1. Introduction
One of the most notorious problems associated with Kant’s account of the categorical imperative in the Groundwork for the Metaphysics of Morals concerns its very core. Although he introduces the Formula of Universal Law (FUL) as articulating the one and only categorical imperative, he nevertheless proceeds to add a series of other formulas. These are known as the Formula of the Law of Nature (FLN), the Formula of Humanity (FH), the Formula of Autonomy (FA), and the Formula of the Realm of Ends (FRE). Kant claims that FLN, FH, and FRE “are at bottom only so many formulas of the self-same law” (GMS 4:436), and that FUL and FH are “at bottom the same [principle]” (GMS 4:438). Because their wording differs significantly and Kant does not clarify their relation in sufficient detail, these claims have long puzzled his readers.
Another question debated extensively in the literature is whether there is a hierarchy among the formulas or whether they all have the same status. Kant claims that FA has an important advantage over FLN and FH (GMS 4:431–432), and that there is a “progression” from FLN, via FH, to FRE (GMS 4:436). Curiously, however, he continues by asserting that for the purpose of moral evaluation it is “better” to use another formula—one that is closer in wording to FUL (GMS 4:436–437). Some authors conclude that Kant’s argument culminates in this other formula, which they call the Universal Formula (UF), or in FRE. Others believe that he is here referring his readers back to FUL as the main formula. Adding to the confusion is the fact that, having earlier formulated FUL and FLN, Kant goes on to call FH “the second” and FA “the third” principle (GMS 4:431). On this basis, many interpreters assume that FUL and FLN are two different versions of the first formula. FA and FRE are likewise often seen as two versions of the same formula, although not everyone agrees that these pairings are warranted.
In the literature, most discussions of the relations among the formulas focus on the extent to which they are equivalent.Footnote 1 Authors examine the extent to which the formulas lead to the same results when they are applied to the same maxims (“extensional” equivalence), as well as the extent to which they express the same principle (often referred to as “intensional” equivalence). Their assessments vary widely, depending not only on which formulas they discuss but also on which specific interpretations of the formulas they favor. As a result, there is by now a wide variety of positions on the issue of the equivalence of the formulas.Footnote 2
Relatedly, there are different views on the issue of whether some formulas are more important or more complete statements of the categorical imperative than others. While most authors regard FUL as the primary formula,Footnote 3 some view FUL as incomplete and take Kant to be building up his account of the categorical imperative via the various other formulas. Henry Allison, for one, argues that FUL is a merely “skeletal, unconstructed formula” that “requires” the other formulas for its application, and that UF is the fully developed formula of the categorical imperative (Allison, Reference Allison2011: 245–260, here 257). Allen Wood goes so far as to claim that “FUL/FLN” is “not a specifically moral or ethical requirement at all” and regards “FA/FRE” as the “complete formula” (Wood, Reference Wood2018: 6, 58). Still other authors either defend a non-hierarchical interpretation, according to which some or all formulas have an equal status,Footnote 4 or attribute fundamentally different roles to the formulas.Footnote 5 In short, consensus on the relations among the formulas seems very far away.
In this article, I aim to shed new light on these issues by exploring, in greater depth than has been done thus far, the philosophical significance of Kant’s comment that FLN, FH, and FRE involve “a certain analogy” (GMS 4:436). I first examine how Kant introduces each of the formulas, with an eye to what this reveals about their relations, before turning to his account of the role of analogy for expounding ideas and principles of reason (Section 2). I then examine Kant’s use of analogy in the formulas, largely drawing on the peculiar brand of republicanism he defended around the time he was writing the Groundwork (Section 3).
The upshot, in very broad strokes, will be as follows. FUL is indeed the main formulation of the categorical imperative. Because FUL is a synthetic a priori principle of pure practical reason, the only way to make it more comprehensible and more engaging is through analogy, and this is the role of the other formulas. This insight makes it possible to solve most—if not all—of the problems mentioned above.
2. Kant’s Introduction of the Formulas and the Role of Analogy
One factor that complicates discussions of the relations among the formulas is the fact that there is no consensus on the meaning of the individual formulas as such. For this reason, I begin this section by examining how Kant introduces each formula and how he describes the relations between them. In this way, I aim to make as much progress as is possible before turning, in Section 3, to the contentious issue of the meaning of the formulas and determining whether they articulate the same moral requirement.
2.a. The Formula of Universal Law and the Formula of the Law of Nature
The FUL is the first formulation of the categorical imperative in Groundwork II. Kant introduces it by explaining that the categorical imperative is a practical synthetic a priori proposition (GMS 4:420)—that is, a law based in pure practical reason. He then uses the concept of a categorical imperative to derive its content, claiming that it can have no other content than demanding that your maxim be in conformity with the universality of a law. He continues:
There is therefore only a single categorical imperative, and it is this:
act only according to that maxim through which you can simultaneously [zugleich] will that it become a universal law. (FUL, GMS 4:421)
Clearly, he introduces FUL as the one and only supreme moral principle. He claims that “all imperatives of duty” can be derived from this principle and thus that it is now possible to show what we mean by moral duty (GMS 4:421).
So why does Kant introduce more formulations? This is not immediately clear. He introduces FLN with merely a sentence, remarking that the existence of things as determined in accordance with universal laws is called nature (in the formal sense), and that, therefore,
the general [allgemeine] imperative of duty could also be expressed as follows:
so act as if the maxim of your action should become by your will a universal law of nature. (FLN, GMS 4:421)
He gives four examples of its application and then claims to have presented the content of the categorical imperative “clearly and determinately for every use” (GMS 4:425).
