2.1 Kant’s Doctrine of the Method

My account relies on an analogy between moral examples and scientific models. This approach is motivated by Kant’s remarks in the Doctrine of the Method and recent scholarship in the philosophy of science.

In the Doctrine of the Method, Kant asks how the laws of pure practical reason can be admitted into the human mind and have influence over one’s maxims. Kant asks how creatures like us can become aware of the moral law and become accustomed to acting from it. He responds that morality should seek out a method like those found in science. He specifically mentions chemistry (CPrR, 5: 163). Though morality is concerned with practical rather than theoretical cognition, Kant thinks it is structurally similar to science. Both are lawful and composed of a priori (rational) and a posteriori (empirical) components. Both involve the exercise of the faculty of reason. These structural similarities permit a similarity in method.

For Kant, the shared method involves separation. In chemical experiments and moral examples alike, experience only provides us with ‘impure’ phenomena. A phenomenon is impure if its a priori and a posteriori components are inextricably coupled. In the chemical case, experience only provides composite substances such as ‘calcareous earth in hydrochloric acid’ as opposed to a pure or isolated ‘alkali’ (CPrR: 5: 92–3). In the moral case, experience only provides an ‘empirically conditioned will’ in which inclination coexists with the moral law; experience does not provide the isolated moral law. Though separation is not empirically possible, Kant insists one must separate the a priori from the a posteriori in thought.

Crucially, Kant’s method of separation requires us to idealize beyond the objects given in experience. Kant’s discussion of regulative ideas in CPR expands on the claim. He explains that ideas such as the totality of empirical causes and pure chemical elements (‘pure air’, ‘pure earth’, ‘pure fire’) are ‘necessary concepts of reason to which no congruent object can be given in the senses’ (A644/B672). We never encounter such a thing as ‘pure air’ in real life. Nevertheless, ‘pure air’ qua regulative idea plays a necessary role in cognition, which allows us to formulate scientific laws and principles. By idealizing from what is empirically given by positing regulative ideas, one can decouple the a priori from the a posteriori in thought. Idealization, thus, facilitates separation.

2.2 Models and the philosophy of science

Kant’s discussion of regulative ideas has been immensely influential in debates on scientific modelling. Most notably, Hans Vaihinger (Reference Vaihinger1911) argued for a fictionalist view of scientific models based on his interpretation of Kantian regulative ideas. Vaihinger went on to influence the subsequent debate (Bokulich Reference Bokulich and Suárez2009; Fine Reference Fine1993; Suárez Reference Suárez2009), and there have been recent appeals to Kant’s discussion in the literature (Massimi Reference Massimi2017; Spagnesi Reference Spagnesi2023; Weisberg Reference Weisberg2007a).

As these debates suggest, Kant’s claims about scientific knowledge are deeply connected to models. In the philosophy of science, modelling is standardly distinguished from other forms of theorizing by two characteristic features: (1) idealization and (2) indirect study.

Nearly all models exhibit some degree of deliberate idealization. From frictionless planes to point masses, scientists often prefer idealized models to more accurate ones. Their ubiquity and success show that models can give us knowledge about target systems without perfectly representing those systems (Bokulich Reference Bokulich and Suárez2009; Potochnik Reference Potochnik2017; Strevens Reference Strevens2004). Still, models need to be representative to some degree; only then can they stand in an analogical relation to their respective target phenomena. The point is that the cognitive value of a model does not depend solely on its power to represent. Accordingly, idealization promotes crucial theoretical virtues such as simplicity, fecundity, and familiarity.

Indirect study further distinguishes modelling. Instead of studying a target system directly via techniques of observation, models are investigated as independent objects of study. Then, conclusions about the model are analogized to generate conclusions about its target system. For instance, instead of studying a hydrogen molecule directly, modellers study the Bohr model. They form conclusions about the electron’s orbit in the Bohr model and analogize those conclusions to the experimental behaviour of actual electrons in a given hydrogen molecule.

