1. Introduction: Thought Experiments and Imagery

Thought experiments are tools of the imagination that have contributed to significant scientific developments. My aim here is to draw on discussions of the imagination in the philosophy of mind to give an account of the nature of the imagination involved in their conduct. I begin by outlining the common view that the imagination in thought experiments is imagistic; that is, when engaging with thought experiments, we form pictures in our mind of the scenario described. I then discuss a recent alternative to this view, Salis and Frigg’s (Reference Salis, Frigg, Godfrey-Smith and Levy2020) propositional account, which sets out to demonstrate that imagery plays no important role. After presenting a series of worries with these monistic accounts, I propose that we ought to adopt a pluralist stance when thinking about the type of imagination involved in scientific thought experiments. This best captures the ways in which scientists use thought experiments for a range of purposes.

It is widely recognized that the term ‘imagination’ picks out various acts and is too broad for a single characterisation. Given what Kind (Reference Kind2013) refers to as the ‘heterogeneity’ of the imagination, we can consider what different forms it can take.Footnote ¹ One way to categorize the imagination, which broadly follows the distinction Salis and Frigg present in their account of the scientific imagination, is to distinguish between (1) ‘propositional imagining’ and (2) ‘nonpropositional imagining’. Propositional imagining is a matter of imagining that something is the case. I can imagine that there are flowers on my table, for instance. Propositional imagination does not require the use of mental imagery. Nonpropositional imagining, however, can be as follows: (a) objectual imagining—this involves mental imagery; for example, I imagine flowers on my table by forming an image in my mind of flowers on my table. This is not limited to visual imagery; I can have imagery that correlates with other sense modalities as well. And (b) phenomenal imagining—this consists in imagining seeing, hearing, touching and so on, for example, imagining seeing flowers on my table or hearing a dog barking or feeling an emotion (Stock Reference Stock2017, 24). Now that we have an idea of the different forms the imagination can take, we can turn to existing views of the imagination in scientific thought experiments.

Although little attention has been paid to the question of what kind of imagination is involved in the conduct of a thought experiment, it has typically been taken to be like forming a picture in the mind’s eye; a visual form of imagination.Footnote ² Brown states that “we typically ‘see’ something happening in a thought experiment” (Reference Brown and Hitchcock2004, 25). Similarly, for Gooding, “the ability to visualize is necessary to most if not all thought experiments” (Reference Gooding, Hull, Forbes and Okruhlik1992, 285). Miščević and Nersessian use the cognitive science literature on mental modeling. For Miščević (Reference Miščević1992), thought experiments consist in building a quasi-spatial “picture” of the scenario described. Nersessian’s account is slightly different in that it does not involve “pictures in the mind” (Reference Nersessian, Hull, Forbes and Okruhlik1992, 294); it can be a matter of forming more abstract analogical representations. Yet the reasoning involved is of a nonpropositional nature; “inferences subjects make are derived from constructing a mental model of the situation, rather than by applying rules of inference to a system of propositions representing the content of the text” (293).Footnote ³

Although there are some thought experiments that employ our other sensory modalities such as Strawson’s philosophical thought experiment that asks us to imagine a purely auditory world, the type of imagery relevant to scientific thought experiments is typically taken to be visual. This may be because many have drawn comparisons with ordinary experiments in which the primacy of visual perception is typically assumed. For example, Brown states the “only difference [between a thought experiment and an ordinary experiment] is that the perception is not a sense perception but, rather, is an intuition, an instance of seeing with the mind’s eye” (Reference Brown and Hitchcock2004, 35).

We can see, then, that many accounts of thought experiments that highlight a crucial role for the imagination have characterized it in broadly imagistic terms. I now turn to a view of the imagination that departs from such accounts.

2. The Propositional Alternative

Salis and Frigg (Reference Salis, Frigg, Godfrey-Smith and Levy2020) have developed an account of the scientific imagination that they apply to both scientific models and thought experiments. Although they agree that thought experiments involve the imagination, they propose that imagery (of any sensory modality) is unnecessary for their performance. For them, it is only the propositional form of the imagination that is relevant in the scientific domain.