Kant does not clarify the relation between FUL and FLN here. FLN is often taken to be a somewhat more engaging reformulation of FUL with no significant difference in status or function. If FLN has advantages, however, this raises the question of why Kant would choose FUL for the most prominent formulation of the categorical imperative. Why does he not lead with FLN instead? Moreover, why does Kant, in a later passage, insist that, for the purpose of moral evaluation, we would do better to use not FLN but rather a formula that sounds very much like FUL (GMS 4:436–7)? I propose that the answers to these questions lie in his conception of the role of analogy.
In this later passage, when reflecting on the relation between several formulas—the first of which is FLN—Kant writes that these are different “ways of representing” (Arten… vorzustellen) the principle of morality but “at bottom” different formulas of the same law (GMS 4:436). He writes that they “bring an idea of reason closer to intuition and thereby to feeling (according to a certain analogy),” which can be “very useful” for “obtaining access for the moral law” (GMS 4:436–437).Footnote 6 Presumably, the idea is that FLN and later formulas, by using analogy, present FUL in more familiar and engaging terms. They formulate the moral principle in terms of concrete things with which we are familiar, such as laws of nature, whereas FUL is formulated more abstractly in terms of universal law. In light of this passage, Kant’s introduction of FLN via the formal notion of nature appears to be not a mere rewording of FUL but an introduction of the first analogical way of representing FUL, namely, an analogy with laws of nature.
Kant’s reference to the reformulations as involving “ways of representing” the principle of morality and his claim that they involve analogy provide crucial clues for determining the relation between FUL and FLN and—subsequently—the other formulas. Several other commentators have noted that Kant speaks of analogy in this passage (e.g., Allison, Reference Allison2011: 248–249; Duindam, Reference Duindam2023; Timmermann, Reference Timmermann2007: 110–111), and some have elaborated Kant’s use of analogy in the case of particular formulas (e.g., Kisner, Reference Kisner2019; Timmons, Reference Timmons, van der Rijt and Cureton2022). In order to fully grasp its significance for determining the relation between the formulas, however, we must look more deeply into Kant’s conception of analogy and its philosophical importance.
2.b. The importance of analogy: The relation between FUL and FLN
Analogy, for Kant, plays a crucial role in clarifying and illustrating ideas and principles of reason. Because ideas and principles of reason transcend the world of appearances, it is impossible to give empirical examples. Because they do not involve our sensibility directly, it is also impossible to provide a schema of sensibility. The only possibility, Kant argues in publications both before and after the Groundwork, is to use analogy. As he puts it in Religion within the Boundaries of Mere Reason, “in order to make supersensible characteristics [übersinnliche Beschaffenheiten] comprehensible to us, we always need a certain analogy with natural beings” (RGV 6:65n.). FUL is a supersensible principle, and thus making it more comprehensible requires analogy.
In the Prolegomena, Kant explains analogy as follows:
[Analogy] does not signify, as the word is usually taken, an imperfect similarity between two things, but a perfect similarity between two relations [Verhältnisse] inFootnote 7 wholly dissimilar things. (Prol 4:357)
In Lectures on Metaphysics, Kant gives the example of an analogy between a republic and a human body: in both cases, “all members constitute a whole” (V-Met-L1/Pölitz 28:238). Although a human body is entirely dissimilar to a republic, in each case the relevant relation between their parts is perfectly similar.Footnote 8 In the Critique of Judgment, Kant discusses the example of an analogy between a “monarchy that is ruled in accordance with internal laws of the people” and an organism (KU 5:352). Drawing this analogy does not amount to saying that such a monarchy resembles an organism. Rather, it clarifies the idea of such a monarchy by indicating that the relation among its members is perfectly similar to that among the body parts of an organism. In both cases, the parts and the whole mutually determine each other, and, as Kant also puts it, in both cases, every member is not merely a means but also an end (KU 5:375n., 376).
In the Critique of Judgment, Kant describes analogy in the same terms as in the Groundwork: it is a “way of representing” an idea or principle (Vorstellungsart, KU 5:353) that clarifies how a principle is to be applied or an idea is to be understood (KU 5:351–353; cp. KpV 5:70). In Religion, he similarly writes that we can make an idea of reason more comprehensible “by analogy with something sensible,” and that this “way of representing” (Vorstellungsart) a supersensible idea serves “for clarification” (zur Erläuterung, RGV 6:65n.). The empirical element used in the analogy is called a “symbol” (KU 5:352).
Kant’s technical–philosophical conception of the role of analogy illuminates the role of FLN. He not only explicates that FLN involves analogy but also uses the associated terminology of “ways of representing” (Vorstellungsart, GMS 4:431; Arten … vorzustellen, GMS 4:436) when referring to FLN and the later formulas. Because FUL is a synthetic a priori principle of pure practical reason, it cannot be illustrated or clarified with empirical examples or schemata of sensibility, but only through analogy. Whereas FUL is formulated abstractly in terms of a relation between a maxim and “a universal law,” FLN makes it more concrete by formulating the criterion in terms of empirical laws with which we are familiar, namely laws of nature.
The role of FLN in the Groundwork resembles the role of the law of nature as the “type” of the moral law, as Kant describes it in the Critique of Practical Reason (KpV 5:67–71). There, he explains that the moral law cannot be given a schema for the purpose of its application in concreto, but that a law of nature can (and does) serve as an analogue to aid moral judgment, since everyone has the law of nature “always at hand” (KpV 5:70). Kant does not say that using the analogy is always necessary.Footnote 9 In fact, he adds an important warning: while the analogy with a law of nature is useful and legitimate, one should be careful not to mix any associated empirical elements into moral judgment. The law of nature is “merely a symbol,” and the supersensible moral law should not be brought down to the level of a law of nature (KpV 5:70–71).
