that can serve as a principle for all rational beings. Since at 4: 436 Kant is stating the supreme principle of morality as the practical law, the context indicates that he is interested in the features of objective principles. As a result, I will consider maxims that are moral laws – i.e. cases in which a person is acting from duty. At this stage, Kant is neither testing maxims nor providing a procedure for testing them. Kant might highlight the form or matter in a diagnosis of faulty subjective principles. Numerous passages indicate that he is interested in the diagnostic project. However, I set merely subjective maxims aside to consider the structure of the moral law as revealed in the first remark.

The first point of the remark suggests a distinction between the law and its form. A moral law holds for everyone. For Kant, if a principle is to be a law, it must have the form of universality. Otherwise, it is not that it is a deficient or ill-formed law, but rather that it is not a law at all.

What does Kant mean by universality? And what is entailed by the claim that law, and the moral law specifically, has a form of universality? I will address these questions in turn. First, in the B Introduction to the first Critique, Kant distinguishes between comparative or empirical universality, which results from inductive generalisation, and what he calls ‘strict universality’. Law has the form of strict universality: ‘no exception at all is allowed to be possible’ (B4). Strict universality indicates a priori judgement (B3-4). Since Kant takes the categorical imperative to be synthetic strictly universal law, we are interested in synthetic a priori judgement. In the discussion following the forms of judgement, Kant says of a universal judgement that the ‘predicate therefore holds of that concept without exception’ (A71/B96). Compare this with a line from the Jäsche Logic: ‘In the universal judgement, the sphere of one concept is wholly enclosed within the sphere of another’ (9: 102). Saying ‘every event has a cause’ is strictly universal because the predicate concept has a cause applies to the concept event without exception; the sphere of the concept event is entirely enclosed within that of the concept caused. Universality concerns the formal relations among the concepts that make up the judgement.

Second, for Kant, strict universality is the form of laws. There are different types of laws for Kant: namely, laws of nature and moral laws. Although Kant is considering theoretical cognition in the B introduction and the Jäsche Logic, the same account holds for practical cognition. Many passages indicate that the form of universality in theoretical and practical judgement is the same form – and there are no passages where Kant distinguishes the form of a natural law from the form of a moral law. Accordingly, I follow Eric Watkins in claiming that there is a generic and univocal concept of law under which both natural laws and moral laws fall. Watkins surveys many passages in support of this reading (Watkins Reference Watkins2019: ch. 1). If this reading is right, Kant’s claim that the principle of morality is a law implies that the principle is universal. If the principle is a law, it must have the form of universality. If both natural laws and moral laws share the same form, there is a question of how they are distinguished. I will address this when I consider the other half of the hylomorphic pair. But at this point, we can recognise that the answer cannot be the form of the principle.

Kant’s examples are meant to illustrate the universality of the moral law. A prohibition on lying is universal in the sense that it applies to all wills. Although the principle might include various components, it is in virtue of its form that the practical principle cannot allow exceptions. Objective principles are universal. Thus, when a liar attempts to make an exception for themselves, moral evaluation need only refer to the principle’s form. The liar knows implicitly or by implication that the prohibition applies to all cases, and thus their own. The result is a conflict between the liar’s subjective principle and the objective principle. When the liar universalises the subjective principle, the principle states that it is permissible to lie in a certain set of cases (e.g. when a person needs a loan they cannot repay). But the cases also fall under the prohibition stated in the objective principle. After all, this is how the liar intends to get away with the lie. Hence, the liar attempts to will two conflicting objective principles.Footnote ¹⁷ The example illustrates that (a) universal form is constitutive of a moral principle and (b) it is in virtue of the form that the principle is objective. Kant makes this argument directly in the second Critique (5: 27–8).

A similar analysis is available for the second point of the remark. There is a distinction between the moral law and its matter. If a moral principle is a type of unity, and the account of unity is hylomorphic, the principle will have matter. Without it, the form is empty. The principle would not be about anything. So what does matter contribute?