While idealization figures in many forms of theorizing, what most clearly distinguishes modelling is indirect study (Weisberg Reference Weisberg2007b; Hesse Reference Hesse1963). Modelling is neither the application of a pre-given concept to a particular object (e.g., subsuming a particular dog under the universal concept dog) nor an exercise in logical deduction (e.g., deducing Kepler’s laws from Newton’s laws of motion). Rather, modelling is a reflective and exploratory activity that generates new conceptual connections instead of merely applying existing ones. It enables a reciprocal exchange between abstract structures and empirical phenomena, rendering each more intelligible through the other. In this way, models are said to mediate between theory and observation (Morgan and Morrison Reference Morrison, Morgan, Morgan and Morrison1999).

Models are further distinguished by their level of generality. While theory-building seeks universal principles, model-building has a narrower scope, aiming for local rather than global unity. This is evident in nuclear physics, where incompatible models – such as the liquid-drop, shell, cluster, and quark models – each offer coherent yet mutually contradictory accounts. For instance, the liquid-drop model (falsely) treats the nucleus classically and explains fission, while the shell model treats it quantum-mechanically and explains spin. Despite their mutual inconsistency, both are accepted because modelling involves indirect study. We learn from a model only if it is itself a unified and intelligible object of study. Hence, each model must achieve internal coherence even if collective consistency is sacrificed.

The key point is that models differ from other forms of theorizing in their level of generality and in their mediating role. While theories, especially moral ones, have been criticized as ‘empty formalisms’ (Hegel Reference Hegel, Nisbet and Wood1991; O’Neill Reference O’Neill1987), models are more localized and enable a bidirectional information flow between abstract principles and particular phenomena.

Although Kant did not know about the contemporary definition or use of models in scientific inquiry, there is a rich history of taking Kant’s remarks on separation and regulative ideas as bearing on contemporary debates about scientific models. Moreover, learning from Kantian moral examples involves the two characteristic features of scientific modelling – idealization and indirect study. Suppose we are given in experience an example of dutiful moral action. Kant claims that we learn about our own moral capacity from the example. Already, Kant is calling for indirect study. Namely, we learn about ourselves indirectly by studying another and coming to conclusions about their act. Moreover, because these conclusions concern the moral law, we must idealize beyond the exemplar’s empirically conditioned will by positing an idea of the ‘pure’ moral law. In later sections, I provide a detailed picture of how exactly this process takes place. For now, the key point is that Kant’s remarks on moral method show that learning from example involves the two defining features of scientific modelling: idealization and indirect study. This methodological connection grounds an analogy between moral examples and scientific models, dismissing any objections that such a strategy is ad hoc.Footnote ⁵

3.1 Learning from models

This paper’s central claim is that Kantian moral examples are analogous to scientific models in an epistemological sense. Specifically, it concerns their cognitive role and argues that how we learn from moral examples is analogous to how we learn from scientific models.

Since the publication of Morgan and Morrison’s seminal Models as Mediators (1999), philosophers of science have made great progress with respect to the latter question. Some even suggest that models give rise to their own style of reasoning dubbed ‘model-based reasoning’ (Magnani, Nersessian, and Thagard Reference Magnani, Nersessian and Thagard1999; Nersessian Reference Nersessian, Magnani, Nersessian and Thagard1999). Contemporary work in the philosophy of science typically begins from a general characterization of models and proceeds to examine how, in virtue of this characterization, models play a distinctive role in scientific reasoning. This paper follows suit. For our purposes, it is not necessary to decide whether models are fictions, set-theoretical structures, or something else entirely. We are interested in how we learn from models, where this requires only the assumption that models involve idealization and indirect study. As such, our conclusions are compatible with various metaphysical views of scientific models.

A model’s cognitive value arises both from its representational accuracy and from the process of modelling. We draw inferences from a model because it accurately captures the salient features of the target phenomenon, but we also gain insight from a model through the very activity of constructing and manipulating it – by determining what fits together and how different structural assumptions serve scientific aims (Knuuttila and Boon Reference Knuuttila and Boon2011; Cartwright Reference Cartwright1983; Woodward Reference Woodward2003).Footnote ⁶

Consider the emergence of the liquid-drop model of nuclear structure. In their landmark paper, Bohr and Wheeler (Reference Bohr and Wheeler1939) modelled it by treating the nucleus as a classical drop of charged fluid. Strictly speaking, this is false: nuclei are quantum systems with discrete energy levels. Yet no quantum model at the time could account for the smooth, collective energy changes observed during fission. Despite its representational inaccuracy, the liquid-drop model was the only one at the time to successfully explain how heavy nuclei split. Aware that this classical assumption was necessary for a coherent model, Bohr and Wheeler deduced that fission occurs at a macroscopic level beyond the quantum scale of individual nucleons. In this way, introducing a representational inaccuracy (a classical nucleus) is exactly what allowed the liquid-drop model to be a unified object of thought that could generate understanding. By constructing and manipulating the liquid-drop model, Bohr and Wheeler engaged in a reflective activity that made them conscious of exactly which assumptions were necessary for an intelligible explanation of nuclear fission.

