CEEOL copyright 2017 CEEOL copyright 2017 9 Croatian Journal of Philosophy Vol. XVII, No. 49, 2017 Imagination: A Sine Qua Non of Science MICHAEL T. STUART Centre for Philosophy of Natural and Social Science London School of Economics, UK What role does the imagination play in scientifi c progress? After examining several studies in cognitive science, I argue that one thing the imagination does is help to increase scientifi c understanding, which is itself indispensable for scientifi c progress. Then, I sketch a transcendental justifi cation of the role of imagination in this process. Keywords: Imagination, understanding, thought experiments, scientifi c progress, schema, problem of coordination. Blaise Pascal called the imagination that "deceitful part in man, that mistress of error and falsity." He said it was "all-powerful," and the "enemy of reason." Malebranche referred to imagination as the "madwoman in the house," and many fi ctional and historical catastrophes can indeed cite specifi c over-active imaginations at their roots. It is imagination that leads Goethe's young Werther to his infamous sorrows, and it is behind the ambition of Macbeth. Chapter eleven of Mein Kampf provides an actual and far more horrifying instance of the imagination being used to justify evil actions. According to George Orwell, Hitler saw himself as "the martyr, the victim, Prometheus chained to the rock, the self-sacrifi cing hero who fi ghts single-handed against impossible odds. If he were killing a mouse he would know how to make it seem like a dragon" (Orwell 1940). Yet, to reverse the sexist skepticism of Pascal and Malebranche, without imagination we could have no goals, no ethics, no knowledge. In the refl ections of scientists we see tribute paid to the imagination quite regularly. Francis Jacob, a Nobel Prize winning biologist, recently wrote: It was not a simple accumulation of facts that led Newton, in his mother's garden one day, suddenly to see the moon as a ball thrown far enough to fall exactly at the speed of the horizon, all around the earth. Or that led Planck to compare the radiation of heat to a hail of quanta. Or William Harvey to CEEOL copyright 2017 CEEOL copyright 2017 10 M.T. Stuart, Imagination: A Sine Qua Non of Science see in the bared heart of a fi sh the thudding of a mechanical pump. In each case they perceived an analogy unnoticed up till then. As Arthur Koestler pointed out, everything in this way of thinking seems different from that of King Solomon when he compares the beasts of his beloved Shulamite to a pair of fawns, or that of Shakespeare's Macbeth, when he sees life as "a tale told by an idiot, full of sound and fury." And yet, despite the very different means of expression used by the poet and the scientist, imagination works in the same way. It is often the idea of a new metaphor that guides the scientist. An object, an event, is suddenly perceived in an unusual and revealing light, as if someone abruptly tore off a veil that, till then, had covered our eyes. (Jacob 2001: 119) Jacob reminds us that no agglomeration of facts can give us the power over nature that science seeks, or the beauty and novelty of art. Dustin Stokes (2014) argues that even if Bach had known all there was to know about musical relationships, this still would not have been suffi cient to compose The Well-Tempered Clavier (159–160). This resonates with Jacob's claim above; whatever is going on in scientifi c discovery, it is not merely the collection of facts. Other Nobel Prize winning scientists gesture to similar senses of imaginative artistry and its necessity in their work (e.g. Einstein 1931, 97, 1934, 163; c.f. Holton 1996, Hadamard 1996). However, it was common in the philosophy of science for a long time to hold that the imagination was not epistemologically relevant other than in the context of discovery. Partially thanks to the growing infl uence of science studies since the 1960s, many philosophers and cognitive scientists have reversed this trend, and now see the imagination as an important factor in the production of knowledge and other epistemological desiderata. One reason for this change was the dissolution of an absolute distinction between the contexts of discovery and justifi cation. Another is the recently emphasized role of the imagination in scientifi c thought experiments. René van Woudenberg, in his introduction to a special issue of Metaphilosophy on thought experiments, claims that "the imagination, perhaps surprisingly, plays an important role in the process of obtaining knowledge: knowledge of certain normative issues, of possibilities, of moral truths, of certain physical matters, of one's self, and more" (van Woudenberg 2006: 160; see also Byrne 2005, Currie and Ravenscroft 2002, Kind 2016, Kind and Kung 2016, McGinn 2004, Salis and Frigg forthcoming, Stuart et al. 2017). To support such a claim, some philosophers have argued that because normative, modal and ethical truths are not accessible to empirical investigation, they must be the result of mental investigation (whether rational, as in Brown 2012, or naturalistic as in Nersessian 2007 or Miščević 2007). Considering possible worlds is one way the imagination might play a role in the divination of such truths. For example, the imagination is crucial in making the inference from conceivability to possibility, which is attacked and defended as a means (or mere guide) to modal knowledge (see Gendler and Hawthorne 2002). CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 11 I would like to look again at the epistemological role of the imagination in science, specifi cally through the use of thought experiments. Assuming that thought experiments play some role in scientifi c progress, I want to fi nd out the nature of that role, and the nature of the epistemic good produced. To do this, I am going to present some results from cognitive science that ask what scientists and students of science learn from thought experiments, and how. One problem with discussing the role of the imagination is that cognitive science studies rarely refer to the imagination in a general way. Instead they refer to mental images, analogy, metaphor, counterfactual reasoning, mental models, and so on. We fi nd something similar in mainstream analytic philosophy, which deals with the imagination as something that tests modal propositions by seeing whether they are conceivable, or produces psychological states which obey special norms, and much else. (See Gendler 2013 for a sample of ways philosophers characterize imagination). In order to connect empirical and epistemological issues, then, I maintain an inclusive reading of the imagination, delimiting not much more than the mental ability to interact cognitively with things that are not now present via the senses. These cognitive interactions need not be propositional or static (like images), and to allow conceptual space for rationalism, their content need not consist entirely of permutations of previous experience. If we like, we could add the requirement that the cognitive interactions depart from the truth (following Stokes 2014), which is a reasonable requirement if we want to defi ne the sort of imagination that goes into creating something truly novel, but I do not think it is necessary at this level of investigation. Imagining a Boeing 747 at the bottom of the Mariana trench is no less an imagining if there is in fact a Boeing 747 there. One preliminary