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.

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 theme of the essential activity of the mind provided the exciting intellectual setting that made a compelling case for psychology’s founding, and also gave rise to competing models of psychology. Structural or content psychology, championed by Wundt and Titchener, defined psychology as the experimental study of the data of immediate experience through the method of trained introspection. This natural science model sought to reduce the contents of consciousness to constituent elements of sensory origin. The restricted definition and ambiguous methodology led to challenges. Nevertheless, structural psychology secured recognition of psychology as a science, and Müller, Hering, and Ebbinghaus, attempted to modify structural psychology. Additionally, Mach and Avenarius bolstered the justification for psychology as a natural science. An alternative, described as a human science model, proposed more open definition and methodologies. Brentano’s act psychology stated that the phenomenological processes of psychological events are inseparable from the environment and consciousness. The works of Stumpf, Külpe, Dilthey and Bergson all fall into the human science model, but the lack of systematic theory reduced their successful competition with structural psychology. In many respects, the “founding” of modern psychology was a false beginning, and neither model established a lasting framework for psychology.