To demonstrate their view, Salis and Frigg provide an example from Galileo, namely, his thought experiment that was used to answer the question: Is a force required to keep an object moving with constant velocity? Galileo asks us to imagine a frictionless U-shaped cavity. If a ball is dropped from one side, it will continue to move until it recovers the original height it was dropped from on the other side of the cavity because of the law of equal heights. We then imagine that the second side of the U-shaped bend is flattened, so that the ball is now being dropped from a height and then travels along a straight line. The law of equal heights still applies, yet the ball can never recover its original height, and so it will continue moving. This thought experiment exposes a contradiction in Aristotle’s theory that moving objects will come to a stop. From this, Galileo establishes the law of inertia; no force is needed to keep an object moving with constant velocity.

Salis and Frigg state that mental imagery is insufficient: “When considering Galileo’s cavity we do not seem to have a perception-like representation of the cavity being frictionless or the lack of air resistance” (Reference Salis, Frigg, Godfrey-Smith and Levy2020, 17). It seems true that we cannot have a visual image of frictionlessness, but perhaps Salis and Frigg are mistaken to claim that any kind of mental imagery is irrelevant. A different sensory modality could be more important when detecting friction, and so we could have a tactile image of frictionlessness instead. Or we could think about how we might represent absences in the imagination, in this case, subtract friction from the scenario imagined. Galileo, through Salviati, provides descriptions of experiments previously performed to help convince Simplicio that certain mathematical results apply to nature and to make certain theoretical claims plausible. In one section, he describes cutting a channel along a piece of wood and states “having made this groove very straight, smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball” (Galileo 1914, 178). Here, Galileo helps us imagine the effects of frictionlessness, that is, what it would look or feel like, by providing us with descriptions whereby friction is reduced as much as possible.Footnote ⁴

Putting to one side issues with this particular example, Salis and Frigg are correct to say that in order for thought experiments to be successful, we must have certain conceptual knowledge, and thought experiments are going to include steps that are best captured as propositional reasoning (see also Arcangeli Reference Arcangeli, Magnani, Carnielli and Pizzi2010).Footnote ⁵ Further, to maintaining that mental imagery is insufficient, Salis and Frigg take it to be unnecessary. They argue that it is a propositional form of the imagination, imagining that something is the case, that is necessary for conducting thought experiments, insisting that we “need to grasp the relevant concepts, with or without forming a mental image of the objects and the transformations they stand in for” (Salis and Frigg Reference Salis, Frigg, Godfrey-Smith and Levy2020, 18). They generalize this claim to cover all cases of the scientific imagination in modeling and thought experiments.

I agree that the propositional form of the imagination has a place in thought experiments, and Salis and Frigg have mapped out a useful way of categorizing the imagination when thinking about its role in the scientific domain. However, I have some worries with their view, and my account developed in the following sections differs in significant respects.

First, there are close connections between a propositional view of the imagination in thought experiments and Norton’s argument view. Norton analyzes thought experiments as arguments and maintains that all thought experiments can be reconstructed into argument form without any epistemic loss and that the “actual conduct of a thought experiment consists in the execution of an argument” (Reference Norton and Hitchcock2004, 50). Norton has reconstructed many thought experiments into arguments and holds that there are no examples that cannot be handled in such a way. Consequently, their typical narrative form and any of their creative or, to use Norton’s terminology, ‘picturesque’ qualities are deemed epistemically redundant.

Salis and Frigg aim to offer an alternative to Norton, arguing that his view misses the importance of the imagination and the use of imagined particulars. They state that characterizing thought experiments as arguments “presupposes a propositional kind of imagination” (Salis and Frigg Reference Salis, Frigg, Godfrey-Smith and Levy2020, 7), and “the arguments leading to the general conclusions involve imagined scenarios and particulars” (16). However, it is difficult to see how their account departs in any significant respect from an argument view. In their analysis of Galileo’s case, which is the only thought experiment they discuss, they state: “Galileo deliberately imagines a certain hypothetical scenario, he develops a deductive reasoning leading to a contradiction, and he quarantines its content since he explicitly invites us to imagine a non-actual situation” (16).