The fact that FUL can be made more comprehensible through analogy does not entail, therefore, that FUL is unclear or cannot be applied without it. Indeed, in Groundwork I Kant does not use analogy at all in his discussion of the principle of morality. The principle he formulates resembles FUL, as it requires that one act only on maxims that one can also will to become universal laws:
I ought never to proceed except in such a way that I could also will that my maxim should become a universal law. (GMS 4:402)
Having identified this principle, Kant proceeds immediately to illustrate it, without introducing an analogy. He explains the example of a maxim of false promising by showing that it is impossible to will to act on this maxim while also willing that this maxim become a “universal law” (not: “law of nature”). He claims that common human reason always has this principle—the moral principle—before its eyes when engaging in moral evaluation (GMS 4:402). Notably, the fact that Kant provides an example of the application of the supreme principle of morality in Groundwork I may explain why he does not do so again after introducing FUL in Groundwork II but only after introducing FLN.
In sum, the role of FLN as an analogical representation of FUL explains both why Kant introduces FLN as a way of clarifying FUL and why he nevertheless does not lead with FLN. FUL is the supreme principle of pure practical reason. FLN serves to make it easier to grasp, but it cannot—and should not—replace it.
2.c. The other formulas: FH, FA, and FRE
2.c.1. Formula of humanity
Only at a later stage of his Groundwork II argument does Kant introduce FH. He claims that this formula too is a “way of representing” the principle of morality through analogy (GMS 4:436–437; cp. 431). It is not immediately clear that this description is fitting, however, as the wording does not include an explicit analogy.Footnote 10 Moreover, FH results directly from Kant’s argument to the effect that if there is a categorical imperative, then rational beings must be objective ends. Although there are different reconstructions of the details of this argument in the literature,Footnote 11 it is not necessary to enter the exegetical debate here, as the claim that FH follows from it is not contentious.
FH emerges as a result of the next step in Kant’s Groundwork II argument. Having determined the content of the categorical imperative, he now turns to the “connection” between this imperative and the will of rational beings (GMS 4:426). FUL is a principle of pure practical reason, and Kant argues that if it is possible for pure practical reason to determine the will by itself, then there must be some a priori connection between the two. For if the connection were contingent and depended on subjective ends stemming from human nature, then all imperatives would be hypothetical. Thus, if there is a categorical imperative (an issue Kant postpones until Groundwork III), there must be an objective end that serves as the ground of the will’s determining itself to act morally, and this objective end must be connected with reason a priori (GMS 4:426–428). An objective end is an a priori necessary end for all rational beings as such. It is an “end in itself” and something of “absolute worth.”
Kant then provides an argument to identify the objective end. He considers what he sees as the set of candidates: objects of inclination, the inclinations themselves, things (a category that here includes non-human animals), and rational beings.Footnote 12 He rules out the first three on the grounds that their worth is necessarily conditional and argues that only rational beings qualify as objective ends. Thus, if there is a categorical imperative, rational beings must be ends in themselves. Kant uses the term “humanity” to refer to the rational nature of human beings, which leads him to conclude that if there is a categorical imperative, then humanity must be an end in itself (GMS 4:428–429). Once this conclusion has been reached, he can then use it as the basis for formulating a categorical imperative in terms of humanity as an end in itself, namely FH:
So act that you use the humanity, in your own person as well as in the person of any other, always simultaneously as an end, never merely as a means. (FH, GMS 4:429)Footnote 13
Kant reintroduces the four examples used to illustrate the application of FLN and argues that FH yields the same verdicts. He clearly sees these formulas as extensionally equivalent.
Neither Kant’s discussion leading up to FH nor the wording of the formula itself explicitly includes an analogy. FH does not include phrases such as “acting as if” or “regarding as” to indicate that the formula is an analogical representation. Kant argues not that humanity is analogous to an objective end but that humanity is an objective end (if there is a categorical imperative). This makes it difficult to see why he later includes FH in the line-up of analogical representations (GMS 4:436). In Section 3, I discuss this difficulty in more detail and propose a possible solution.
2.c.2. Formula of autonomy
Immediately after his discussion of FH, Kant introduces FA as “the third practical principle,” adding that it “follows” from the first two (GMS 4:431). It is clear that by “the first two” he here means FLN and FH, as he explains that FA combines the idea of the universality of a law of nature with the idea that each rational being is an end in itself. FA presents an analogy with political legislation and requires that one regard oneself as giving universal law, through one’s maxims, to all rational beings as ends in themselves. Kant offers several versions of FA, including the following:
[A]ct only so that the will could regard itself as simultaneously giving universal law through its maxim. (FA, GMS 4:434)
and
[S]o act as if your maxim were to serve simultaneously as a universal law (of all rational beings). (GMS 4:438)
FA not only combines core elements of FLN and FH but also has the great advantage, Kant writes, of expressing in its very formulation the idea that one ought not to act on maxims based on merely private interests. It does this by requiring that one’s maxim be able simultaneously to serve as a universal law for all rational beings. FA would therefore be “well-fitted to be the categorical imperative,” if there really is one (GMS 4:432).
Neither FA’s advantage over FLN and FH nor the fact that it combines elements of both makes any difference to its application, however. To illustrate the application of FA, Kant refers the reader to the very set of examples he used in the case of FLN (GMS 4:432n.). This indicates that he regards these formulas as extensionally equivalent.
2.c.3. Formula of the realm of ends
FRE is often regarded as a mere rewording of FA, but this is not how Kant introduces it. Rather, he writes that FA “leads to a very fruitful concept attached to it,” namely the “ideal” of a realm of ends (GMS 4:433, emphasis added). This is the ideal of the systematic unity of all rational beings under common laws. An ideal, on Kant’s conception, is a representation of an individual thing that is determined only by a particular idea or principle (KrV A568/B596). Thus, the Stoic sage is the ideal of an individual who fully corresponds to the idea of wisdom (KrV A569/B597). In the present case, the ideal of the realm of ends is the individual entity that fully corresponds to FA. It is the world that would be brought about by the universal application and implementation of FA.