As we saw, for Kant, universal judgement can be either theoretical or practical. The form of universality alone is unable to distinguish between laws of morality and laws of nature. Kant indicates this in numerous places. When he does, he also indicates what role the matter of law has. For example, he says in the Lectures on Ethics, ‘Practical philosophy is practical not by form, but by the object, and this object is free acts and free behavior’ (L-Eth Collins, 27: 243). On the practical/theoretical distinction he says:

The claim appears to be that, while the form of universality is shared between the types of laws, and therefore practical and natural laws are distinguished by something besides form, laws also invoke a modal concept, namely, necessity. The type of necessity has the role of setting the type of law. On Kant’s hylomorphic analysis in the Groundwork, we can identify the type of necessity characteristic of a moral law by examining its matter.

What type of matter makes a law moral? What makes the necessity practical? In the passages from the Lectures, Kant mentions free actions. According to the remark, the answer is an end. Kant talks about ends in two senses, both of which appear in the remark (see Guyer (Reference Guyer2005b: 148–9)). An end can be:

1. (1) humanity or rational nature, or

2. (2) the object that a rational being seeks to bring about through (free) action.

Humanity, and human action specifically, is characterised by the capacity for setting ends. An end in the first sense is identified through its capacity for setting ends in the second sense. In short, humans have wills (MM, 6: 387; L-Eth Vigilantius, 27: 671; R, 8: 26). Thus, the end of a moral or practical law implies, or ultimately is, a will.

Further, the remark says that a rational being as an end is the limiting condition on ‘all merely relative and arbitrary ends’. So an end in sense (1) ought to respect the end in sense (2). Kant’s invocation of hylomorphism at 4: 436 suggests that, whatever the end of the moral law, the matter is indeterminate, though determinable, when considered on its own. An end alone cannot constitute a law, regardless of its nature. Recognising the irreplaceable dignity of persons, or even recognising that morality concerns the dignity of persons, is not by itself a principle, moral law, or categorical imperative. It is a manifold without unity.

Where does this leave us? On Kant’s hylomorphic view, the form of universality and the matter of ends are both constitutive features of a moral law. While they can be distinguished in the abstract, any objective principle of acting includes them both. The first remark at 4: 436 does not lay this out in detail, but it does provide an impetus for seeing the thread of hylomorphism that runs through G II. It demonstrates Kant’s underlying interest in the individuality of the moral law. If there is a single supreme principle, it is characteristic of Kant to employ his hylomorphism: the principle results from unifying a manifold, determining a determinable, informing a matter. In the practical context, the form makes the law objective, while the matter sets the type of the law as moral or practical. As I will explore in more detail below, however, there is a limit to how cleanly the two components of the law can be distinguished.

3.2 Formulas

I can develop the account further by considering the vehicles through which Kant identifies the hylomorphic features of the moral law. The references to the formulas in the first remark encourage the reader to see them as steps in the analytic transition to a determination of the principle of morality. Kant is signalling, as he frequently does, the methodological arc of the book. On the analytic method, the formulas and their use in examples identify specific features of the moral law. The first point says that the Formula of Universal Law and the Formula of Law of Nature highlight or make explicit the form. This is not to say that the formulas themselves have universal form (though they do). Rather, the two formulas include the concept of universality (or universal law) in their statements. The Formula of Universal Law says, ‘act only according to that maxim through which you can at the same time will that it become a universal law’ (4: 421).Footnote ¹⁸ The formula might be used in explaining examples of duties, but it is also a formula about the form of the law. From the perspective of the overarching G II argument, the Formula of Universal Law shows that maxims that can be objective principles are universal. When the moral law is eventually identified in the metaphysics of morals, the end of the section’s transition, it will be determined to have this formal feature.

The moral law will also have other features. The next formula along the arc is the Formula of Humanity: ‘So act that you use humanity, in your own person as well as in the person of any other, always at the same time as an end, never merely as a means’ (4: 429). Here Kant states that the matter of the moral law is an end of a particular kind, namely, humanity. Why and how this is the matter is a complex issue that involves autonomy, but it is important first to situate the formula in the G II transition. Making good on the promises in the preface, the identification of the single principle of morality at 4: 436 says that the principle will be a hylomorphic composite. This enables Kant to claim that the principle is represented in multiple formulas, each of which highlights different features of the composite. Given that the first formula highlighted the form of the principle, the next one concerns the matter. The formula includes in its statement the concept of humanity as an end in itself. When the moral law is eventually identified, it will be determined to have this material feature.