Their view actually comes out stricter than Norton’s in certain ways. Norton has expanded his position to allow that the notion of argument involved in carrying out a thought experiment is broad, where valid logical inferences include informal reasoning and even reasoning with imagery; for example, a picture can be a premise in an argument as seen in some mathematical cases. Thought experiments are governed by a “very general notion of logic” (Norton Reference Norton and Hitchcock2004, 54). There is a worry with Norton’s view that the notion of argument becomes so broad that his position ends up trivial—the claim amounting to the idea that there is some reasoning or inference involved (Stuart Reference Stuart2016a). In light of this, I take Norton, as many have done in the literature, to be restricted to a narrower sense of argument.

The worry is that either Salis and Frigg’s propositional account, although insisting that there is a role for imagination, is stricter than Norton’s (broad) argument view or it is difficult to see what the distinction between Salis and Frigg’s propositional account and Norton’s (narrow) argument view is. A propositional view of the imagination in thought experiments therefore appears to collapse into Norton’s (narrow) account.

Salis and Frigg situate their account within a broader view of modeling and representation in general. They endorse the claim that models and thought experiments are examples of make-believe. The idea is that modeling involves engaging with fictions in a way that is analogous to our engagement with fictions in art such as reading literature and watching films. The make-believe view was developed by Walton (Reference Walton1990) in the context of representations in art. Simply put, the view is that models are representations that function as ‘props’ that prescribe imaginings.

Given my claim that their account is strongly aligned with Norton’s narrow view, what is the role for make-believe? And what is the relation between propositional imagination, argument, and make-believe?Footnote ⁶ The problem is that it is hard to see the benefit of treating thought experiments as fictions in the Walton sense over Norton’s narrow view if the nature of the imagination is propositional (belief-like) and thought experiments involve deductive reasoning.Footnote ⁷ Meynell gave an earlier account of thought experiments as make-believe and raises a similar concern. She argues that if we were to maintain that the imaginings prescribed follow the logical form of beliefs, and the relations between beliefs, then it is not clear how they would differ from Norton’s background assumptions (Meynell Reference Meynell2014, 4165).Footnote ⁸

Second, although my focus is on thought experiments, I want to suggest that there are relevant differences between thought experiments and models that may affect the nature and role of the imagination in their conduct and, thus, undermine a “one size fits all” account of the scientific imagination. Salis and Frigg are right to stress similarities between thought experiments and models, and they show that bringing the two together offers a fruitful way of thinking about the imagination in science. Both involve creating and engaging with idealized hypothetical scenarios, and because of this, some have argued that “models are often experiments in thought” (Cartwright Reference Cartwright, Frigg and Hunter2010, 19) or that models are cases of “extended cognition” (Thoma Reference Thoma2016). Further, it is often claimed that they share important similarities with experiment: they offer a description of an initial setup that is then manipulated for us to consider what would happen. Yet they each depart from experiment in that they do not involve intervention in the world. Salis and Frigg also acknowledge some distinctions between thought experiments and models, such as the fact that the former does not include the ‘formal apparatus’, that is, mathematical reasoning to provide a formal proof, which is present in the latter.

I agree that scientific models involve the imagination in some way, and perhaps refer to imaginary objects or systems, and I do not want to advocate a strict distinction between models and thought experiments. However, I want to note that we should attend to their differences when giving an account of the imagination involved in their use: (a) imagination is sufficient for carrying out a thought experiment but not a model that has an underlying formal apparatus. No calculations on paper or a computer are required when we carry out, for example, Galileo’s thought experiments. To use Thoma’s phrase “the phenomenon is established purely in the imagination” (Reference Thoma2016, 136). Therefore, thought experiments rely on an imaginative process in a way that models do not. Additionally, (b) the level of complexity in models is a key difference between them and thought experiments; the latter are typically simple, and in fact much of their value seems to rest on this simplicity. Whereas, as Weisberg highlights, imagery is limited in many cases of modeling: “while it is relatively easy to imagine [to form ‘mental pictures’ of] the content of finite, deterministic, individualistic models like a population of genes undergoing assortment, it is unclear that this procedure could generalize to more complex cases” (Reference Weisberg2013, 63).

