Henry Smith – 10/02/2020
Our typical view of the sciences is of a rational enquiry into the world. This enquiry is supposedly rigorously conducted with the ‘truth’ sought out. It seems peculiar then for science to make so much use ‘modelling’ in which, broadly speaking, a scientist posits a scenario, enquires into that scenario and then uses their results to make claims about the real world. This seems divorced from the empirical enquiries we expect of science. In philosophy of science, concerns about modelling are one of the prime areas of enquiry. In his article ‘Imagination in scientific modelling’ (2016), Adam Toon lays out the state of what is now a complex area of scholarly debate. He depicts two antithetical factions, direct and indirect representationalism. The former holds that when scientists posit models, they are asking us to imagine things about the real world, rather than creating a complete imaginary world (2016, p. 458). The latter hold that modelling creates wholly imagined universes that bear similarities to our own. Adherents in each camp argue by analogy: Toon (2011) makes the case that scientists engaging with models can be likened to children playing with dolls whilst Peter Godfrey-Smith (2009, pp. 110-114) likens models to fictional characters such as Sherlock Holmes. Toon eruditely states that if we are to address the philosophical problems of modelling then we need to “provide a convincing analysis of the practice of modelling” (2011, p. 580).
I believe Toon’s (2016, p. 452) call to arms must go further. We must extend our analysis to include the field in which the scientist is embedded. If we are to look at scientists engaging with a model of the solar system, we need to look at the practices of astronomy, astrophysics and physics in general; in Kuhn’s (1962) terms, the “paradigm” in which thescientist is working, as well as the specific practices of those scientists doing the modelling. In this essay I shall propose my own analogy of what scientists do when modelling; that of them being akin to people playing tabletop roleplaying games. I shall outline the direct and indirect representationalist schools of thought and Toon’s analogy of scientific modelling as playing with dolls. I shall then articulate what I feel to be the shortcomings of the directrepresentational position, and Toon’s analogy, before moving on to argue for my own analogy. I shall begin by first explicating what a tabletop role-playing game is.
Tabletop role-playing games emerged in the 1970s, with ‘Dungeons and Dragons’ (or D&D as it is also known) being the first, and the most well-known, games of this type (Budra, 2012, p. 2). Unlike traditional board games, such as Monopoly, the game is ‘played’ by one member of the group taking on the role of a narrator, or ‘gamemaster’, with the others playing characters, sometimes called ‘adventurers’ (Budra, 2012, pp. 2-6). There does not have to be a board; the game does not come in a box complete with dice, rules, counters etc, like Monopoly. Instead, the game is more abstract with a series of rulebooks giving people the framework by which to create a game. The participants’ imagination, some dice, ‘character sheets’ (containing the details of the player’s characters) are all aspects of the enactment of the game with the imagination and interaction of the participants the necessary and sufficient components of this. Everything else facilitates specific mechanics of the game but are neither necessary nor sufficient (Budra, 2012, p. 3).
The gamemaster composes a story in which the players characters are embedded (Mearls, 2014, p. 5). The players do not follow a prescribed role within the story, instead possessing agency with the gamemaster managing and narrating the consequences of their actions (Budra, 2012, pp. 8-9). The design and enactment of the player’s characters is a collaborative process with the gamemaster. A rulebook defines how characters are created, what things they can and cannot do and what challenges they can face. A looser set of cultural norms also mediate the interactions of players, rules, narrative and gamemaster (Mearls, 2014). The gamemaster has a broad understanding of where the story is directed, and the players react to the stimuli the gamemaster gives them. The narrative of the game is a case of co-creation between players and gamemaster in the course of one or multiple sessions (Budra, 2012, pp. 8-9). The success of characters actions is determined by rolling dice and adding a number to this – called a modifier – depending on the characters attributes and abilities – a level of strength and wisdom, for example. Players and the gamemaster aim to roleplay; they attempt to get into character and make in-game decisions based on ‘what the character would do’ rather than what they personally might want. The game is not played combatively with the gamemaster trying to defeat the players and the players in opposition to the gamemaster, with one side winning (Mearls, 2014, p. 5). Instead, the gamemaster attempts to challenge the players – even kill or defeat their characters – but only in order to explore and engage with the world in dramatically satisfying ways (Budra, 2012, p. 9).
According to indirect representationalists, when a scientist posits a model – a physical model such as a scale model of a bridge or a theoretical model – they create a ‘model system’ (Toon, 2016, p. 451). Theoretical models can be more or less mathematical in nature: a set of interwoven equations can render a theoretical model whilst a vivid description similarly does so in different circumstances. Models are also either illustrative or generative – the model demonstrates principles and phenomena we already know or it helps us discover new phenomena. For instance, Newton’s model of the solar system allowed us to discern that orbits of planets are elliptical. Some philosophers attempt to break down and taxonomize the types of modelling employed, even claiming that mathematical models to be distinct from theoretical models (Garding, 1999, pp. 4-5). For our enquiry, such detailed exploration is not relevant, merely worth noting – my analogy applies to all models. With physical modelling, the model system is the scale model of the bridge; in theoretical modelling, this system is an abstract object (Toon, 2016, p. 453). This model system bears some key similarities to the real things it represents, which the scientists will exploit for their enquiry, and some discrepancies, which the scientist has built into the model in order to make it wieldier. This leads to some quandaries, exploration of all of which is beyond the scope of this essay so I shall focus on just a few.