The examples provided alongside the two formulas show both hylomorphic features. Although Kant discusses contradictions that result from the universality of laws, concrete examples would be impossible if they did not also include, at least implicitly, some matter or other. By making the matter the ends of rational beings, Kant types the examples as moral. The cases he considers are about self-love and life, need and communication, comfort and natural talents, aid and sympathy (4: 420). Each instance of possible moral law concerns a rational will. All are or indicate the matter of the maxims that Kant is exploring, despite the fact that he is yet to have introduced the formula that highlights the matter. Further evidence is the incorporation of the concepts of maxim and will into the statement of the Formula of Universal Law. The point is more straightforward in the Formula of Humanity because, when he introduces it, he has already made explicit the universality feature of the law. To illustrate:

Although there is a conceptual distinction between the roles of matter and form, the relation also includes their inseparability in any statement of the moral law, including in the formulas. The matter and form are found together in particular cases, even if the formulas are used to highlight one or the other as features of the single moral law. By beginning with the remarks and their place within the Groundwork arc, the reader sees the formulas as steps along a progression that takes place within the section’s broader transition to the determination of the moral law. Kant is gradually making explicit features of the moral law that are implicit in, as he calls it, ‘popular moral philosophy’. Only at the peak of the arc, stated explicitly in the remarks, does the reader see all of the features and how they constitute a single moral principle.

3.3 Separable and inseparable

The issue of inseparability is informative and foregrounds some upshots of my reading. Kant structures the Groundwork argument on the methodological assumption that matter and form can be distinguished in critical philosophy. There is a sense in which he separates the matter and form in the first remark and the argument preceding it. The Formulas of Universal Law and Humanity are discussed one at a time. But it is useful to explain how matter and form can be both separable and inseparable. In the theoretical philosophy, the answer relies on the distinction between the theoretical and transcendental. The practical requires a different distinction. The distinction will help explain why Kant presents the formulas in the order he does and what kind of philosophical illumination he intends the reader to have upon reaching the peak of the Groundwork arc.

Kant is interested in both the applied domain of moral philosophy and the abstract metaphysics that supports it. The distinction occurs frequently in the Groundwork. He gives a straightforward statement early in G II: ‘Pure philosophy of morals (metaphysics) may be distinguished from the applied (viz. applied to human nature)’ (4: 410, cf. MM, 6: 217). Kant is aware of the connection between the two sides of the project.Footnote ¹⁹ If ethics is to have any use, what he uncovers in the speculative or metaphysical side will translate to the other. Echoing ancient traditions, ‘The object of practical philosophy should be praxis’ (L-Eth Collins, 27: 245, cf. 4: 389). Kant occasionally signals the praxis, even in the thick of metaphysics. But his practical project, as he conceives it, has the two distinct sides.

The distinction between the applied and pure sides of ethics enables Kant to use his hylomorphism in metaphysical analysis while retaining the individuality of the moral law. In action, when we are concerned with the application of principles to cases, matter and form are inseparable. In metaphysics, when we are philosophising about the internal relations among the features of the moral law, they are separable. Both sides together comprise the practical project and explain the two superficially inconsistent claims.

The point, however, is deeper than an evasion of inconsistency. The dual interests are not merely mentioned but built into the Groundwork arc. Kant begins and ends with common knowledge and application but progresses through metaphysics in between. The references to subjective practicality and intuition/feeling before the remarks, and his claim about the usefulness of formulas after, are also references to the distinction. At 4: 436, where Kant has fully stepped into the metaphysics of morals, he emphasises the distinctive conceptual roles of matter and form, but he also reminds the reader that the Categorical Imperative is a principle meant to be applied. The fact that the parts of the Groundwork are steps along a progression often makes it difficult to tell on which side Kant is operating. Stating the formula relation requires him to (appear to) pull apart the relevant concepts in the moral law. But understanding the formula relation also means understanding the inseparable combination of the concepts. Kant’s presentation is based on the awareness that sometimes one can only see inseparability, and see it in the right way, after taking the parts one at a time in a particular order. These types of considerations are pertinent to system thinking and in the conception of philosophy as anabasis and katabasis. Kant judges, rightly or wrongly, that he can more effectively aid the reader in identifying the moral law by beginning with universality and then making explicit the concept of a rational being that a practical moral law necessarily assumes. While the method involves distinguishing different aspects of the moral law for the purpose of showing their interdependence, by beginning and ending in practical application, Kant intends not to lose sight of the fact that even the most metaphysical treatment of morals aims at human action.

