This chapter lays out the ways in which Hans Christian Ørsted (1777–1851) influenced the development of the concept of thought experiment. Ernst Mach (1838–1916) is currently more often credited with laying the foundations of contemporary views, and he is sometimes thought to have been little (if at all) influenced by Ørsted. Against these standard accounts, I will show that Ørsted’s and Mach’s descriptions have key features in common. Both thinkers hold that thought experiments: (1) are a method of variation, (2) require the experimenter’s free activity, and (3) are useful in educational contexts for guiding students to arrive at certain conclusions on their own (i.e., to genuinely appropriate new concepts). The process of variation is guided by the search for invariants, some of which do not directly appear in experience. Since it is important that teachers and students be able to bring the same ideal objects to mind, thought experiments play a key role for both Ørsted and Mach in math education. While Ørsted’s emphasis on the role of thought experiments in math has been proposed as a reason why his descriptions are not relevant for contemporary use of thought experiments, I will show how their role in mathematical thinking – stemming from Kant’s descriptions of the method of construction in geometry – are part of a wider account of thought experiments that encompasses their role in the sciences and also philosophy.

This chapter develops and analyzes how thought experiments connect thinking with actuality. Superficially, imaginary constructions are mere possibilities that diverge from actuality. However, Kierkegaard also characterizes thought experiments as a kind of experience, providing concrete, fulfilling content for an otherwise empty concept – that is, providing what Kant calls a “synthesis” between thought and experience. Two Ages shows how the work of synthesis can begin from observations and move toward understanding or from understanding toward fulfillment in experience. In Works of Love, I propose, we find material for a basic taxonomy of thought experiments that distinguishes them by whether the thought experiment offers cognition of (a) objects or (b) concepts and whether it (a) proceeds from existing concepts or (b) guides the reader in gaining new ones. This taxonomy mirrors Kant’s distinctions between constitutive and regulative concepts and determining and reflecting judgments. It also anticipates the proposals of recent rationalist accounts of intuition that thought experiments provide nonsensory presentations.

Kant thinks it is possible to achieve nonperceptual cognition in three ways: (1) through practical action, (2) by analogy, and (3) through construction. The type of cognition available depends on the kind of object or concept being cognized. The fact that cognition of nonperceptual objects is possible in some cases opens the way for thought experiments to provide cognition in ways that go beyond providing fictional examples and exemplifications. In this chapter, I describe these other possibilities for cognition and show how they are at work in different kinds of thought experiments in philosophy.

The conclusion outlines key points in the book. On a Kantian-Kierkegaardian account, thought experiments lead to presentations that justify calling a thought experiment an experience, though not an empirical or sensory one. Without a sensible object, we can nevertheless have givenness, or presence, but not existence. Cognition, for that reason, is not necessarily truthful: although object-directed, cognition on its own does not justify belief in any particular object’s existence. My conclusion that thought experiments provide cognition rather than knowledge echoes Michael Stuart’s claim that thought experiments increase understanding. Cognition is a common basis for knowledge in Kant, but it is not the same thing as knowledge. The conclusion also draws implications for how we understand faith (religious belief) in Kierkegaard and how thought experiments make sense of the complexity of reality.

Rationalist accounts of thought experiment in epistemology offer an alternative to the more predominantly empiricist approaches in philosophy of science. In this chapter, I will pose a Kantian critique of recent rationalist accounts of intellectual intuition. Some epistemologists have recently argued that intellectual intuitions can provide prima facie justification for judgments. In this chapter, I highlight some promising elements of recent rationalist accounts, especially the proposal that there can be nonsensory presentations analogous to empirical perceptions. If they are right, then thought experiments can provide new experiential content even without empirical confirmation. However, I also draw attention to Kant’s objections to the possibility of purely intellectual intuitions.

In philosophy of science, Mach’s account of thought experiments is more often described as relevant for contemporary usage than Ørsted’s. In this chapter, I survey recent Kantian accounts of thought experiment, arguing that the leading views inspired by Kant in philosophy of science remain broadly empiricist. This tendency may be due to their focus primarily on the role of thought experiments in the sciences. In later chapters, I will argue – against recent Kantian views – that Kant understood cognition more broadly to include not only sensory perception but also mathematical construction. Acknowledging that cognition does not always require empirical fulfillment opens new ways of understanding how thought experiments work in philosophy, which may rightly differ from their use in the sciences.

The purpose of this chapter is to analyze Kant’s approach to writing philosophical texts, as such. By his own admission, Kant struggled with making his texts clear. He viewed this problem as not only technical, but as properly philosophical. It will be demonstrated that Kant carefully analyzed different types of linguistic clarity in his Lectures on Logic, that he fully recognized the difficulty of achieving them in practice, and that he nevertheless granted his readers the ‘right’ to ‘legitimately demand’ a certain level of clarity in principle. It will then be examined how and why Kant deployed various forms of metaphorical language to meet this challenge – a strategy which has, in turn, opened promising avenues for scholars interpreting his works. An analysis of the Critique of Pure Reason will illustrate how Kant ingeniously exploited metaphors to combine “discursive (logical) clarity” with “intuitive (aesthetic) clarity,” aiming for an ideal he termed “lucidity [Helligkeit].” In particular, the discursive structure of the Critique is represented here through an analogical model based on Kant’s vividly metaphorical description of moral character formation in the Anthropology.