To move from FA to FRE, Kant performs a synthesizing operation. He moves from the principle that each individual rational being should regard itself as simultaneously legislating to all through its maxims to the ideal of all rational beings together united under a system of moral laws they all follow. This ideal is the realm that “would actually come about through maxims the rule of which the categorical imperative prescribes to all rational beings, if they were universally followed” (GMS 4:438, original emphasis). FRE states that one ought to act on maxims that would be suitable for such a realm:
[A]ll maxims from one’s own legislation ought to harmonize [zusammenstimmen] with a possible realm of ends as a realm of nature. (FRE, GMS 4:436)
FRE again involves analogy. The ideal of a realm of ends is developed from FA’s analogy with political legislation, and FRE presents the realm of ends by analogy with the realm of nature (cp. GMS 4:436n.). Kant does not provide a set of examples to illustrate the application of FRE. Given the role of FA in the construction of FRE, however, FRE must of course lead to the same results as FA.
2.d. Kant’s comments on the relation between FLN, FH, and FRE
Having introduced these formulas, Kant then offers a brief but important comparative discussion of FLN, FH, and FRE. This is where we find the curious combination of claims mentioned at the beginning of this essay. He first writes: “The above three ways of representing the principle of morality are, however, at bottom only so many formulas of the self-same law, of which the one unites the other two within itself” (GMS 4:436). He then explains that there is a “progression” from FLN, via FH, to FRE, only to add, in the next sentence, that for the purpose of moral evaluation it is “better” to use another formula, one that resembles FUL. It sounds strange to say that the formulas are all expressions of the same law, that one of them is in some way a fuller expression of this law than the other two, and that it is nevertheless better to use another formula. Further puzzling features of Kant’s comparison of the formulas are the fact that FUL and FA are missing from this line-up and that the difference between the formulas is described as “subjectively rather than objectively practical” (GMS 4:436).
The above account of analogy, however, explains how all these claims go together. Kant is here comparing three ways of representing the principle of morality—that is, three analogical representations of FUL. This explains not only the sense in which they are expressions of the same law—namely, of FUL—but also why FUL is not on the list. The fact that the three formulas are different ways of representing the same objective law, namely FUL, further explains that the differences indeed lie on the side of the subject who represents the law (via analogy) rather than on the side of the objective law. This is the sense in which they are subjectively but not objectively different.
Kant’s remark that “the one” formula unites “the other two” is grammatically ambiguous and could mean either that each formula unites the other two within itself or that only one does so. Only the second possibility makes sense here, however, and “the one” must refer to FRE. FLN emphasizes that maxims ought to have the form of universal law; FH brings out that their matter ought to be limited to what is compatible with the status of all rational beings as ends in themselves.Footnote 14 Neither formula involves a “unification” with another. The only formula Kant explicitly describes as combining two others is FA (GMS 4:431, see above). Although FA is not included in the line-up, FA is used to construct FRE, and his description of FRE in this passage does indeed include elements of FLN and FH (realm of nature, realm of ends). Therefore, “the one” is best read as referring only to FRE.
Kant does not comment on why he leaves FA out of the line-up. Perhaps he considered it present implicitly, as FA is the principle that thoroughly determines the ideal of the realm of ends that is central to FRE. Or perhaps FA fell victim to his desire to describe the progression from FLN, via FH, to FRE as moving from the category of unity (universality of the form of the will), via the category of plurality (of ends), to that of allness (systematic totality).Footnote 15 Since there are only three categories and four analogical formulas, perhaps FA was dropped because it is present in FRE.
Kant’s account of the progression in no way entails that FUL is somehow incomplete or cannot be applied, as some authors have suggested (e.g., Allison, Reference Allison2011; Wood, Reference Wood2018, see above in Section 1). The progression includes only ways of representing FUL; the primacy of FUL, as the main formula, is thus unaffected. Moreover, the fact that Kant provides an example of the application of the supreme principle of morality in Groundwork I both explains why he does not do so in Groundwork II and confirms that he sees no problem in applying the categorical imperative in its main formulation.
This leaves Kant’s puzzling claim, immediately following his account of the “progression” of the formulas, that, for the purpose of moral evaluation, it is nevertheless better to use another formula, which he calls the allgemeine (general, universal) formula (GMS 4:436). What is the nature of this formula?
2.d.1. The general formula
This formula reads as follows:
[A]ct according to the maxim that can make itself simultaneously a universal law. (GMS 4:436–7)
Except for the terminology of “making” rather than “willing” (about which more in Section 3), this principle sounds very much like FUL, which in turn sounds very much like the principle of morality identified in Groundwork I. The above account offers an explanation: this formula is FUL. FUL is the general principle, and the other formulas are ways of representing it. Kant’s cautionary words in the Critique of Practical Reason make it possible to explain why he deems it better to use FUL for the purpose of moral evaluation: this prevents empirical elements associated with the analogy from getting mixed in.
Therefore, allgemeine Formel is best translated as “general formula” and used without capital letters, so as not to suggest that it is yet another formula.Footnote 16 This conclusion matches Kant’s own usage elsewhere: when introducing FLN, he had already referred to FUL as the “general [allgemeine] imperative of duty” (GMS 4:421, quoted above).
The German word allgemein (general, common, universal) is usually translated as “general” in the context of Kant’s political philosophy (e.g., “general law,” “general will”) and as “universal” in the context of his ethics or his moral theory more generally (e.g., “universal law,” “Universal Formula”). The choice of “universal” is understandable in light of Kant’s claim that we should not take moral principles to hold merely generally, in the sense of “for the most part” (GMS 4:424; cp. also MS 6:215–216). Yet the first meaning of allgemein is “general,” and in this case he is not addressing the scope of moral principles. Instead, by allgemeine Formel he is simply referring to FUL as the general formula, as distinct from its various analogical representations.