conclusion after looking at results in cognitive science is that an important and mostly overlooked use of scientifi c thought experiments is to create understanding as opposed to knowledge. Even though explaining how thought experiments increase scientifi c understanding would partially address the "primary philosophical challenge" of thought experiments (see Brown and Fehige 2011), many writers focus on the ability of thought experiments to provide new knowledge, empirical evidence or empirical information. Still, increasing understanding is just as epistemologically interesting as providing new knowledge, and in the second half of this paper I will investigate this use of thought experiments. Let us now turn to results in cognitive science. Kosem and Özdemir have recently claimed that imagination "is an indispensible component of scientifi c reasoning" (2014: 887), and many others agree (e.g., Brown 2006; Clement 1993, 2008, 2009; Gilbert and Reiner 2000; Klassen 2006, Lattery 2001; Reiner and Burko 2003; Reiner and Gilbert 2004). Still, it is not immediately obvious how we should go about investigating scientifi c imagination. One way is to consider historical cases. CEEOL copyright 2017 CEEOL copyright 2017 12 M.T. Stuart, Imagination: A Sine Qua Non of Science Stephens and Clement (2012) argue that even though such an exercise may be helpful, it is not enough to discern the cognitive mechanisms that underlie imagistic mental reasoning of the type we fi nd in scientifi c thought experiments. They write: It is diffi cult to analyse the mental processes that allow a scientist to generate and run a thought experiment during an investigation by using historical data because the original thought process can easily be buried under many changes and refi nements the author carries out before publishing a thought experiment. Also, for many thought experiments it is hard to know whether they were originally part of a discovery process or created after the investigation to convince others. (Stephens and Clement 2012: 160) Historical details can only take us so far; we must also study thinking agents in real-time. I will summarize the results of several such studies here. First I will look at studies done on thought experiments in science education, and then I will consider studies of the way thought experiments are spontaneously invented in scientifi c problem-solving, both by students and experts. Reiner and Gilbert (2000) discuss thought experiments in textbooks by fi rst cataloguing which thought experiments appear where, and for what purpose. Then they compare the original and textbook presentations of famous thought experiments. They conclude that thought experiments help students and scientists understand scientifi c concepts. What does it mean for a thought experiment to help us understand something? They cite Stephen Toulmin (1972) who explicates understanding a concept in terms of being able to use it. A concept of any kind is capable of use, and therefore understood, if two criteria are met: it is meaningful, in that the user knows what it means; and it is fruitful, in that it enables the user to achieve a goal or to identify new possibilities. (For an extended discussion of these criteria as evidence of the achievement of understanding in science, see Stuart 2016). I highlight this characterization of understanding because most of the below-mentioned studies are easily brought under its framework – especially if we include not just concepts but what can be called theoretical structures, a term I use to refer to concepts, models, theories, principles, laws, etc. Scientists and their students must be able to use new theoretical structures, otherwise they serve no purpose. And one cannot use a structure without knowing what it means, or in other words, without the structure being meaingful. Meaningfulness is not always so easy to achieve, especially in science, and we will see that thought experiments can sometimes assist in affording this desideratum. Also, if one understands a theoretical structure, one can usually achieve something with it. Thought experiments help us explore the consequences of adopting certain structures, and see how conceptualized phenomena interrelate, and this opens up new possibilities for theorizing, modeling, and constructing experiments. Building on this framework, Reiner and Gilbert argue that thought experiments in science textbooks (as opposed to those in scientifi c jourCEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 13 nals), are not used as effectively as they could be. In scientifi c literature, most thought experiments are presented in the following way: We begin with a scenario or problem-statement. We create an imaginary world to help us explore the scenario or problem. We "set up" or "design" a thought experiment in this imaginary world, which we then "run" and "observe." Finally, we draw a conclusion about the initial problem or scenario. This presentation-style spurs members of its audience to make new connections on their own. Textbooks, on the other hand, often present the conclusion of the thought experiment fi rst, and then the imagined scenario is introduced, which lends credence to the conclusion. In this style of presentation, students do not vary variables in their minds; they simply follow along a text (Reiner and Gilbert 2000). This is suboptimal for achieving the conditions of meaningfulness and fruitfulness. If you do not perform the thought experiment or otherwise establish the semantic connections for yourself, a theoretical structure will have diminished meaning for you. It is also less likely that you will see all the ways to make the structure fruitful. (For other ways of making theoretical structures meaningful and fruitful see Stuart 2017). Velentzas, Halkia and Skordoulis (2007) look at textbooks as well, and they show that what James R. Brown calls "constructive" thought experiments (Brown 1991: 36), i.e., those that provide evidence for or establish a theory, are preferred by textbook authors to what Brown calls "destructive" thought experiments (Brown 1991: 34), which function as counterexamples. The thought experiments used most commonly in physics textbooks are Einstein's train, Einstein's Elevator, and Heisenberg's Microscope, which the authors classify as constructive. Perhaps these are so popular because thought experiments like these show students how their everyday experiences relate to modern day physical theory (Velentzas, Halkia and Skordoulis 2007: 365ff.). In other words, such thought experiments might "build bridges between students' knowledge and everyday experience and the new or modifi ed concepts and principles which have to be learned" (359). Building such bridges would certainly help to make new concepts meaningful and fruitful for students. This study inspires several more by Velentzas and Halkia. In the fi rst (2011), they discuss Heisenberg's Microscope "as an example of using thought experiments in teaching physics theories to students." They begin by citing Alexander Koyré, who claims that thought experiments "help scientists to bridge the gap between empirical facts and theoretical concepts" (Koyré 1968). Agreeing, they argue that while Heisenberg's microscope thought experiment is not generally well regarded by physicists (either at Heisenberg's time or now), the thought experiment is still quite useful for introducing the uncertainty principle in quantum mechanics, which