I can extend the point by considering the formulas again. Until now I have been mainly focusing on the Formulas of Universal Law and Humanity as representations of the moral law. The G II argument is carried out through the sequenced introduction of formulas, each of which highlights a particular constitutive feature and concept. But the issue is less about how the formulas relate to each other and more about how they relate to the Categorical Imperative. This point is already a significant contribution to the formula relation. It shifts the focus away from the formulas and towards the conceptual composition of the single moral law. However, I should not be interpreted as diminishing the importance of the formulas. They are not a ladder to be thrown away. In the Groundwork, the pure/applied distinction is closely related to the formula/concept distinction. The formulas can be seen in two respects, corresponding to the two sides of Kant’s practical project. First, as I have been emphasising, they should be read within the context of the Groundwork arc. The discussions of the formulas, and the order in which they are presented, are meant to drive the transition towards the identification of the supreme principle of morality. Speaking loosely, one might say that the formulas are a means to the end of highlighting features of the principle. At 4: 436, Kant reveals that the relation among the formulas themselves is, in one respect, less significant than the hylomorphic relation they express between universality and ends. This is because the formulas are a mechanism or vehicle for taking the argument further into the metaphysics of morals. The four examples of duties are the remnants of the starting point of the G II transition. The reader feels the intuitive relevance of universality to moral philosophy and is accordingly drawn into Kant’s analysis. With the final formulas later in G II, Kant has fully abstracted away from concrete cases. What is left to show is the result of the combination of the features highlighted by the first two formulas. This is in part why the examples do not appear a third time. Kant has already illustrated that the formulas help to make sense of moral duties. In the metaphysics of morals, he now needs to consider the result of the combination of matter and form. This is not an issue of the application of a formula to cases and cannot be explained by using a new formula to explain duties. In fact, Kant repeatedly reminds the reader that examples have no place in the metaphysical stretch of the arc (e.g. 4: 408, 418, 432).Footnote ²⁰ Matter and form are constitutive features of the law, as seen in the four cases, but their unity is not a separate third thing. It was the object of the preceding hylomorphic analysis.

Second, although the formulas are a means, they are not merely a means. Kant is still engaged in a practical project that includes a concrete applied side. It is difficult to read the Groundwork without the distinct impression that Kant believes the formulas to be useful in our lives. As he says, they can be regarded as a compass, helping us navigate what is good and evil (4: 403–4). Immediately after the two remarks, Kant gives the so-called ‘universal formula’:

Kant is promptly returning to praxis. He is aware that the formulas serve a second function. As metaphysics, the formulas are a means to the end of identifying or determining the supreme principle. But as applied moral philosophy, the formulas are, so to speak, ends in themselves. At Kant’s behest, we should feel free to use them. At the same time, we must be vigilant not to collapse the two sides of his project. A formula is a single representation of the moral law that, when read as a piece of practical advice, masks internal structural complexity. And it masks complexity in a strategic way when placed within the context of the G II transition to metaphysics. This role of the formula can be forgotten when we are seeking a principle that assists us in a concrete case of moral judgement. But at 4: 436, the role becomes Kant’s central focus.

According to Kant, the two points about the role of the formulas are complementary. The usefulness of the Formulas of Universal Law or Humanity in daily life is owed to the success of the broader G II argument. At the applied level, the formulas are not meant to be used in a vacuum, divorced from the general understanding of the moral law that Kant believes we all possess. And the application of the formulas to examples (as follows the first two formulas) is meant to illustrate that Kant is highlighting genuine features of the moral law. My view is also consistent with the possibility (which Kant hints at in places) that certain situations might lend themselves more to one formula than another, or that people might differ with respect to the formula they find most helpful.

3.4 Controversies

To emphasise how my reading and approach can contribute to resolving significant controversies regarding the formulas of the categorical imperative and their relation, I will briefly discuss several examples. However, I wish to note that, because my primary contribution is that a new perspective on the formulas and Groundwork II argument shifts our interpretative priorities, expending more effort on the controversies as they are conventionally framed works against my aim.