Modelling is an open-ended, non-algorithmic process in which learning occurs at two stages: construction and manipulation (Morgan Reference Morgan, Morgan and Morrison1999). Model construction emphasizes making an abstract structure intelligible and idealizing from the right features of a phenomenon, while model manipulation involves negotiating between that abstract structure and the target phenomenon. Both stages involve a back-and-forth between theory and observation, though each emphasizes one direction more than the other. For our purposes, we consider how learning occurs at both stages.

3.2 A chemical case study

To demonstrate how we learn from models via the open-ended activity of modelling, I analyse and illustrate the development of Jean Dumas’s famed model of the chemical reaction between alcohol and chlorine. I choose Dumas’s case for two reasons: First, Dumas worked shortly after the chemical revolution, within the tradition of chemistry that influenced Kant’s remarks on separation; second, Dumas overcame a problem analogous to Kant’s formal epistemological worry (Klein Reference Klein, Morgan and Morrison1999; Dumas Reference Dumas1834, Reference Dumas1835, Reference Dumas1840).Footnote ⁷ Namely, he lacked sufficient empirical evidence to establish the causal mechanism driving the reaction. Nevertheless, he overcame this limitation by modelling.

I reconstruct Dumas’s modelling as a four-part process adapted from Boumans (Reference Boumans, Morgan and Morrison1999). This is just one conception of model construction among many. Importantly, different conceptions maintain that these four steps are completed at some point when constructing and manipulating a model.Footnote ⁸ Thus, the key point that we learn from the reflective process of modelling is not unique to this specific account.

3.2.3 Integrating

The third step is to integrate one’s resources to create a unified model. Integration is an active process that involves reinterpreting each resource and its relation to the others such that they all cohere and answer to the motivating question. One works back and forth among their various resources until a unified model is achieved; often this involves trial and error. In virtue of this process, the relations between the components of the model become explicit.

For Dumas, this process was far from formulaic (Klein Reference Klein, Morgan and Morrison1999; Dumas Reference Dumas1834, Reference Dumas1835, Reference Dumas1840). After separating his resources, he reinterpreted the transformation as a chemical reaction between two chemical compounds expressed by Berzelian formulas. He set up the following equation:

where x is the mysterious ‘oily’-then-crystalline substance.

Factoring in the observed quantities of each substance, he balanced the equation via basic arithmetic principles. He concluded that the mystery substance was C₈O₂ H₂Ch₆, meaning that upon the addition of chlorine, each alcohol molecule (C₈H₁₂O₂) lost ten atoms of hydrogen (H) and gained six atoms of chlorine (Ch).

Now, Dumas needed to explain why this transformation occurred over several days and produced an intermediary ‘oily’ substance. After much trial and error, he concluded that it was a substitution reaction. This means atoms of hydrogen were withdrawn stepwise and substituted one by one with atoms of chlorine. Because this was his only way to unify all relevant resources and to answer his original motivating question, Dumas knew that he had produced a model that could be analysed as an intelligible object of study.

4.1 Kant’s Boleyn man

Kant’s example is inspired by the case of Anne Boleyn, who was accused of treason by Henry VIII. In the incident, an unnamed man is pressured to testify falsely against Boleyn. Kant details how the man was bribed with ‘large gifts and high rank’ before being threatened with defamation, lost friendships, familial disinheritance, and ‘unspeakable pain’. Despite this, the man did not testify falsely. He told the truth and ‘remain[ed] faithful, without wavering or even doubting’ (CPrR, 5: 156). Kant claims that even a ten-year-old child would be moved by the example; she would come to admire the man and realize that she too can act morally.