they taught to 40 high school students in grade 11 using the thought experiment. First, they introduced some important concepts from quantum mechanics, and then let the students work through the thought experiment mostly on their own. CEEOL copyright 2017 CEEOL copyright 2017 14 M.T. Stuart, Imagination: A Sine Qua Non of Science That is, through Socratic question and answer, the students were allowed to work through their guesses, and if they went too far off track, they were gently guided back. Velentzas and Halkia recorded the sessions in order to code and analyze them, and two weeks later administered a test for comprehension. They concluded that many students did come to understand the uncertainty principle from the thought experiment. And not merely for the case of gamma rays and microscopes; they appreciated the principle independently of any considerations of specifi c measuring apparatuses. Next they turned to special and general relativity (2013a). Again the authors found that thought experiments in relativity make it possible for students to "grasp physical laws and principles which demand a high degree of abstract thinking, such as the principle of equivalence and the consequences of the constancy of the speed of light to concepts of time and space" (3026). They found this achievement more surprising than in the case of the uncertainty principle, because students have very strong folk intuitions which interfere with understanding General relativity theory. Students generally did not understand the concept of inertia and they assumed that their intuitive concept of simultaneity could not be wrong, that space is empty and separate from time, and that an observer's point of view has no bearing on physical laws as there is always an encompassing frame from which an objective state can be observed (Arriassecq and Greca 2012). However the authors did manage to convey the concepts of relativity theory to the students successfully, letting them work through Einstein's elevator and train. They recorded the sessions and analyzed them, and then administered a test two weeks later for comprehension. From their success they concluded that thought experiments are used "both for clarifying the consequences of physics theories and for bridging the gap between the abstract concepts inherent in the theories and everyday life experiences" (3027). Finally, in their (2013b) the authors turned to Newton's Cannon. As in the above two cases, the authors got a group of students to work through the thought experiment on their own, and to see that projectile motion and orbital motion are governed by the same laws. The authors claim that Newton's thought experiment "can act as a bridge which enables students to correlate the idea of the 'downward' motion of objects drawn from their everyday experience with the same objects' motion 'to the center of the Earth'" (2623). To make this possible, students had to see the Earth as if from above, and extend their knowledge of regular projectile motion to a scale large enough to represent both suborbital and orbital motion. This allowed them "to link the motion of a projectile as it can be observed in everyday situations with the possible case of a projectile that can move continuously parallel to the ground in a context where the whole Earth is visible" (2623). The metaphor of "bridging" is common to all of these studies, and continues to be invoked below. I think it is signifi cant because it relates to both meaningfulness and fruitfulness. When a bridge opens, new terCEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 15 ritory becomes accessible. The territory was already there, but we did not have access to it. A theoretical structure is not made fruitful by a thought experiment if that thought experiment does not make possible new and identifi able uses of the structure, and one way it might do this is by connecting the theoretical structure via "bridges" to existing concepts, background theoretical knowledge, experiences and skills. Such activity can also provide semantic content to the theoretical structure, rendering it (more) meaningful. Velentzas and Halkia conclude that thought experiments are useful in education because they help students learn to apply diffi cult scientific concepts. But there are two other interesting conclusions they draw in their (2013b). One is that thought experiments are pedagogically superior to computer simulations, because only in a thought experiment is it completely up to the student to determine how the outcome of an imagined scenario results from the set-up. A computer simulation where the earth is seen from above and the student can program in different projectile velocities and see how these changes affect the motion of a projectile was useful, and certainly better than merely calculating consequences of Newton's laws. But in these cases the student takes a passive role by setting the parameters and waiting to see what happens. In a thought experiment, students mentally "set" the parameters, and then in addition have to fi gure out what will happen. And instead of trusting to the algorithms of a computer, students must provide some reason to believe the system will evolve as it does in their imaginations. Also, talking through imaginary scenarios enables teachers to see where a student stands with respect to their comprehension of the theory. Therefore the authors conclude that there is good evidence that thought experiments will not be replaced by computer simulations in the near future, at least in the classroom. This is related to their second important conclusion, that "in any experiment, the manipulation of ideas is more important than the manipulation of materials" (2638). That is, "hands on is less important as compared to minds on" (Duit and Tesch 2010). Presumably the authors mean that manipulating laboratory equipment is pedagogically less useful to a student who does not grasp the deeper meaning behind these events. And with respect to the goal of increasing scientifi c understanding, this is something worth stressing. Now that we have discussed some of the fi ndings of thought experiments in science education, let us look at how thought experiments originate in situ. In "The Symbiotic Roles of Empirical Experimentation and Thought Experimentation in the Learning of Physics," Reiner and Gilbert argue that in the course of solving empirical problems, subjects often construct and run thought experiments spontaneously. They conclude that "the process of alternating between these two modes-empirically experimenting and experimenting in thought-leads towards a conCEEOL copyright 2017 CEEOL copyright 2017 16 M.T. Stuart, Imagination: A Sine Qua Non of Science vergence on scientifi cally acceptable concepts" (2004: 1819). In other words, thought and empirical experiments appear in conjunction, and this is for the best, because together they enable us to go from "seeing" a physical phenomenon to "knowing" about it (1820). The evidence for this is the following. Reiner and Gilbert asked students to analyze a physical mechanism that behaved in an unexpected way. Two heavy wheels were set next to one another into a base, and each was free to spin. If one was made to spin quickly, the other would do nothing. But as it slowed down, the other would begin to spin and speed up, until the fi rst came to a complete stop. When the second wheel began to slow down, the fi rst would start spinning again. The