And so, there might be differences with regard to the type of imagination involved in various areas of scientific practice. In the remaining sections, I turn to the varied nature of the imagination across scientific thought experiments.

3. What Kind of Imagination Do Thought Experiments Invite?

So far, we have seen that the imagination in thought experiments has been taken to be imagistic. Salis and Frigg propose a different, propositional view. I agree with Salis and Frigg that the imagination in thought experiments should not always be characterized in terms of imagery, and it can be a matter of entertaining propositions. We can also hold that some aspects of conducting individual thought experiments will not require sensory imagination. But I disagree with the scope of this claim. While we can attempt to rationally reconstruct thought experiments into a propositional or argument form, the idea I wish to defend is that, at least sometimes, this will lead us to miss important features involved in their use in scientific practice. This includes the ways in which scientists call on our imaginative capacities to convince us of an outcome or help us understand a theory or problem.

Further, it seems plausible that some people will find reasoning via visualizing more useful than others and may even require this form of imagination in order to arrive at an outcome. For some, accompanying imagery will not or cannot be present, or if it is, it will not always be necessary. Because of this, I want to shift the attention toward a different, but related, issue. This is the question of: What do thought experiments ask us to do? What kind of imaginative engagement do they invite? I draw on Balcerak Jackson (Reference Balcerak Jackson, Kind and Kung2016), who argues that imagining, conceiving, and supposing are three different cognitive activities that each plays a distinct epistemic role. For example, Thomson’s violinist thought experiment invites us to “vividly represent the scenario from the perspective of the experiencing subject” (45), whereas supposing that there are, say, finitely many prime numbers does not require us to picture or simulate an experience. Instead, we are asked to use our ability to ’‘think a thought with a particular content” (51).Footnote ⁹ I will stick to the broader distinction between propositional and nonpropositional imaginings.Footnote ¹⁰ My aim is to show that in the spirit of Balcerak Jackson’s account, different thought experiments invite different types of cognitive activity.

This emphasizes the importance of paying close attention to particular examples. Salis and Frigg rely on one case and then generalize to all other scientific thought experiments. Similarly, the mental model theorists often talk in very general terms about reasoning in problem-solving contexts to then make claims about scientific thought experiments. I argue for a pluralist view: if we look to a range of cases, and think about what their function is, we can see that there are different requirements of our imaginative capacities when engaging with different thought experiments.

4. Pluralism

Let’s begin with a case of a scientific thought experiment that seems to invite us to propositionally imagine only, where any objectual or experiential component is unnecessary. We can look to one of Darwin’s “imaginary illustrations” as an example: “Let us take the case of a wolf, which preys on various animals, securing some by craft, some by strength and some by fleetness; and let us suppose that the fleetest prey, a deer, for instance, had from any change in the country increased in numbers, or that other prey had decreased in numbers, during that season of the year when the wolf is hardest pressed for food. I can under such circumstances see no reason to doubt that the swiftest and slimmest wolves would have the best chance of surviving, and so be preserved or selected” (Reference Darwin1964, 90).

The function of the thought experiment is to demonstrate Darwin’s theory’s explanatory potential, as opposed to provide evidence in support of natural selection (Lennox Reference Lennox, Horowitz and Massey1991). Here, it seems that we are not required to picture the wolf and the properties it is described as possessing. Nor does the thought experiment ask us to adopt a perspective of the scenario. The language is descriptive, the thought experiment refers to concrete objects and processes, and it is of course possible to visualize aspects of it. But I think a Salis and Frigg–type analysis would be right in this case: to succeed, the thought experiment merely requires that we grasp its propositional content—we imagine that there is a wolf, and so on, with no mental imagery of a wolf or phenomenal component of seeing or feeling a wolf required.