According to Cassirer, Kant’s Critique achieves a new look at the dichotomy between “consciousness and actuality, the I-world and the world of things.” Indeed, the Critique of Reason “sets out a new positive concept of subjectivity and objectivity […]. The world of the subject and objects no longer stands as two opposing halves of one absolute being; rather, being constitutes one and the same realm of spiritual functions through which we obtain the content of both […]. This abstract result was introduced by Humboldt, through the mediation of language in the concrete consideration of spiritual life.” Humboldt seizes on a possibility indicated in the first Critique and builds his philosophy of language as a mediation of the subjective and the objective. This is an original way of understanding Humboldt. Understanding Humboldt’s philosophy of language in light of Kant will constitutes the first part of this chapter. In the second part, I spell out what this Humboldtian interpretation of language means for Cassirer. Cassirer sees Humboldt as a precursor to his own work on language. My chapter sheds light on a possibility regarding language indicated by Kant, worked out by Humboldt, and then exploited by Cassirer.

Much useful attention has been focused on Kant’s views of the relation between language and thought, as well as the relation between grammar and logic, asking especially whether Kant thinks that the activity of thinking depends on or involves linguistic phenomena – that is, whether Kant upholds the linguisticality of thinking. Here I focus instead on the relation between language and ‘the senses,’ and sensibility more generally. After sketching what such an interpretation might look like and providing some initial textual grounds for its support, I then turn to some of the details of accounts of the linguisticality of sensibility among Kant’s historical predecessors (Berkeley, Baumgarten), to help round out and deepen our understanding of what sorts of commitments might go into such a view, before returning to the closer examination of Kant’s own texts. I conclude that Kant does in fact maintain a fairly well-developed version of the linguisticality interpretation of sensibility, and raise some questions about what this means for the linguisticality of thought itself.

Kant is often cited by contemporary expressivists as an early proponent of expressivism. But that association remains controversial. In this chapter, I consider whether Kant is best read as an expressivist, focusing on his account of practical thought and language. In doing so, I present a variety of reasons for thinking that Kant’s views are similar in central respects to contemporary forms of expressivism. But I also argue that there are good reasons for the Kantian to resist any such assimilation – reasons for them to think that Kant’s view is not a form of expressivism, but something better than it.

Descartes and Kant strike us as the necessary poles of a historical and philosophical process that has constantly put the deaf at the center of theories of language. While Descartes grants the deaf intellectual abilities that match other men’s, Kant pronounces in 1798 a radical verdict, asserting that the deaf from birth are bound to remain deprived of any rational capacity. Why does Kant pronounce such a verdict, at the very time when l’Abbé de l’Epée trains with success the deaf and dumb to talk in Paris, when Samuel Heinicke also succeeds through others paths in Leipzig? I shall argue that this radical shift paradoxically stems from a philosophical breakthrough within the philosophy of language, that is, the unprecedented claim that language is decisively involved in the exercise of crucial mental capacities. Because language was deemed by Cartesians to have secondary and accessory functions, its correlation with the exercise of mental capacities had to be reclaimed by anchoring the conditions of all intellectual performances in the material properties of the phonic medium. This principle provides us with a tool to rationally explain Kant’s claims in the Anthropology.

Brandom gives two inconsistent accounts of the prehistory of his inferentialism: that Kant only contributed its concept–>judgment component, which was not taken up again until Frege vs. that Kant also contributed its judgment–>inference component, which was already taken up by Hegel. This chapter supports a version of the latter account. It argues against Brandom both that by 1790 Kant, like Brandom, espoused an inferentialist position incorporating a ‘linguistic turn’ and that Kant’s inferentialism is superior to Brandom’s (by providing better arguments for its concept–>judgment component and a necessary limitation of its judgment–>inference component thanks to the analytic/synthetic distinction). The chapter also argues that Kant’s inferentialism led him to the additional project of a “transcendental grammar.” Finally, it pursues the influence of this whole Kantian version on successors: Hegel did indeed take over Kant’s inferentialism, but whereas Brandom detects this in Hegel’s Phenomenology, it is even more evident in Hegel’s Logic, and whereas Brandom leaves it at that, for Hegel inferentialism was only the beginning of a more original and daring project. Not only did Kant’s inferentialism motivate Humboldt’s holistic conception of language, but in addition Kant’s project of a “transcendental grammar” inspired Humboldt to the same.

In the first, introductory part of this chapter I explain the tension inherent in these dual beliefs by examining the rules that Leibniz set forth for the reform of the philosophical lexicon as well as the attempts to apply these rules made by two key figures prior to Kant, namely, Christian Wolff and Christian August Crusius. In the second part of the chapter, I show how this tension is explicitly discussed and presented as a central problem facing metaphysics in the writings of Johann Nicolaus Tetens, who exerted a profound influence on Kant’s intellectual development in the years leading up to the Critique of Pure Reason. In the last section of the chapter, I explain what I take to be Kant’s solution to this tension by examining hither-to ignored passages in the first and especially the second Critique. The key thesis I defend is that Kant proposes to overcome the above-mentioned tension regarding philosophical terminology using the same, revolutionary conception of systematicity that lies at the basis of his transcendental philosophy.