reason for this behaviour was a set of hidden magnets contained in the wheels. Given a list of the materials out of which the mechanism was built, the students were asked to fi gure out what was going on. Different sets of students were all observed to follow a similar methodology: they began by identifying the various physical mechanisms in a general way using concepts like force, acceleration, weight, direction, and so on. They used these to construct various (mental or physical) models to capture what they observed. Then they abstracted their models further into what the authors called a "representational space," where the relationships between features of the mechanism were represented, often with the help of pen and paper. Finally, the students created and used imaginary worlds to test their models using thought experiments. The authors claim that instances like these show "how concepts emerge out of touching and seeing. A student forges links between the bodily and the mental, between the physical and the cognitive, faculties" (2004: 1831). Despite the reference to knowledge, the epistemological state in question is better described as understanding. Most of the knowledge discussed in traditional epistemology is propositional. And links between bodily, mental, physical and cognitive faculties, while they can be expressed in propositions, are not propositions themselves. Also, establishing connections between parts of theory and experience is typically referred to as "objectual understanding," which is grasping the "coherence-making relationships" in a comprehensive body of information (Kvanvig 2003: 192). And it can be produced by thought experiments (Stuart 2017). In a different study, Kösem and Özdemir (2014) collected three groups of subjects, each with a different level of expertise in physics, and presented them with diffi cult problems drawn from dynamics or mechanics. The fi rst group was made up of doctoral graduates, the second was university undergraduates, and the third was high school students in grade 12. The total number of thought experiments invented by each of the three groups was roughly equal. In terms of the means of the thought experiments, each student either modifi ed an object in an imaginary scenario (for example, the size CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 17 of a car), or a variable (its velocity). When they modifi ed the object, they did so either to match a more familiar case with which they had previous experience, or a simpler case, for example, by dissecting a problem into several smaller, easier problems. When they modifi ed a variable, they either eliminated or minimized the variable's value to eliminate its infl uence altogether, which helped them focus on the relationships of other variables, or they increased the value of a variable to make its effect on the system more obvious. In general, changing the problem to a more familiar case by modifying the object was the most common type of thought experiment strategy used by the undergraduate and high school groups. Modifying the variables was used quite often by the doctoral group, and very seldom by the others. In terms of purpose, there were several. Sometimes a subject would have an intuition, which they explored with a thought experiment. This use was labelled "prediction." Other times a subject might have an independent reason for believing something, which they chose to illuminate with a thought experiment while trying to report or justify it. This was labelled "explanation." Other times the thought experiment played the role of a proof. The undergraduates used thought experiments as a proof more than any of the other groups. The high school students and doctoral graduates very rarely used thought experiments as proof. Across all three groups, however, by far, "the most frequently observed purpose of using a thought experiment is for 'explanation'" (882). That is, "to communicate ideas, or exemplify the solution" (879). Finally, there are studies focused on the use of imagination by expert scientists in vivo. First, Trafton, Trickett and Minz (2005) ask if scientists use the imagination to manipulate mental representations. They conclude that they do. They argue that scientists create what Clement later calls "overlay simulations" (2009) between external and mental representations. That is, they compare and align mental and external representations, checking for fi t or feature-similarity. The authors found that the scientists manipulated spatial representations more often in their heads than they did using their computers (2005: 97). In a second study, Trickett and Trafton (2007) built on these results, arguing that scientists spontaneously invent "small-scale" or "local" thought experiments (867) in times of "informational uncertainty" (843). Scientists perform thought experiments in such conditions to "develop a general, or high-level, understanding of a system" (844). The authors focus on the data analysis phase of research, in which scientists must negotiate uncertainty to see what information the data presents, and interpret it. Employing "what if" reasoning helps scientists test out alternate interpretations of the facts, fi ll in holes in their data, and see how their data fi t with existing research questions and background theories. They predict that thought experiments "will be used by experts when they are working either outside their immediate area of expertise or on their own cutting edge research-that is, in CEEOL copyright 2017 CEEOL copyright 2017 18 M.T. Stuart, Imagination: A Sine Qua Non of Science situations that go beyond the limits of their current knowledge" (867; cf. Corcilius 2017 who argues that this is (roughly) how Aristotle used thought experiments)). If the empirical results I have mentioned are on the right track, there is a great deal that is philosophically interesting here. In almost every one of the above studies, one of the main conclusions is that thought experiments are important because they bridge conceptual/ theoretical knowledge to previous experience, existing knowledge and abilities. What does this tell us about the epistemological role of thought experiments in science? If we separate the action of bridging existing instances of knowledge from the action of creating new instances of knowledge, we see that thought experiments are often instances of the fi rst kind of action, whether or not they are instances of the second. Thought experiments are more often used to explore or interpret conceptual solutions to problems, communicate ideas, or model scenarios, than they are to provide solutions to problems. That is to say, the performance of a thought experiment usually increases understanding rather than producing new knowledge. In fact, Özdemir (2009) argues that students learn to shy away from using thought experiments as evidence in physics as they mature, although they do not shy away from using them to communicate and explore. It is possible that this trend maintains itself in the professional careers of scientists everywhere. It is also important that all of the above studies produce results that support the idea that thought experiments create understanding in one of the two ways mentioned at the start. Velentzas and Halkia showed that students use thought experiments to bridge empirical knowledge and theoretical structures. Gilbert and Reiner saw a symbiotic relationship between thought and empirical