There have been many candidates of thought experiments, or thought experiment–type reasoning, that cannot be reduced to a (narrow) argument form. For instance, those that involve spatial reasoning such as seeing that a square object will not fit through a circular hole (Cooper Reference Cooper2005, 332) or performing mental rotations of shapes. But I will focus on an example from the scientific domain: Maxwell’s demon.

The function of Maxwell’s demon is to help us reconcile our belief in the practical inviolability of the second law of thermodynamics—that the entropy of an isolated system cannot decrease—and the in principle violability that is a consequence of Maxwell’s theory. It describes a demon who can control a “door” separating a box of hot gas with faster moving molecules and a box of cold gas with slower moving molecules. The demon can selectively open the door so that heat flows from the cold gas to the hot gas, making the hot side hotter and the cold side colder. This violates the second law.

The example asks us to adopt the position of the demon who has a capacity greater than our own and to form a visualization of the box and the molecules from the demon’s perspective. This results in our understanding that the fact that we will not experience violations of the second law is down to our lack of capacity to do what the demon does, that is, track the individual molecules. Stuart states that the example works by relating the second law of thermodynamics to experiences that we already have: “We may have trouble imagining a being that can see molecules, but if we imagine ourselves in an analogous position say, in control of a sliding door, surrounded by molecules which act like medium sized rubber balls, we understand the scenario perfectly” (Reference Stuart2016b, 27).

The role of thought experiments is not limited to providing us with propositional knowledge—the function of many is to increase our understanding. Understanding is a topic of significant interest in current philosophy of science, and some have drawn links between scientific understanding and visualization (e.g., de Regt Reference de Regt2017). In the context of theories, he argues that visualization is an effective way to achieve understanding; scientists tend to prefer visualizable theories over more abstract ones and find pictorial representations helpful in understanding. De Regt states that this is to be expected given that imagining in this way involves well-developed visual capacities that are used every day (257). Thought experiments are one way in which theories can be made intelligible, and it appears that in the demon case Maxwell deliberately engages our nonpropositional imagination to help us understand the second law of thermodynamics.

What other candidates are there for thought experiments that ask us to do more than to consider a set of propositions (i.e., those that ask us to put ourselves in a particular situation, visualize a state of affairs, or imagine what we would observe)? An example is Einstein’s elevator. Here, we have a shift in perspective between two different people, and we think about what they would see. Yet another case from Einstein, the chasing a beam of light thought experiment, is similar: Maxwell’s electromagnetism and Newtonian mechanics give different predictions as to what one would observe, and the thought experiment allows us to grasp the force of this tension. Further, Starikova and Giaquinto (Reference Starikova, Giaquinto, Stuart, Fehige and Brown2017) discuss how mathematicians imagine using visual mental imagery (that differs from applying mathematical rules) in examples of thought experiments in knot theory, graph theory, and geometric group theory, which contribute to mathematical knowledge.

As mentioned, a propositional view of the imagination in science does capture some of the reasoning involved in thought experiments, and a proponent of that view may insist that we could reconstruct all of the above examples within the propositional framework. But it is evident that scientists and mathematicians use their visual imaginations while engaging with certain thought experiments and have reason to invite members of the community they are communicating with, whether scientific or public, to do the same. A complete account of the imagination in science needs to accommodate such instances, and a pluralistic view clearly does.

5. Conclusion

We have seen that philosophers have typically taken the imagination in scientific thought experiments to consist in mental images. A recent challenge insists that it is only a propositional form that is required. I have argued that, while I think this offers an important insight into how some thought experiments work, or how aspects of thought experiments work, I disagree with the scope of the claim. If we ask: What do thought experiments ask us to do? it becomes evident that they appeal to a variety of our imaginative capacities, and some demand a type of imaginative activity that goes beyond the consideration of propositions. Consequently, we should embrace the richness of the imagination and the different resources it can bring into play when thinking about how scientists construct thought experiments for different purposes. I have argued that we should adopt a pluralist stance rather than limiting an account of the imagination in thought experiments to one type, whether imagistic or propositional.