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 further situates my Kantian account of thought experiments among competing views. I identify problems for contemporary accounts and contrast epistemological questions (How do thought experiments justify?), which guide most of the current scholarship, with Kant’s emphasis on cognition [Erkenntnis] (What makes concepts meaningful?). I note that metaphilosophical questions on the relationship between conceivability and possibility are not relevant for thought experiments if they are an apparatus for cognition, which is neutral toward the truth or actuality of the objects of cognition. Contemporary accounts that begin with Kuhn’s epistemological question differ on what the basis of knowledge might be. Leading approaches appeal to logic, stored knowledge, and intellectual intuition. I will briefly sketch here some of the basic approaches.

Computational neuroimaging is defined broadly as the use of neuroimaging to investigate the localization and representation of parameters in formal mathematical models. We focus upon models of behavior and neural processing that have been adopted widely in behavioral sciences and cognitive neuroscience, including reinforcement learning, predictive coding, decision theory (drift diffusion and evidence accumulation), population receptive field models, and encoding models (including artificial neural networks). The aim is not to explain all the technical details of the various models, but illustrate and discuss the added value of combining such models with neuroimaging.

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.

The book’s introduction explains the history of thought experiments in philosophy. It also describes Hans Christian Ørsted’s interactions with Kierkegaard and his influence on Kierkegaard’s concept of Tankeexperiment. The introduction outlines the ways in which thought experiments make thoughts meaningful by providing immediate presentations.

Chapter 11 introduces basic EEG and MEG data analysis methods. It begins with an explanation of the noise components in EEG and MEG signals and discusses various methods of noise reduction, including filtering and independent component analysis (ICA). Spectral analysis, event-related response (ERR) analysis, and steady-state evoked response (ssER) analysis are then introduced. Each method is explained in plain language, followed by more detailed explanations to meet the different needs of beginners and advanced readers. Relevant statistical methods and data presentation formats are also introduced, using various data analysis platforms.

In two of Kierkegaard’s earliest works, The Concept of Irony and Either/Or, imaginary construction (i.e., thought experiment, or Experiment) is often characterized negatively. However, the three core features of thought experiment shared by Ørsted and Mach also begin to emerge, laying foundations for a more positive view in other works. Kierkegaard’s characterizations of thought experiment indicate that imaginary construction guides mental action. This focus contrasts with the standard emphasis in Kierkegaard scholarship on thought experiment as supplying the concreteness of (empirical) actuality. In The Concept of Irony, Kierkegaard critiques irony as a retreat from reality but also shows it can be used to achieve new kinds of wholeheartedness and unity. In this chapter, I will argue that thought experiments can similarly lead the experimenter away from reality but, like irony, may also be a useful tool for self-development.

We present the main methods that are used to modulate brain activity directly. These methods are often used in combination or following up on neuroimaging experiments, in a means to test causal hypotheses. We include microstimulation, deep brain stimulation, focused ultrasound stimulation (FUS), transcranial magnetic stimulation (TMS) and its sub-types like single- and double-pulse and repetitive TMS. We end with transcranial current stimulation (TCS), also known as trancranial electric stimulation (TES), which comes in several variants such as transcranial direct current stimulation (TDCS) and transcranial alternating current stimulation (TACS).

This chapter distinguishes the work of thought experiments in exemplifying concepts from their role in aiding cognition of regulative ideas. Contemporary interest in thought experiments as a “method of cases” treats thought experiments as providing instances or exemplars. For regulative ideas as Kant understands them, however, no observable instances or exemplars are possible. Nevertheless, thought experiments can direct attention toward regulative ideas negatively (by distinguishing them from what is observable) or positively by indicating a direction for extrapolation or ongoing inquiry. These positive uses are forms of cognition. The distinction between regulative and constitutive concepts matters for thought experiments that deal with regulative ideas such as the self – for example, for thought experiments about personal identity, where a number of objections to the use of thought experiments have been raised. I argue in this chapter that some of these objections can be answered by distinguishing regulative from constitutive concepts.

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.

This chapter proposes that thought experiments are a cognitive apparatus and situates this view among contemporary accounts of thought experiment. I set forward the project of the book, which is to (1) propose a new account of thought experiments as a method and (2) trace the historical foundations of the term and concept of “thought experiment” from Kant through Ørsted to Kierkegaard. I define “cognition” [Erkenntnis] for Kant as a synthesis of concepts with intuitions and propose that Kierkegaard, like Kant and Ørsted, views thought experiments as useful for achieving cognitions. I introduce the term Tanke-experiment in Kierkegaard and suggest why it has been little emphasized by Kierkegaard scholars and remains widely unacknowledged in contemporary descriptions of the history of thought experiment.