experiments, which were performed in a way that "negotiated concepts" through communication and exploration, making a student's concepts and models intelligible to him or herself, and also to his or her peers. Stephens and Clement argued that thought experiments "appear to have considerable value as a sense-making strategy" (2006: 1). Kosem and Özdemir found that the most common use of thought experiments across different groups was to "communicate ideas or exemplify a solution." Trafton, Trickett and Mintz found scientists employing thought experiments to compare, align and manipulate representations, especially for communication. For each of these cases, the value of sense-making thought experiments derives at least partially from the fact that if we do not make sense of a theoretical structure we cannot make use of it. Let us turn to some considerations of these results. First, these roles that we have just identifi ed are epistemological. And since these roles produce understanding as opposed to knowledge, we are able to draw on the quickly expanding resources in the philosophy of understanding. Understanding, like imagination, was rejected as a topic of CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 19 serious study in the philosophy of science around the time of the logical positivists, because it was associated with a psychological and subjective feeling (especially by Hempel; see de Regt et al 2009: 3–5; de Regt 2009: 22–24). This feeling might be an outcome of good science and provide clues concerning what should be investigated next (see Lipton 2009, Grimm 2009, Thagard and Stewart 2011), but it might also be irrelevant or misleading (see Ylikoski 2009). Leaving the positivistera characterization behind, philosophers now consider understanding in many different senses. As with "thought experiment," a vague but useful term, we can say interesting things to differentiate understanding from other epistemological states in the absence of a necessary and suffi cient defi nition. One kind of understanding is "mediated," that is, it comes by means of a model, an experiment, a theory, a thought experiment, an explanation, or something else. One way to know if such mediating entities provide increased understanding is to ask about abilities. When we understand something, we can use it in new ways. We can relate what is understood to new and old knowledge, and to abilities we already had. This is why I continuously return to the meaningfulness and fruitfulness of theoretical structures. If we look at the thought experiments used in the aforementioned studies and in the history of science, we see that very many make some concept(s) more meaningful and fruitful, and so increase (evidence of) understanding. In Stuart (2016) I showed that Maxwell's demon, Darwin's eye, and the clock-in-the-box all provide this sort of understanding by connecting theoretical structures to experience, existing knowledge or abilities. Others try and fail, including Heisenberg's microscope and Darwin's whale. I think we can extend the argument easily to many other thought experiments including Einstein's elevator and train, EPR, Galileo's falling bodies, and Stevin's prism. If thought experiments perform this function, this is no obstacle to their also serving as evidence for or against theoretical claims. That is, they could provide both understanding and knowledge, although it is understanding I am interested in here. How might thought experiments provide both knowledge and understanding? First, I hope it is clear that the same thought experiment can have several different uses at different times or for different people. For example, Schrödinger's cat was once used to attack the Copenhagen interpretation of quantum mechanics, and now it is used to introduce physics students to superposition and entanglement. One might argue that we have here two different thought experiments, but it is the same imagined scenario drawing on similar underlying assumptions, even if it is used for a different purpose in the two cases. If it is the same thought experiment, then the same thought experiment is at one time used by experts as an argument against a theory, and later by teachers and students for pedagogical reasons (see Bokulich and Frappier 2017 for more on the identify conditions of thought experiments). Now, is CEEOL copyright 2017 CEEOL copyright 2017 20 M.T. Stuart, Imagination: A Sine Qua Non of Science it possible that the same thought experiment can play more than one epistemic role, for the same person (or community), at the same time? Yes: thought experiments like Heisenberg's microscope, Schrodinger's cat, Einstein's elevator and others, are simultaneously used by scientists to make sense of diffi cult new theoretical structures, which increases their scientifi c understanding by helping them connect abstract theoretical structures either to experience or to previously unconnected parts of theory. In addition to serving this purpose, many of these thought experiments simultaneously or derivatively use this new understanding to attack, subvert, popularize or explain a theory or theoretical interpretation. The application of new understanding often results in new knowledge. There is a complementary idea present in the work of Hans Radder on laboratory experiments (1996), which Sören Häggqvist (1996) and Tim de Mey (2003) applied to thought experiments. The idea is that the performance of an experiment is different from the application of the result of that experiment to theory. These two actions are often confl ated in general discussions of scientifi c experiments. What I am suggesting is that sometimes the performance of a good thought experiment yields understanding, while the application of the result of that experiment yields knowledge. What is novel here is that thought experiments are quite frequently signifi cant for scientifi c understanding and not merely for knowledge. This idea has some nice consequences. For instance, it explains why many of the more famous thought experiments appeared in the later stages of their respective scientifi c revolutions. This is because they were meant to make sense of a new theoretical structure that had been introduced during the course of the revolution. If this is the case, the thought experiment could not have shown up earlier. The new quantum formalism was mathematically complete and empirically adequate by 1925, and Schrödinger's cat was not born until a decade later. Similar relationships obtain between Maxwell's demon and the statistical-mechanical interpretation of heat, Einstein's train and general relativity, the clock in the box and quantum mechanics, and many others. This idea also helps to explain the role of thought experiments in the rhetoric of science. If you can provide an intuitive interpretation of a theory, this can be a way to get others to accept that interpretation, and therewith, the theory. If I am convinced of the Copenhagen interpretation of quantum mechanics, it is necessary that I am also convinced of quantum mechanics. Likewise, for those who oppose a new and competing theory, the fi rst reaction is often to look for counterexamples, cases where the theory does not apply or that the theory cannot explain. And searching for counterexamples is itself an attempt to explore the connection between the new theory and the world (i.e., gain understanding of the theory's empirical content), and show that the proposed