Such claims require Kant’s example to do some substantial work, but he leaves it unspecified how the example has such a profound effect on the child. If the example cannot be evidence for moral principles or a call for imitation, how can it cause the child to admire the man and realize that she too can act morally?

Kant, nevertheless, supplies some clues. He remarks that, for the example to work, it must be presented to the child at a stage when she is already able to superficially approve and disapprove of others’ actions. At this stage, she can easily judge that the man’s act is moral and warrants approval. However, she is unaware of the grounds of her judgement as the moral law within her.Footnote ¹² Working through the example, Kant claims, builds on the initial superficial judgement and makes her conscious of the moral law. This, in turn, makes her conscious of her own freedom – both her negative freedom not to be determined by inclination and her positive freedom to determine her will autonomously via the moral law. It encourages her by showing her that she too can act morally.

Though Kant supplies these initial clues, it is still a mystery how the example makes the child conscious of her own freedom and encourages her. In the following section, I show that the four-part framework of scientific modelling can substantiate Kant’s bold claims. The crucial point is that understanding the example requires the child to idealize and engage in indirect study. She cannot directly access the moral law within the man or observe it determining his will. Thus, she must draw upon the moral law within herself and use herself as a model for the man. Moreover, to account for the man’s unwaveringness when presented with bribes and threats, she must posit a conception of the ‘pure’ moral law as the sole source of the man’s act.

While it may seem paradoxical that the child uses herself as a model to understand another human being’s action, this is not an issue. Kant is clear that the point of the example is to teach the child about herself – namely, that she is free and can act morally. Moreover, this is not the first time Kant calls for using oneself as a model in understanding others. In the Paralogisms (CPR, A346/B404-5), Kant says that to represent another mind, we must use ourselves as a model. We cannot have empirical cognition of others’ minds, but we are aware of our own rational activity. Aware of our own rational activity, we can project it onto another and understand them as having reasoned like us. Because we cannot have empirical cognition of another’s reason, we must use our own. Kant says we are ‘entitled’ to do this because it is a necessary condition for the possibility of representing another as minded.

4.2 Modelling Kant’s Boleyn man

4.3 Noble and uncontaminated examples

Any account of Kantian moral examples needs to explain why only certain examples can make us conscious of the moral law. My account has the resources to understand the rationale behind his claim and Kant’s own use of examples throughout his texts. In the Doctrine of the Method, Kant warns against the use of ‘noble’ (CPrR, 5: 157) or supererogatory examples. The key to making sense of this claim is recalling that we learn from models in virtue of their evocation of the moral law. In cases of supererogatory actions, the determining ground is not the moral law, but some other factor such as ‘feeling’ (ibid.). This prevents the modelling process from evoking the moral law, which prevents our ability to learn from the example. For this reason, it is important that our examples avoid depicting overly sentimental, supererogatory actions.Footnote ¹⁹

Additionally, my account implies that we should present models that possess theoretical virtues such as familiarity, fecundity, and simplicity.Footnote ²⁰ This allows us to understand Kant’s claim that moral examples must be ‘pure’ and ‘uncontaminated’. An example is pure if it is not contaminated by experience. It must present the moral law as the sole determining ground of action. Purity makes clear what the moral law can accomplish on its own, and this advances the systematicity of cognition just like the theoretical virtue of simplicity.Footnote ²¹ Understanding purity as a theoretical virtue, we can see why Kant presents cases in which duty and inclination so strongly diverge. Providing an explanans for a pure explanandum necessitates the evocation of the moral law. No other explanation suffices. While some have mistakenly seen this as Kant’s moralistic tendency to make morality seem as difficult as possible, we can understand it as Kant’s way of avoiding contaminated examples where inclination and duty converge. Kant avoids contamination to further the systematicity of cognition. In demonstrating what the moral law can accomplish on its own, he also encourages pupils to believe in their own moral strength.

Finally, my account makes sense of Kant’s own usage of examples throughout his writings. Despite his critical remarks on examples, Kant utilizes many examples throughout his works. Perhaps the most famous is the shopkeeper example from the G, which has been criticized on the grounds that it is under-described (Jensen Reference Jensen1989). In my view, Kant’s under-description is an advantage rather than a shortcoming. The incompleteness and underdetermination of empirical data necessitate the evocation of the moral law for the explanatory task at hand. It also gives us a head start in abstracting from irrelevant particulars.Footnote ²² Because the way we learn from examples comes from our consciousness of the moral law, it makes sense for Kant to avoid clouding the picture with superfluous empirical details.