First, a strength of my reading is that distinguishing the pure and applied functions of the formulas provides a blueprint for those who wish to defend Kant from objections. For instance, it is tempting and common to take the formulas as complete metaphysical statements of the moral law. We might then compare how they apply to cases and use inconsistencies to dispute Kant’s metaphysical account. There is a sense in which the formulas are full representations of the moral law, but this risks ignoring how the pure/applied distinction should shape one’s reading of the formulas. From the perspective of the metaphysical argument running through G II, the formulas have specific roles that culminate in determination of the moral law. This is separate from their use in cases of moral judgement. However, although the pure/applied distinction is crucial for understanding the Groundwork, it is also important to appreciate that Kant is often operating on both sides simultaneously. One and the same sentence, especially in G II, can have significance for both sides. Readers cannot hope to make sense of one side without making sense of the other. Excising the formulas without knowing what they are being excised from makes the project of using them in concrete cases less likely to be instructive. The formulas are indeed meant to be foregrounded, but there is a reason Kant does not hand them to the reader in a list. They are embedded in an argument, and not an argument for the formulas. When the metaphysical account is in place, we can return to the formulas as practical guides. They acquire their usefulness and reliability in virtue of the fact that they represent the moral law. We only fully discover this upon reaching the peak of the Groundwork arc, the conclusion of the transition through various formulas, where Kant explicitly identifies the moral law for the first time in its full complexity. From the higher vantage point, we can look back at the formulas with a more sophisticated understanding of their role.

There is a parallel here to other traditions, like early Stoicism, that conceive of philosophy as an interdependent relation between theory and moral exercise. Stoics produce some logical, physical, and ethical theory, but they also provide the student with a range of instructions and directives for making it through challenging life situations. Ultimately, the student of Stoicism recognises that (a) the theory explains why the directives are what they are and why they are effective and (b) that the experience one has in a moral exercise supplies a type of confirmation of the claims made in the theory. I am not claiming that Kant has the same conception of philosophy as the Stoics, but I believe the parallel is instructive for thinking about how he balances the different aspects of his project.

Second, there is debate about the universal formula. Should it be read as (1) the Formula of Universal Law, (2) another known formula, or (3) a brand new formula? Timmermann takes the first option (Timmermann Reference Timmermann2007: 112). Wood takes the second (Wood Reference Wood1999: 188), arguing that it is the Formula of Autonomy (though he is less confident in (Wood Reference Wood2017)). Allison takes the third (Allison Reference Allison2011: 251–4). My reading suggests that the debate is misconceived. The placement of the universal formula directly following Kant’s identification of the Categorical Imperative indicates that the formulas have, in one respect, fulfilled their purpose. The subsequent formulas now come more explicitly to include features from previous formulas. The universal formula is a harbinger of something ubiquitous in the synthetic portion of the Groundwork and in other of Kant’s practical works: formulas that resemble but differ from those that precede 4: 436. After 4: 436, Kant is free to state formulas differently because they are not steps in the analytic G II argument. He can be less tied to the previous formulas because he takes the G II argument to be finished. Within the Groundwork itself, the formulas in the analytic portion are found in a different context from those in the synthetic portion.

Finally, there is a long tradition of reading Kant as deriving moral duties immediately after introducing the Formulas of Universal Law and Humanity.Footnote ²¹ The debate comes to concern the mechanics of universalisation tests and decision procedures. I believe this makes the Groundwork far less interesting and rich than it is or could be. My reading provides two distinctions. First, there is a difference between a derivation of duties and an exploration of how a formula elucidates a genuine feature of the moral law. With respect to the progression of formulas and argument in G II, Kant is primarily doing the latter. The concrete cases are features of the popular moral philosophy that Kant analyses to identify the principle of morality in the metaphysics of morals. When the reader sees that the formulas make sense of intuitive cases, together highlight constitutive components of the moral law, and, due to the relation among the components, represent one moral law, much of Kant’s stated aim is accomplished. And that aim does not include deriving duties from formulas. The second distinction, as mentioned above, is between deriving duties and using the formulas as a compass. As I argued, although Kant has metaphysical ambitions in G II, the formulas can also be used as decision procedures in real cases. But in the context of the Groundwork arc, there is less expectation that they will always deliver simple and straightforward conclusions. They guide us best when we understand their role in identifying the single supreme moral principle.