connection cannot be made (i.e., gain knowledge through falsifi cation). CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 21 This also explains the prevalent place of thought experiments in science textbooks and websites which aim to describe in general outline how this or that modern scientifi c theory works or what its content is. Thought experiments help students take the steps their intellectual ancestors took in order to understand a theory. And even if someone does not understand all the diffi cult theoretical structures invoked by a theory, they might still grasp some of the relationships between those structures and their previous experiences and knowledge via a thought experiment. This interpretation also sheds light on the role of thought experiments in scientifi c theory proliferation and "public marketing." If a theory has been developed in great theoretical or mathematical detail, but has not yet caught the eye of the greater scientifi c community, perhaps it is time to try some thought experiments. These may assist in securing funding and improving the theory's public image, since granting agencies and the public must be able to understand the theory to see it as pursuit-worthy. Late night infomercials on television encourage you to imagine yourself in some uncomfortable situation, from which only the Brand New Shining Product can save you. Thought experiments can also be powerful tools of advertisement that appeal to our intuitions and emotions via the imagination. Recognizing this power illuminates a new danger in thought experiments that was hidden until now: Since high-level understanding is one of the goals of science and thought experiments can provide it, they might be used (intentionally or not) to deliver merely apparent and not genuine understanding. Heisenberg's microscope is a potential example. While it does provide a way to visualize the uncertainty principle, it has been criticized harshly for doing so in a misleading way (see, e.g., Roychoudhuri 1978). This is an interesting issue, because general understanding, while a desideratum, might not always be achievable. Our cognitive abilities might not always be suffi cient for understanding our theoretical structures. Perhaps it has already happened in science that we have abandoned a good theory for a rival that was more easily intuited and understood, although false. Physicist Paul Dirac "regards models, images, pictures not only as redundant, but as dangerous. As long as the formalism and experimental results dovetail, theoretical physics has achieved its task" (quoted in Yourgrau 1967: 866). The Aristotelian theory of motion including natural places for the fi ve elements strongly appeals to the imagination and is easy to understand, and this is surely one of the reasons it was dominant for so long. This is a problem that needs to be understood, and accounted for, although there is some reason for optimism. It is true that once we pass into the microscopic domain or higher dimensions we fi nd it diffi cult to perform some kinds of imaginings, but this does not stop us from focusing on aspects of those systems that we can imagine. The entities that make up our world display a multitude of interesting properties, many of which stand in relaCEEOL copyright 2017 CEEOL copyright 2017 22 M.T. Stuart, Imagination: A Sine Qua Non of Science tions that can be visualized even if others cannot. The lesson is that, the more complicated our theories become, the more careful we must be with our imaginary examples. Finally, if thought experiments provide understanding, they serve a function which is indispensable for the progress of human science. Without understanding, we cannot use our knowledge, and without knowledge there is less to understand. These two features of science can develop independently for a while, but not for long. Even with the greatest division of intellectual labour, one stagnates in the absence of the other. According to Peter Kosso: "knowledge of many facts does not amount to understanding unless one also has a sense of how the facts fi t together" (2006: 173). He invites us to recall the Omniscienter from Pierre Dumal's novel A Night of Serious Drinking, over whose chair it reads "I know everything, but I do not understand any of it." Kosso suspects that "the Omniscienter has spent too much time gathering evidence and too little time thinking about it. He has taken the piecemeal empiricism too seriously and overwhelmed his science with observation. Too many data have left too little room for understanding. There are examples of knowledge without understanding in the physical sciences, and they are found in the most empirically dependent sciences or in any science at the time of new empirical discovery" (182). To this end, Steven Weinberg remarks that general relativity offers more understanding than does quantum mechanics, because the latter cannot easily be bridged to our other stores of knowledge. He sees the Copenhagen interpretation as a surrender to the incomprehensibility of the theory, throwing up our hands and asking for empirical accuracy only (Weinberg 1992, Kosso 2006: 184). If it is true both that we need to understand our theories, and that quantum mechanics is inherently diffi cult to understand, then we should expect a great deal of thought experiments in quantum mechanics, especially in the fi rst decades after the theory was introduced. And indeed, this is probably the period most replete with thought experiments in the history of science. (See Peacock 2017 for a detailed look at many of them). Many scientists explicitly seek connections between their theories and the world or other pieces of knowledge, which I have characterized above as a search for understanding. Ernst Mach remarked that there has to be what he called "coordination" between the variables of a theory and the aspects of the world to which it refers (see van Fraassen 2008). The temperature reading taken from a thermometer must refer to something real, not to another conceptual entity. Reichenbach extended the problem, noticing that even the coordinating relation, if we could create one, would only be another abstract relation, which we would again need to coordinate (1965). Einstein remarked that if we want to talk about rigid bodies and their behaviour, we must fi rst coordinate "experience[e]able objects of reality with the empty conceptual schemata of axiomatic geometry" (Einstein 1921). Einstein also spoke CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 23 of the "ever-widening logical gap between the basic concepts and laws on the one side and the consequences to be correlated with our experiences on the other-a gap which widens progressively with the developing unifi cation of the logical structure, that is with the reduction in the number of the logically independent conceptual elements required for the basis of the whole system" (1934: 165). In other words, scientists recognize the need for something to bridge the gap between our theoretical structures, including laws, concepts, equations and mathematical models, and the world. Further, Einstein considers the possibility that as physics becomes more refi ned and united, it must make use of more and more abstract notions and relations to connect all its information to experience. There is evidence that scientists have intentionally used thought experiments to solve this problem of coordination. Heisenberg showed in 1925 that