3. Structural Similarities between the Formulas: Republican Motifs
My aim thus far has been to make as much progress as possible in determining the relations among the formulas without relying on specific interpretations of what they demand. A full account of their relation must also examine the content of the formulas in more detail, however. Kant describes analogy as a perfect similarity between relations in wholly dissimilar things. A full account of the connections between the formulas therefore requires determining the extent to which they do indeed contain a similar relation (or have the same “internal structure,” as I will also call it). To this aim, I first identify the relevant relation internal to FUL.
3.a. Self-contradictions of the will: The roots of FUL in Rousseau’s republicanism
3.a.1. The Formula of Universal Law
On Kant’s conception of it, the term “formula” refers to “a rule whose expression serves as a model [Muster] for application” (V-Lo/Wiener 24:866). A formula expresses a rule in a way that makes it easy to apply, and what makes it easy is that the rule is expressed as a model for application. Kant’s examples include formulas in mathematics and grammar. If you know the formula, you know what you need to do to apply the rule. In the Critique of Practical Reason, Kant indicates that this understanding of “formula” is also the understanding at work in the Groundwork (KpV 5:8n.).Footnote 17 The question then becomes: what is the relevant “model for application” stated by FUL?
Here again is FUL:
Act only in accordance with that maxim through which you can simultaneously will that it become a universal law. (GMS 4:421, original emphasis)
Standardly, this formula is read as saying that you should act only on maxims that you can will to become a universal law. Kant’s inclusion of the word “simultaneously” in FUL is often tacitly ignored or treated as redundant. Authors who do address the role of “simultaneously” understand it to indicate that it should be possible, in the world in which your maxim is a universal law, simultaneously to will to act on the maxim.Footnote 18 Kant’s formulation of FUL, however, places the simultaneity condition prior to the world of the universalized maxim: you should be able simultaneously to will that your maxim become a universal law—not that you should be able, after the maxim has become a universal law, simultaneously to will to act on it.
Elsewhere (Kleingeld, Reference Kleingeld2017, Reference Kleingeld2023), I have argued on textual grounds that FUL instead requires that you be able both (1) to will to act on the maxim and, simultaneously, (2) to will that it become a universal law. If, in moral reflection, a contradiction arises between (hypothetically) willing the maxim as your own maxim of action and willing that it become a universal law, then acting on the maxim is morally impermissible. Because the diagnostic contradiction is a contradiction between two hypothetical volitions entertained in moral reflection, and hence a self-contradiction in the will, I call this reading of FUL the Volitional Self-Contradiction Interpretation.
In the present article, I do not presuppose this reading of FUL. I present an independent argument based on its own textual evidence—one that coheres with but does not assume the Volitional Self-Contradiction Interpretation. Relatedly, I do not argue against alternative readings of FUL and the other formulas, such as the Practical Contradiction Interpretation and the Logical Contradiction Interpretation. If defenders of these or other interpretations believe that the textual evidence is compatible with their reading, then perhaps the account of the relations among the formulas that follows can be adapted in terms of these other interpretations, but I will not pursue this possibility here.
I first show that the relation at the heart of FUL is a relation of agreement between a maxim and that maxim as a universal law. I subsequently use this result to examine whether this relation is perfectly similar to that found in the other formulas, as Kant’s conception of analogy requires. I start by drawing on the origins of FUL in his reception of Rousseau’s republican political theory, for reasons that will become clear.
In the Social Contract, Rousseau distinguishes between the “private will” and the “general will” of the citizen. Qua private individuals, people pursue their private ends, and qua citizens, that is, qua members of the body politic, they pursue the general good of the republic. The two can come into conflict within the citizen, however, in that one’s private will can contradict one’s general will as a citizen. As Rousseau puts it, “Each individual may, as a man, have a particular will contrary to or different from the general will he has as a citizen.” Such a conflict constitutes “injustice” and may lead to the “ruin of the body politic” (Rousseau, Reference Rousseau and Gourevitch1997 [1762], I.7). In the case of such a conflict, citizens ought to bring their private will into harmony with their will as citizens of the republic, rather than giving priority to their private interests.
Although he disagreed with Rousseau on important issues, including the nature of the general will, Kant’s early discussions of the idea of a “self-contradiction of the will” suggest a close connection with Rousseau’s notion of a contradiction, within the will of the self-interested citizen, between his particular will and his general will. In notes from the mid-1760s,Footnote 19 Kant illustrates the relevant self-contradiction with the example of taking another person’s grain. While as a private individual the agent wills to steal the grain, “from a public perspective” he is opposed to theftFootnote 20:
[F]rom a private perspective I will something and from a public perspective I reject the same thing. … The will of human beings would contradict itself if they were to will what, from the standpoint of the common will [ex voluntate communi], they would recoil from.Footnote 21 Moreover, in case of conflict, the common will outweighs one’s own will. (HN 20:161)
In the case of this example, there is a contradiction between two volitions: my private will contradicts what I will from the standpoint of the general or common will. In such cases, Kant adds, I ought to bring my private will into agreement with the general will.