4.4 Disanalogies

While the account I provide emphasizes the similarities between a scientist like Dumas and a moral agent like the child, it is important to keep in mind their disanalogies. Two notable disanalogies need to be addressed concerning the sophistication of scientists and the role of emotion. In each case, I argue that the disanalogy does not undermine the account.

The first disanalogy is a familiar one in the philosophy of science. Dumas, a trained chemist, engages in modelling with a degree of sophistication that far exceeds that of the child. It may therefore seem that a model-based account risks over-intellectualizing the child’s activity. This concern, however, rests on a misunderstanding of the level of generality at which the analogy is drawn. The point is not that the child engages in the same technical practices as the scientist, but that her reasoning exhibits the same form of reflective and exploratory engagement characteristic of modelling, as distinct from mere concept application, deduction, or imitation. The four-part structure of modelling invoked in Dumas’s case could equally well be illustrated by toy scientific models, such as the Lotka–Volterra model of predator-prey dynamics taught to school children. In all cases, the key point is that learning occurs in the same form via the construction and manipulation of a model. Differences in instrumental or mathematical sophistication are too fine-grained to undermine the analogy at this level of generality.

A similar point can be used to address the role of emotion. At first, it may seem that emotion plays a much larger role in morality than science. However, as important work in the feminist philosophy of science has shown, affective dispositions affect judgements of salience in scientific inquiry. They affect what a priori and a posteriori come to mind when modelling. Similar claims apply in the moral case. In both cases, modelling allows for emotion to play a nontrivial, supportive role. Of course, it may play other roles. The point is that the role of emotion, however large or small, is compatible with modelling in either case. Given the contentious nature of the role of emotion in Kantian ethics (Grenberg Reference Grenberg2013; Ware Reference Ware2015), it is a virtue of the modelling account that it does not come with a particular view of emotions baked in.

5.1 Experiments and moral justification

Recently, there has been some interest in how the sciences influence Kant’s view of morality (Ameriks Reference Ameriks2000; Rosenkoetter Reference Rosenkoetter2011; Sticker Reference Sticker2017). This is due to Kant’s remarks on chemical experiments as a paradigm for practical philosophy. For historical context, Kant witnessed the Chemical Revolution spearheaded by Lavoisier. Fully aware of the revolution’s advances, he saw empirical experiments as playing a unique role in chemistry that morality should emulate.

As mentioned, both morality and science can benefit from a method of separation. In the Doctrine of the Fact of Reason (CPrR, 5: 31–2), Kant furthers the similarity. He states that a moral philosopher can establish another’s consciousness of the moral law by setting up an experiment akin to a scientist setting up a chemical experiment. Willascheck (Reference Willaschek1992) was the first to read this as Kant’s call for moral philosophers to employ thought experiments, interpreting the Fact of Reason as a kind of ‘act’ or ‘deed’. Since Willascheck’s influential reading, philosophers have noted that calling for thought experiments has interesting implications for Kant’s thinking on moral justification.

Ware (Reference Ware2014, Reference Ware2021), for instance, utilizes Willascheck’s reading to deduce that moral justification takes place from the first-personal, common standpoint of ordinary life as opposed to the third-personal standpoint of philosophical speculation. Following Willascheck, Ware takes Kant to present a thought experiment in the Fact of Reason when presenting the example of the Boleyn man. Imagining the hypothetical scenario makes the reader conscious of the moral law and of her own freedom. As Ware explains, the thought experiment demonstrates ‘the way we separate duty from happiness and acknowledge the authority of the former’.Footnote ²³ After arguing for his reading, Ware notes there remains an unresolved inconsistency: Why does Kant treat the reader as a passive spectator of the Fact of Reason while also seeming to call for the moral law from a practical, first-person perspective?Footnote ²⁴

One contribution of my account is that it resolves this inconsistency. We can understand the thought experiment as presenting an example that initiates the self-conscious activity of modelling. Crucially, this involves using ourselves as a model. Exactly because we cannot directly observe another’s rational activity, it involves reasoning from our own point of view and projecting that line of reasoning onto another. This explains how we can make sense of another’s action while reasoning from the first-person perspective of an active participant. Modelling involves recognizing that we are using ourselves as a model. That is why we project our line of reasoning onto another and combine it with our other resources to construct a coherent model. As such, learning from examples involves a participatory dimension despite not bringing us into the narrative scene. The universality of moral principles enables us to learn about another’s motive and about our own moral capacity.