the matrix and wave-mechanical formalisms of quantum mechanics were mathematically equivalent. Still, Schrödinger was set on the wave mechanical interpretation, and Heisenberg on the particle interpretation. According to Marten Van Dyck, Schrödinger called Heisenberg's theory a "formal theory of frightening, indeed repulsive, abstractness and lack of visualizability." And "'Heisenberg's theory in its present form is not capable of any physical interpretation at all,' was another claim made at the same time" (2003: 81). In response, Heisenberg began considering whether an interpretation focused on the particle nature of atomic elements could be visualized, and specifi cally whether in-principle observables could be simultaneously measured. "This was a turning point for Heisenberg's theory, because it led him to propose a visualizable interpretation of quantum mechanics through thought experiments based on the limits of measurement. Heisenberg wrote out all his ideas in a letter to Pauli at the end of February [1927], in an attempt, he said, to 'get some sense of his own considerations' as he groped towards a consistent theory" (Beller 1999: 105; emphasis added). Kristian Camilleri writes, "Heisenberg's introduction of the imaginary gamma-ray microscope was not intended primarily to demonstrate the limits of precision in measurement. Though it certainly did this, its real purpose was to defi ne the concept of position through an operational analysis. This becomes evident once we situate Heisenberg's use of imaginary gamma-ray microscope within the context of his concerns over the meaning of concepts in quantum theory" (2007: 179). Heisenberg's thought experiment was therefore a way to link the new theoretical structure to some empirical content, whether through operationalization or visualization, for Heisenberg, in dialogue with his peers. And this goes for many of the physicists of the period. Mara Beller writes, "most physicists, Bohr and Heisenberg included, wanted more: some feeling of understanding, of illuminating, or explaining the kind of world that quantum formalism describes. The need for this kind of CEEOL copyright 2017 CEEOL copyright 2017 24 M.T. Stuart, Imagination: A Sine Qua Non of Science metaphysical grasp is not merely psychological but social as well-the power of a successful explanation and the power of the effective legitimation and dissemination of a theory are connected" (Beller 2002: 107). This supports the notion that the understanding provided by thought experiments is important for many reasons, including pedagogy and popularization. But more importantly, it shows that scientists have been aware of this, and have used thought experiments for this purpose. What have we learned so far? Thought experiments have many epistemological uses, many of which generate understanding as opposed to (or in addition to) knowledge. And the imagination plays some role in this. How does it work? Perhaps those who characterize thought experiments as mental models have an answer. Nenad Miščević (2007) argues that the power of the imagination results from its having evolved as a useful predictive tool with its roots in normal perception. Nancy Nersessian agrees, stating that "the perceptual system plays a signifi cant role in imaginative thinking," which "makes sense from an evolutionary perspective" (2007: 136). While Nersessian does not claim that all the content that is manipulated by our mental models is perceptual or imagistic (142), she does "contend that a wide range of empirical evidence shows perceptual content is retained in all kinds of mental representations" (139). What grounds the epistemic use of thought experiments for Miščević and Nersessian is experience itself, and the usual cognitive and sensory faculties that provide empirical knowledge. Perhaps their justifi cation of the outcome of thought experiments through mental or neural mechanisms can also be used to help explain the epistemic value of thought experiments conceived as producing understanding. Let us examine this claim. The idea that we manufacture complex ideas from sensory experience via reason and imagination has its modern roots in British Empiricism. It is still well-supported empirically (see e.g., Prinz 2002) and is introspectively attractive. Nevertheless, there is something about the use of imagination in producing scientifi c understanding that seems left out of such a justifi cation. The thought experiments discussed above do not succeed because the imagination has its roots in perception or other cognitive processes that evolved to represent the world accurately. We might be right to trust knowledge claims concerning the output of an imaginary scenario that accurately models a system with which we have relevant experience. But in producing new meaning or new abilities, we do not need representational accuracy; we only need to create the right bridges between theory and experience, however that is done. And sometimes increasing representational accuracy would hinder rather than help. It's hard to conceive of Maxwell's demon in a more realistic way doing the same job. Einstein's elevator succeeds in giving content to the equivalence principle because it takes us away from normal perception and gives us a new means of conceiving CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 25 the world. Since this use of the imagination is different from the one that generates new knowledge, we need a different justifi cation for it. To do this, I will set up an analogy. Just as imagination can help to determine the content of perception, thought experiments can help us to determine the content of theoretical structures. There is support in cognitive science for the view that imagination can infl uence the content of perception. First, patients who have damaged parts of their neocortex sometimes cannot see conceptualized objects, like, e.g., ducks. They can only see lines, shapes and patches of colour (Thagard 2010: 70). One explanation for this phenomenon is the absence in these patients of "top-down processing," which is now "central in modern neuroscience" (Burchard 2011: 69). Top-down processing occurs when we fi rst categorize or cognize things in broad strokes, and work through the details later. Those details are perceived as aspects of the more general conceptualized object, which means that the higher centers of our brain help to determine what we perceive. When topdown processing is operative, higher centers in the prefrontal cortex of the brain track and modify what happens in lower centers. When something new or diffi cult to identify is presented to a subject, top-down processing starts before recognition of the object is accomplished. According to Miller and Cohen (2001), the prefrontal cortex accomplishes this by providing bias signals to lower brain structures. These bias signals guide the fl ow of neural activity along certain pathways. In other words, when we see something new, parts of our brain normally associated with conscious thought are already involved in categorizing and making sense of the thing as it is presented to us (see also Buschman and Miller 2007). And imaginings can certainly be conscious. For example, it is well-known that if we approach an ambiguous fi gure (like the duck-rabbit of Gestalt psychology) with a certain mental image in mind, this can determine what we will see when we look at it. There is also support from the literature on "cognitive