Accordingly, in the same set of early remarks, Kant describes the positive ideal of morally good willing as follows:
This will contains bothFootnote 22 the merely private [blos eigenen] and the general will [den allgemeinen Willen], or the human being considers himself simultaneously [zugleich] in consensu [in agreement] with the general will. (HN 20:145)
In each of these passages, Kant mentions a contradiction or agreement between two volitions, namely between the agent’s particular will and the general will—or, as he also puts it, between what the agent wills from a private perspective and what he wills from a public perspective. As Kant’s inclusion of “simultaneously” indicates, his point is not that agents can endorse different things from different perspectives and switch back and forth. Rather, his point is that in a morally good will, the agent’s private will is in harmony with the general will. In later years, Kant gradually moved in the direction of the Groundwork’s terminology. In the Lectures on Ethics, in a student transcript stemming from the mid-1770s, he formulates the supreme principle of morality in terms of an agreement between the “intention of the action” and “the intention of the action, when made into a universal rule” (V-Mo/Mron, 27:1428). In the Groundwork, he settles on a formulation in terms of the “maxim” and the maxim as a “general/universal law” (allgemeines Gesetz; see the comment above on the different translations of allgemein).
His change in terminology notwithstanding, Kant retains the idea that the good will is characterized by an agreement between the particular and the general/universal, now expressed in terms of the agreement between one’s maxim and that maxim as a universal law. FUL requires that one’s maxim of action be “in conformity” with the universality of a law: “this conformity [Gemäßheit] alone is what the imperative actually represents as necessary” (GMS 4:421).
The model of application at the core of FUL, then, is the conformity of one’s maxim to itself as a universal law. In FUL, Kant explicates this relation in terms of the simultaneous willability of one’s maxim and that maxim as a universal law. If a maxim cannot be conceived as a universal law, or if it cannot rationally be willed to become a universal law to begin with, then by implication one cannot will to act on the maxim and simultaneously will that it become a universal law.
In the previous section, I argued that the “general formula” that Kant says should be used in moral evaluation is FUL, but there are differences between his formulations of the main principle. FUL states that I should be able simultaneously to will that my maxim become a universal law, but the later formula states that my maxim should be able simultaneously to make itself into a universal law. What should we make of this difference?
Reading the formulas as “formulas” in Kant’s technical sense suggests an answer: these differences are not part of the model of application that is essential to the formulas. What is essential is the requirement that the maxim be in conformity with itself as a universal law. Whether, in moral reflection, I imagine this conformity as willed by me or brought about by the maxim does not affect the result—not to mention the fact that it is difficult to imagine my maxims “doing” anything without this happening through my will. This explains how Kant could regard the principle of morality in Groundwork I, as well as FUL, the “general formula,” and several other formulations in Groundwork II as versions of the same principle.Footnote 23 They all require the conformity of one’s maxim with itself as a universal law.
Given Kant’s definition of analogy, if the other formulas are analogical ways of representing FUL, they should exhibit the same internal structure. That is, they should require the same model of application. Since a model states a relation, we can also put this in terms of Kant’s definition of analogy: they should require a perfectly similar relation of agreement between one’s maxim and one’s maxim as a universal law. I first discuss the formulas that include the terms “maxim” and “universal law,” leaving the discussion of FH to the end.
3.a.2. The Formula of the Law of Nature
The distinctive difference between FUL and FLN is that whereas FUL speaks abstractly of a “universal law,” FLN speaks of a “universal law of nature.” Kant provides two versions of FLN. The initial formulation asks you to act “as if the maxim of your action should become by your will a universal law of nature” (GMS 4:421). This version leaves the moral criterion implicit: what exactly am I supposed to ask once I imagine my maxim as a universal law? Whether I would like there to be such a law? Whether it would have beneficial consequences overall? Whether I could still achieve my purpose under it? The first version of FLN does not tell me. Understandably, this formula has provoked criticism, most notably the Hegelian objection that it is empty.
A later version of FLN does include the complete criterion, however, stating that you ought to “act according to maxims that can simultaneously have as their object themselves as universal laws of nature” (GMS 4:437). Here the relevant relation is the harmony between the maxim and that maxim as a universal law (of nature). This means that FLN does have the same internal structure as FUL, as an apt analogy requires.
Kant’s discussion of the four examples (GMS 4:421–423) confirms that he understood the first version of FLN along similar lines.Footnote 24 For instance, he explains the diagnostic contradiction in the case of the false promising example as follows: “I then see at once that it [viz., my maxim of promising falsely to repay a loan, when I am in need of money] could never hold as a universal law of nature and harmonize with itself, but must necessarily contradict itself” (GMS 4:422, emphasis added). The problem Kant points to here is not simply that the maxim could never hold as a universal law of nature but that the maxim cannot hold as a universal law of nature and harmonize with itself as the agent’s action principle (because it cannot hold as a universal law in the first place).
In short, the relation at the heart of FLN is “perfectly similar” to that at the heart of FUL: both formulas require that one’s maxim harmonize with itself as a universal law.
3.b. Legislation in a republican spirit
3.b.1. The Formula of Autonomy
In FA and FRE, the agreement between one’s maxim and one’s maxim as a universal law is expressed in terms of an analogy with political legislation. FA requires that you act only on maxims that can simultaneously serve as universal laws for all rational beings. This formula clearly seems to contain a relation structurally similar to that in FUL and FLN. This impression is confirmed when we read FA in light of Kant’s conception of the criterion for good political legislation, which serves as the basis of the analogy.
In the Feyerabend Lectures on Natural Law—the student transcript of a course he taught during the semester in which he wrote the Groundwork—Kant formulates the normative principle governing political legislation as follows: the supreme principle of right is “the agreement of private freedom with the general freedom” (V-NR/Feyerabend 27:1328). In his copy of the handbook for the course, Kant wrote down what this principle demands of the legislator:
All laws of the highest ruler … must originate as if from common agreement, namely, they should not necessarily contradict it … If laws are possible only on the basis of a private choice (one against all), they are … despotic. (HN 19:346, #7373)
Kant gives an example of a law that fails to meet this standard, namely, a law that imposes taxes on all merchants except the ruler’s personal favorites (V-NR/Feyerabend 27:1382). This law is possible only on the basis of the ruler’s private choice, and it is inconsistent with a general tax law imposed on all merchants.