5.2 Other minds and ‘mind-reading’

A model-based account shows how we can learn from moral examples by using ourselves as a model. This is, of course, not the first time Kant suggests using ourselves as a model for another. In the Paralogisms, Kant claims we must model to understand another as minded. He justifies this move in his statement that ‘we must necessarily ascribe to things a priori all of the properties that make up the condition under which alone we think them’ (CPR, A346/B404-5). To understand another human being as minded, we must ascribe to them a priori the properties that constitute being minded. However, the only way to uncover these properties is from within. We observe in ourselves the qualities of being minded (e.g., that a mind understands its states as connected), and we project these qualities onto the other. We are entitled to do this because it is the only way we can represent them as minded.

Kitcher (Reference Kitcher2011: ch. 15 [‘Kant our Contemporary’]) points out that Kant’s view has the potential to fill a gap in current theories of how humans can understand other minds. In the last few decades, these debates have centred around questions about ‘mind-reading’: how one knows the content of another mind’s thought.Footnote ²⁵ In contrast, Kant’s discussion in the Paralogisms is about how we can represent another mind as such. My model-based view extends Kant’s discussion to contemporary cases of mind-reading in which we attempt to know the content of another’s mind. The subtle distinction allows it to overcome limitations suffered by the two leading theories of mind-reading.

The two leading accounts of children’s mind-reading – the theory-theory (Gopnik, Meltzoff, and Kuhl Reference Gopnik, Meltzoff and Kuhl1999) and the simulation theory (Gordon Reference Gordon1986; Goldman Reference Goldman2006) – are distinguished by how they explain the Maxi Experiment. In the classic experiment, a child sees a puppet, Maxi, place a chocolate in one location. Then, the child observes the chocolate being moved without Maxi’s knowledge; the child is then asked where Maxi will look for it. According to the theory-theory, children possess primitive psychological theories that guide their inferences about beliefs and desires; this enables them to predict that Maxi will look where she last left the chocolate rather than where it is actually located. Simulation theorists, by contrast, argue that children do not require such theoretical knowledge; they simply imagine themselves in Maxi’s situation and reason about what they would do.

While both accounts capture aspects of children’s reasoning, they face limitations. The theory-theory struggles to explain the role of experience and education if children already come equipped with robust theories, whereas the simulation theory cannot easily handle cases in which the other’s situation is dissimilar from our own, such as imagining the pains of labour or perspectives very unlike our own.

A Kantian model-based account resolves these limitations by combining insights from both approaches. Rather than positing innate theories, it holds that humans are born with minimal, latent categories and principles of rationality that allow them to model others as minded and to generate hypotheses about their reasoning. In familiar cases, the child may project or apply their first-personal model. In dissimilar or complex situations, however, alternative hypotheses can be generated and evaluated against one another, much like how scientists test rival models. This approach explains how children actively reason about others without requiring them to simulate every possible perspective or rely on pre-formed theoretical knowledge. Learning, then, is not passive manifestation or simulation but active engagement with examples that elicit reasoning according to latent principles.

The Paralogisms demonstrates how we can know another mind as such. My model-based theory demonstrates how we can know the particular content of another mind. By using ourselves as a model to understand another, we recognize that others enjoy the property of mindedness and are capable of thinking just like us. We also recognize that in any particular instance, they do not have to think like us. The innate scaffolding of the mind allows us to develop alternative hypotheses. In particular cases, we evaluate rival hypotheses with respect to their ability to coherently account for all relevant details.

My model-based view demonstrates in detail how we model the particular content of another by combining empirical details with a priori categories and principles. Uncovering this mechanism reveals how abstract principles make contact with particular situations, how latent principles can become known, and why modelling other minds is beneficial for tasks like moral education. As such, my model-based theory has the resources to extend Kant’s theory of practical reason to a theory of moral development. For Kant, children are neither scientists nor simulation machines. They are modellers.