penetrability" (see e.g., Arstila 2017). I take all of this as evidence that the imagination, insofar as it is located in the higher centers of the brain, can play a constitutive role in determining the content of sense-experience. Second, Mark Johnson writes in the Body in the Mind that we "connect up" (1987: 152) abstract mental structures with the contents of our sense perception using what he calls "schemata," which are "nonpropositional structures of imagination" (19). He says "Even our most simple encounters with objects, such as the perception of a cup, involve schemata that make it possible for us to recognize different kinds of things and events as being different kinds" (20). Johnson's schemata have been very infl uential in cognitive science, and after the idea was re-expressed in Lakoff and Johnson (1999), it spawned what may be called a subfi eld of research. The basic idea is that through the imagination, we create schemata that give content to our beliefs, and structure perception and thought. CEEOL copyright 2017 CEEOL copyright 2017 26 M.T. Stuart, Imagination: A Sine Qua Non of Science Nigel Thomas, a long time researcher of mental imagery, understands schemata as data structures in the brain that make possible our perceptual experience of the world (Thomas 1999). Thomas understands schemata slightly differently from the Johnson-Lakoff school, but he admits that the views are compatible, and again the imagination plays a crucial role. Thomas argues that schemata are not things that we experience, although they are necessary for experience in general. Finally, there are sources of support for the fundamentality of imagination for sense experience that are more general. Stokes argues from a philosophical perspective that imagination is necessary (although not suffi cient) for the formation of new beliefs, desires, intentions, as well as for learning new concepts and skills (Stokes 2014: 179–180). And Colin McGinn (2004) argues that imagination is necessary for all cognition, since it is necessary for grasping meaning. If we grant the possibility that imagination can structure perception in a subconscious or non-occurent way, we can begin the analogy to thought experiments and the theoretical structures of science. Just as the imagination functions at the most fundamental level with respect to conceptual content, as it does for the Lakoff-Johnson school and Thomas, there is a sense in which we can understand the imagination playing this role at a conscious level to determine the semantic content of theoretical structures through thought experiments. Here, we occasionally use the imagination to settle on what a diffi cult new theoretical structure means, and in so doing, understand it by relating it to other concepts, increasing its empirical content, or becoming comfortable with it through repeated use. Instead of using the imagination to create a meaningful image of a duck from lines and colours and shapes, we use it purposely to assign new meaning to a theoretical structure via a thought experiment. For Kant, the imagination is the link between the senses and the understanding. Every time we use a concept, we perform an action, or in Kant's words, create a schema, that links a specifi c experience to our concept. I think something like this becomes very plausible if instead of linking individual sense experiences to individual categories, we consider linking experience as a whole (or in swaths) to the partiallyinterpreted theoretical structures of scientifi c theories via uses of the imagination, whether consciously or unconsciously. In this case, an action is performed, which may sometimes take the form of a thought experiment, which connects theoretical structures to experience. The thought experiment can make these structures, which are often developed in a formal or mathematical way, meaningful and fruitful. No amount of mathematics, laboratory experimentation or computer simulation will establish for us the semantic content of the principle of equivalence, the uncertainty principle, or Newton's laws, because grasping semantic content is something we must do for ourselves, not something that can be done to or for us. The imagination is useful here CEEOL copyright 2017 CEEOL copyright 2017 M.T. Stuart, Imagination: A Sine Qua Non of Science 27 because through it we forge new connections between affective, sensorial, memorial and rational elements. All high level theoretical structures will require some act of semantic comprehension on our part if we are to make scientifi c progress by means of them, whether that act is prompted by a thought experiment, a simpler act of imagination, or an automatic act of imaginative association. And this act of schematization, which would be described by Kant, Johnson, Lakoff and Thomas as an act of imagination, cannot be justifi ed by cognitive science or by philosophy. It is only justifi ed in a transcendental sense because it is always necessarily presupposed by both. That is why it is a sine qua non of scientifi c understanding. I hope this characterization of the role of the imagination in thought experiments sheds some light on the common conclusions of the empirical studies I considered above, namely, that thought experiments increase scientifi c understanding by bridging theoretical structures with existing knowledge or experience. Of course, there are different kinds of understanding thought experiments can produce. These are distinguished elsewhere (see Stuart 2017). There are also different kinds of imagination that are important for the discussion. In this paper, I considered imagination as an ability (or faculty, capacity); in future work I will turn to imaginative processes (actions or practices), which can be thought of as exercises of our ability to imagine. Unlike the imaginative faculty, imaginative acts can be discussed in a non-transcendental way. That is, we can say directly what makes different imaginative acts epistemically valuable. But at the level of generality I've taken up in this paper by discussing the faculty of imagination, we can only give something like a transcendental justifi cation. In this, I follow Marco Buzzoni, on whose work I have drawn extensively (see Buzzoni 2008, 2013, 2016, 2017). Speaking in Buzzoni's terms, this paper takes up the transcendental perspective on thought experiments, where in future work I will be taking up what he calls the operational perspective. To conclude, in the cases considered above where novel understanding is produced, it is often due to creating a connection between some theoretical structure(s) of science and existing knowledge, skills or experience, via an exercise of the imagination. We have substantiated this idea by considering the imagination as a key component in building these bridges. Thought experiments are instances of the sort of conceptual exploration that is needed to understand theoretical structures in science, which are themselves a necessary condition for the possibility of a working science. This argument, that thought experiments increase understanding by means of the imagination, which is fundamental to all theoretical understanding, suggests a novel way to justify the role of the imagination in creating scientifi c understanding, one that does not confl ict with any of the existing accounts that aim to justify empirical knowledge produced by thought experiments. 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