4.1 Autonomy

The relation between the form of universality and rational nature has implications for autonomy. On my view, the hylomorphic inseparability of the matter and form of the moral law is a description of autonomy, the concept highlighted in the Formula of Autonomy. That is, to have a rational nature is to will universal laws. The act of willing universal laws brings with it the will’s standing as an entity with unconditional worth. To will universal laws is to be an end in itself, and vice versa. The combination is autonomy. The autonomous will is hylomorphic. It gives laws to itself in the sense that, in its capacity for legislating laws with universal form, it is the matter of moral law. This is a meaning of Kant’s claim that the first two formulas combine in the third.

And how does Kant conceive of a plurality of autonomous wills? The Formula of the Kingdom of Ends shows that Kant is interested in a system of wills. In the remarks, he uses complete determination to explain the system. On my view, system is crucial for understanding what the Categorical Imperative is.

4.2 Complete determination

In the section of the Critique of Pure Reason titled ‘On the Transcendental Ideal’, found early in the Ideal of Pure Reason, Kant talks about the ‘principle of determinability’ and the ‘principle of thoroughgoing determination’. The principle of determinability says that, with respect to what is not analytically contained in a concept, ‘of every two contradictorily opposed predicates only one can apply to it’; the principle of thoroughgoing determination (durchgängigen Bestimmung) says, ‘among all possible predicates of things, insofar as they are compared with their opposites, one must apply to it’ (A571-2/B599-600).Footnote ²² The principles serve the role of individuation: the difference between a single entity and all that falls under a concept is that the former is thoroughgoingly determined. For a single entity, of all possible contradictory pairs of predicates, one in each pair applies. For example, the particular plant on my desk is determined with respect to the two predicates ‘green’ or ‘not green’. It is green. However, not all plants are green. As a result, the concept plant is not thoroughgoingly determined: it is not the case that for all contradictory pairs of predicates, one of the predicates in the pair belongs to the concept. The predicate green does not belong to all plants – and neither does not green. But when, for some entity, one of each pair of contradictory predicates belongs, the entity is an individual.

With the two principles, Kant is distinguishing concepts and things. Concepts can apply to numerous things because their extensions are indeterminate with respect to some predicate pairs. Things, however, are not general but thoroughgoingly determined. Kant uses the above principles to introduce the idea of the totality of reality (omnitudo realitatis) – a transcendental substratum consisting of all possible affirmation (A575/B603). The omnitudo realitatis is an idea, in his technical sense of the term, which leads Kant to describe the ideal he calls the ens realissimum: ‘the concept of an individual being, because of all possible opposed predicates, one, namely that which belongs absolutely to being, is encountered in its determination’ (A576/B604). This most real being is what he calls the ‘transcendental ideal’.

Kant takes the Kingdom of Ends to be completely determined, and it is completely determined with respect to all possible maxims or moral laws. This picture raises a number of questions. For example, is there any role for an omnitudo realitatis or transcendental ideal in practical philosophy? On my view, reading the remark in light of the theories of reason and system from the first Critique’s Dialectic unites hylomorphism and individuation into the view that, for Kant, the moral law is necessarily systematic. The ultimate form of universal law is system. The single moral law Kant is seeking is a systematic whole. Further, there is a practical parallel to ens realissimum that provides all positive content of the moral law. That is, I believe that debates about moral knowledge that is presupposed in the Categorical Imperative can be resolved here. Kant’s reference to the categories of quantity at the end of the 4: 436 remark further emphasises the crucial foundational role of the ideal of the kingdom of ends.

4.3 Categories of quantity

Kant uses the categories of quantity to describe the relation among the formulas of the Categorical Imperative as a ‘progression’, language that does not appear in the first remark. The key is in understanding how the categories hang together as a class. Kant briefly considers the topic in a passage that follows the first Critique’s Metaphysical Deduction.Footnote ²³ There are three categories in each class, and ‘the third category always arises from the combination of the first two in its class [die dritte Kategorie allenthalben aus der Verbindung der zweiten mit der ersten ihrer Classe entspringt]’ (B110, cf. P, 4: 325n.). This supplies a further look into how the combination relation works. Kant’s position appears to be that the relation among the formulas of the Categorical Imperative, or the concepts they highlight, is the same, or has the same structure, as the relation among the three categories in a class. And the categories of quantity specifically apply to or describe the progression of the formulas. Accordingly, the second remark provides two insights into the relation among the formulas.