Rulers ought to use the republican idea of popular self-legislation as a normative criterion.Footnote 25 They ought to choose laws that harmonize with what the people as a whole could impose on themselves as general laws. But they need not ask whether their subjects actually do support these laws (V-NR/Feyerabend 27:1382). In parallel fashion, a moral agent acting in accordance with FA ought to act on maxims that could simultaneously serve as universal laws for all rational beings, without (per impossibile) having to consult them all.
In sum, FA expresses a political analogy that matches Kant’s conception of the task of a good legislator. It contains a relation of agreement between maxim and universal law that is structurally similar to that contained in FUL.
3.b.2. The Formula of the Realm of Ends
As explained above, FRE transforms FA from an analogy according to which individual moral agents are to regard themselves as giving laws to all rational beings to the ideal of the totality of all rational beings as acting morally, united in a moral community under moral laws. Kant formulates FRE in terms of a requirement that your maxims be “in conformity” or “in agreement” with the ideal: they ought to “harmonize” with a possible realm of ends (GMS 4:436, 436n.). Clearly showing FRE’s provenance in FA, Kant writes that you ought to act “as if” through your maxims you are “at all times a legislating member of the universal realm of ends” (GMS 4:438).
As the phrase “legislating member” indicates, the “realm of ends” is conceived as structurally similar to a republic, that is, a body politic whose members legislate the laws to which they are subject. Given how Kant describes them, it seems that, when considering a prospective law, these members should ask themselves whether it harmonizes with a system of laws given by the people as a whole, or whether it merely reflects their private choice or special interest. As Kant presents it, they can answer this question entirely by themselves, using the very same criterion the ruler ought to use as a normative criterion to guide his legislation.Footnote 26 Therefore, the basic model of application at the core of FRE is similar to that in FUL, FLN, and FA: the maxims of your will ought to harmonize with themselves as universal laws.
The intermediate conclusion, at this point, is that FLN, FA, and FRE are analogical expressions of FUL and do indeed have the same internal structure as FUL. This does not make them “intensionally equivalent” in the strict sense of the term, however. For example, FLN demands that one’s maxims be able simultaneously to have as their object themselves as universal laws of nature, whereas FA demands that they be able simultaneously to become universal laws for all rational beings. These formulations do not have the same meaning. Nevertheless, “at bottom” they express the same moral principle. FUL, FLN, FA, and FRE express the same moral criterion, as they all present the same model of application: they all require a relation of agreement between maxim and universal law. As a result, they are extensionally equivalent.
3.c. Republican freedom and the formula of humanity
One question remains to be answered: whether FH involves analogy, and if so, whether it includes a “relation” that is “perfectly similar” to the relation at the core of FUL. On the face of it, both look unlikely.
One might perhaps think that Kant regards the ends mentioned in FH as analogous to the ends of natural teleology. This is not how Kant develops FH, however. As became clear in the discussion of his argument leading up to FH (Section 2.c.), he introduces the terminology of rational beings as “objective ends” via the contrast with “subjective ends,” and the phrase “ends in themselves” via the contrast with “mere means,” not by reference to natural teleology.
Moreover, the wording of FH makes it look unlikely that the formula includes analogy. FLN, FA, and FRE all include the phrases “as if” (als ob) or “regarding as” (betrachten als), indicating that our maxims do not literally become laws of nature, and that we do not literally give laws to all rational beings or to a realm of ends. By contrast, FH literally prohibits using humanity merely as a means and tells us not only to preserve but also to promote humanity as an end qua end—that is, not as if it were an end. As Kant puts it, if there is a categorical imperative, “a human being and generally every rational being exists as an end in itself” (GMS 4:428, original emphasis).Footnote 27
Furthermore, although Kant understands FH to state a constraint on maxims (GMS 4:436, 438), the formula seems to present a fundamentally different model of application than that presented in FUL. Rather than formulating the constraint in terms of the harmony of the maxim with itself as a universal law, FH formulates it in terms of humanity as an end in itself. It requires that the subjective ends that you include in your maxim harmonize with humanity as an objective end. As Kant also puts it, every rational being ought simultaneously to “count as end in itself in your maxim” (GMS 4:437). Given their very different terminology, it looks unlikely that FH and FUL contain a perfectly similar relation.
In the rest of this section, I propose a tentative solution. In the case of FH, I will suggest, the analogy is not expressed within the formula. Rather, Kant takes the formula as a whole to express an analogy. Specifically, the equal moral standing of rational beings as ends in themselves, expressed in FH, is analogous to the equal political standing of citizens in a republic. This, in turn, makes it possible to explain why the relation at the core of FH is “perfectly similar” to that at the core of FUL.
3.c.1. How FH involves analogy
The textual clue to this solution is a sentence leading up to FA in which Kant characterizes the way in which FLN and FH represent the categorical imperative. Central to FLN, he writes, is a conformity with law similar to that of an order of nature, while central to FH is the “universal Zwecksvorzug of rational beings in themselves” (GMS 4:431, original emphasis). The term Zwecksvorzug seems to be a neologism created on the model of political terms such as “estate privilege” (Standesvorzug) and “birth privilege” (Geburtsvorzug).Footnote 28 “End privilege” or “privilege of ends” would therefore be suitable translations. Kant was critical of the inherited privilege of the nobility, as is clear from his discussion of the Standesvorzug in the Metaphysics of Morals (MS 6:369). A “universal privilege of ends,” by contrast, would be a privilege that belongs equally to every rational being as such. Thus understood, the term refers simultaneously to the equal standing of all rational beings as ends in themselves and to the fact that they have a special rank (or a dignity), such that they ought never to be degraded to the level of mere means in the hands of others.