First and more generally, Kant describes the internal structure of a class of categories as involving the combination of the first two. This point is familiar. Yet, when Kant discusses the relations among the categories in the first Critique and elsewhere, he gives the third category some type of foundational or grounding role. When plurality is considered as a unity, the category of totality arises. However, there would be no unity and plurality could not be combined without the totality. A part of the discovery of the third category is the further discovery that the third category, in some respect, underlies or makes possible the first two. These relations are a theme of the Transcendental Dialectic in the first Critique.

After mentioning a combination relation among categories, Kant attempts to forestall an objection or confusion. He says, ‘But one should not think that the third category is therefore a merely derivative one and not an ancestral concept of pure understanding. For the combination of the first and second in order to bring forth the third concept requires a special act of the understanding, which is not identical with that act performed in the first and second’ (B111; cf. L-Met Vigilantius, 29: 988, Corr, 10: 366–7). The two sentences present a contrast. He first says that the category relation does not make totality merely derivative (bloß abgeleiteter). The tone of the comment is that there are no second-class categories. Kant seems initially to affirm a category egalitarianism: there is no priority or hierarchy among the categories; all are ancestral concepts equally and to the same degree. In saying that the third category is not merely derivative, Kant only means that it is not a predicable, a pure concept that owes all of its content to categories (A82/B108, L-Met Vigilantius, 29: 984, 988). The third category in a class will have new content not found in the other two.Footnote ²⁴ This poses the question of whether and how derivation has a part in the category relation.

In the contrasting second sentence, Kant says that, despite the egalitarianism, there is something distinctive about the third category. Its discovery requires ‘einen besonderen Actus des Verstandes’. Kant’s reference to a special act of the understanding is vital to the category relation. Yet he says little about the act and how it is special. After mentioning it, he supplies examples. With respect to quantity, he says, ‘the concept of a number (which belongs to the category of allness) is not always possible wherever the concepts of multiplicity and of unity are (e.g. in the representation of the infinite)’ (B111). (Earlier in the paragraph, Kant indicates that he uses ‘totality’ and ‘allness’ interchangeably (B111, see also A322/B379).) The general point seems to be that the simple conjunction of the concepts plurality and unity is not enough to yield totality. This is because there are cases in which unity and plurality are applicable but totality is not. The special act combines the two concepts in a special way.

The special act of the understanding and internal relation among categories are little understood. Yet the same mereological or compositional relation, however it should be characterised, is meant to hold in the practical philosophy. Considering humans as rational natures willing universal laws leads to the idea of a whole community – a totality called a Kingdom of Ends. Yet, as with the categories of quantity, the willing takes place within the context of the totality of moral law. The kingdom of ends underlies or makes possible an act of willing universal law, just as the totality makes possible the combination of unity and plurality. A particular moral law must fit within a systematic totality of moral law. The second remark can be seen as substantiation and, to an extent, expansion of the formula relation.

In light of the second remark, Kant’s prior comment about the combination of formulas opens up into a more sophisticated picture. The combination relation is only one feature of the complex structure of the Categorical Imperative. The categories are all ancestral or root concepts (B111). The third is not derived from the first two through their combination (at least, not in the sense in which predicables are derived). So the progression is not one of standard logical inference. On my view, the same is true of the progression through the formulas of the Categorical Imperative. As I stated above, the main argument in G II is not an argument for formulas or the concepts they highlight. Instead, the formulas can be regarded as clues. The goal is the identification of the supreme principle of morality represented by the formulas.

Second, Kant specifically uses the categories of quantity in the remark. And he blends the first remark into the second. He says that there is the ‘the unity of the form of the will (its universality), the plurality of the matter (of objects, i.e. of ends), and the allness or totality of the system of these’. Each point follows the same pattern:

The will has a unity in that it wills only universal law. The laws are about ends. And together, there is a system of ends, completely determined with respect to moral laws.

While autonomy, complete determination, and the role of the categories warrant more attention, in this last section I have highlighted some of the benefits of an interpretative hypothesis that emphasises the 4: 436 remarks and their place within the Groundwork arc. With my method, the task of understanding 4: 436 is the same as answering a classic question of Kant scholarship: what is the relation among the formulas of the Categorical Imperative? A full answer requires an exploration of many features of Kant’s philosophy, but I hope to have shown that the first steps take us in a promising direction.