If this is indeed what Kant aims to convey with the term Zwecksvorzug, it suggests that FH, too, expresses an analogy with core ideas of political republicanism, in particular with the republican conception of freedom and equality. Central to the republican tradition is its characteristic definition of freedom via the contrast between freedom and slavery (or dependence, domination, and other similarly asymmetrical power relations).Footnote 29 In the Feyerabend Lectures—from the months in which he was writing the Groundwork—Kant reportedly said: “If a being is not free, then it is in the hand of another, thus … a mere means” (V-NR/Feyerabend 27:1322). Being “in the hand of another” means being unfree, that is, subject to the unilateral power of another, as in the case of enslavement.Footnote 30 Being free, by contrast, means not being dominated, not being subject to the dictates of another who has unilateral power over you.Footnote 31 In the republican tradition, the freedom and equal rank of all citizens therefore go hand in hand.Footnote 32 Given this conceptual constellation, the relation among rational beings, who all have the same special rank or privilege of being ends in themselves, is analogous to the relation among free and equal citizens in a republic.
3.c.2. How FUL and FH express a perfectly similar relation
This leaves the question of whether FH and FUL express a perfectly similar relation. In order to develop a positive answer, I first turn to a passage in which Kant compares FUL and FH, arguing that they are “at bottom the same [principle]” (GMS 4:438). Here is his explanation:
The principle: so act in relation to every rational being (to yourself and others) that in your maxim it simultaneously counts as an end in itself, is thus at bottom the same as the principle: act on a maxim that simultaneously contains in itself its own universal validity for every rational being. For to say that in the use of means to each end I ought to limit my maxim to the condition of its universal validity as a law for every subject is tantamount to saying: in the use of all means, the subject of ends, i.e. the rational being itself, must be made the basis of all maxims of actions, never merely as a means, but as the supreme limiting condition, i.e. always simultaneously as an end. (GMS 4:437–438)
To put this slightly more colloquially: to say that, in my maxims, I ought to let all rational beings count as ends in themselves (FH) is tantamount to saying that I ought to act only on maxims that can simultaneously be valid as laws for all rational beings (FUL). After all, if I were at moral liberty to use or disregard rational beings at my discretion, I would not be required to restrict myself to acting on maxims that can simultaneously be universal laws for all rational beings (since, by hypothesis, I would be at liberty to use or disregard them as I please). In this way, the requirement that my maxims be universal in their form is the reverse of the requirement that, as far as their content is concerned, all rational beings ought to count as ends in themselves.
The fact that Kant presents FUL and FH as being at bottom the same principle approached from two different angles does not alter the fact that FUL has primacy in the order of argumentation. As explained above, Kant first derives the content of FUL from the concept of a categorical imperative. He then argues that if there is a categorical imperative, there must be an objective end, and he provides a separate argument for the thesis that only rational beings qualify as such. Only once he has identified rational beings as objective ends can he restate the categorical imperative in these terms.
As mentioned, Kant regards the requirement that maxims have universal form as the reverse of the requirement that maxims, as far as their content is concerned, value all rational beings as objective ends. This suggests that, on his view, they contain the same relation, but described from different perspectives, much as “a is above b” and “b is under a” describe the same relation between a and b. FUL states the moral requirement in terms of the form of your maxim: you ought to be able to will your maxim and simultaneously will that it become a universal law. FH formulates the requirement in terms of the contents of your maxim: your subjective ends ought to harmonize with humanity as an objective end. According to FUL, you ought not to act on maxims that make an exception for yourself; you ought to act on maxims that you can simultaneously will to become universal laws for all rational beings. According to FH, you ought not to take yourself to have a higher moral rank than others, using them as mere instruments at your disposal; you ought to promote not only your own legitimate ends but also those of others. Although the two formulas offer different models of application, they express a perfectly similar relation: they both express the equal moral status of all rational beings.
4. Conclusion
Kant’s conception of analogy sheds new light on the relations between the formulas of the categorical imperative and suggests solutions to most—if not all—of the difficulties mentioned at the beginning of this article. FUL is the main formula of the categorical imperative. Because it is a principle of pure practical reason, it can be illustrated only by means of analogy. Analogy, on Kant’s conception of it, involves a perfect similarity of relations in dissimilar things. The relevant relation at the heart of FLN, FH, FA, and FRE is indeed perfectly similar to that in FUL. This explains the sense in which these formulas are “at bottom” different formulas of the same law.Footnote 33
Abbreviations
- GMS
-
Groundwork for the Metaphysics of Morals
- HN
-
Notes and Fragments
- KpV
-
Critique of Practical Reason
- KrV
-
Critique of Pure Reason
- KU
-
Critique of Judgment
- MS
-
Metaphysics of Morals
- Prol
-
Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward as Science
- RGV
-
Religion within the Boundaries of Mere Reason
- ÜGTP
-
On the Use of Teleological Principles in Philosophy
- V-Anth/Dohna
-
Dohna Lectures on Anthropology
- V-Lo/Wiener
-
Vienna Lectures on Logic
- V-Met-L1/Pölitz
-
Pölitz Lectures on Metaphysics
- V-Mo/Mron
-
Mrongovius Lectures on Moral Philosophy
- V-NR/Feyerabend
-
Feyerabend Lectures on Natural Law
Funding statement
Open access funding provided by University of Groningen.
Pauline Kleingeld is Professor of Philosophy at the University of Groningen. Her research focuses on moral and political philosophy, with an emphasis on Kant and Kantianism. Her publications include Fortschritt und Vernunft: Zur Geschichtsphilosophie Kants (1995), Kant and Cosmopolitanism: The Philosophical Ideal of World Citizenship (2012), and articles on Kant’s moral and political theory.
Open access