Firstly, what is the relation of the model to the real world such that an enquiry into the model can yield results fruitful in reality? Secondly – and relatedly – what is the extent of the universe in such a model? This latter question seems peculiar as it is tempting to claim that a model system has clear borders, it does not suppose a whole model universe around it. To contend as much would be tantamount to the model bridge being a member in a whole universe of similarly scaled structures. However, scientists enquiring into their theoretical models necessarily must go beyond the confines defined by them in their model description in order to find answers to their questions; it is as if they are venturing into a world and discovering things which they can then utilize upon returning to the real world. There must be whole territories of the system never explored, yet there, ready to be explored. The analogy of fictional characters is made use of by appealing to the “reality principle” (Toon, 2016, p. 456) which states that, just as we take a world from a novel to be as similar to our own world as plausible, so too is the model universe similar to ours. Sherlock Holmes has oxygen in his blood and lives in an England broadly the same as the real England; so too does Newton’s solar system model including perfect spheres inhabit a model universe akin to ours (Toon, 2016, pp. 456-457). As the limits of models are not set out in their model description, the model can be explored and the results of exploration fruitful for application in the real world because the two systems have everything, barring the imagined differences, in common. This view thus answers both quandaries.
There are a plethora of rule systems – in D&D these are referred to as ‘editions’ but there are other tabletop roleplaying games too – which allow different types of games, emphasizing combat, roleplaying, narrative creation and or the determinacy of the story to varying degrees. Some systems dispense with any distinction between player and gamemaster such that all involved have equal say in the ‘world’ in which they are playing. I contend that tabletop roleplaying games offer us tools for understanding, and a fruitful analogy for, modelling in science. I shall now detail the state of the field in philosophical discussions of scientific modelling practice before applying (and defending the application of) tabletop roleplaying games to modelling.
Direct representationalists disagree from the outset with indirect representationalists. They hold that ontological questions raised by the positing of model systems are too problematic to easily sidestep. The positing of fictionalised universes when we speak of ‘model systems’ is deemed an unnecessary overcomplication. It seems necessary to attribute some peculiar form of existence to these model universes and we appear to be deferring deeply important philosophical matters to philosophers of fiction, making indirect representationalism little more than a “promissory note” according to Toon (2016, p. 457). Direct representationalists avoid this by excising the model system entirely; instead, when a scientist posits a model, they “represent the world directly, by asking us to imagine things about it…” (Toon, 2016, p. 457). Some of the things they ask us to imagine are true – a Newtonian model of the solar system deals with the real sun, Earth etc. – and some are consciously false – that there are perfect spheres. When we are ‘exploring’ a model, what we are actually doing is exploring the “the web of imaginings prescribed by a scientist’s model description” (Toon, 2016, p. 459).
To illustrate this, Toon (2011) argues that modelling is akin to children playing with dolls. He uses the case of a laboratory expert teaching a student about the construction, orientation and motion of molecules using both a physical model and a virtual modelling system (2011, pp. 580-582). He contends that the scientists, to an extent, believe themselves to be actually engaging with the molecule itself, not the model of it. When they look at the model they conceive of themselves as actually looking at the molecule it represents. They speak as if their interactions with the model are actual interactions with the molecule, not simply informative of what interacting with the molecule would be like (Toon, 2011, pp. 582-587). This is just like children playing with a doll who speak as if the doll is a real baby, conceive of themselves as looking at and interacting with a real baby etc. The doll, just like the molecule models, is said to act as a prop for the imaginations about the real world which the children and scientists perform (Toon, 2011, p. 583). Further, just as a child learns something of how to interact with a baby through this, so too do scientists learn something about the nature of molecules through their modelling (Toon, 2011, pp. 587-588). I believe the principles espoused by the direct representationalist school of thought, in general, are flawed and the analogy Toon uses, whilst worthy in some regards, is limited in utility. I shall deal with the general and specific concerns in turn, before proposing my alternative analogy, aiming to redeem the indirect representationalist view in so doing.
When modelling, direct representationalists contend, scientists do not create a fictional system, merely add imagined aspects to the real-world system which they then imagine. This assumes that one can coherently speak of ‘fictionalised imaginations of’ a real-world without this entailing the existence of a wholly fictional imagined system, rather that you are still simply imagining the real world. For this to be possible though, the scientists must do one of two things. Either, the only thing being fictionalised are these imagined qualities – the frictionless-ness of a surface, but not the surface itself (as the surface does exist in the real world), or a perfect spherical-ness (as ‘imperfect’ spheres exist in our world). Or, the scientist holds both the real world in their head plus these aspects they have added – or perhaps subtracted in the case of removing friction from a surface. If we accept the latter scenario then it seems the direct representational view is, at best, trivially distinct from the indirect representationalist view of a model system being an imagined representation of the world with some simplifications (but in all other regards being the same). At worst, it is fatally incoherent.
The aforementioned ‘reality principle’ is rejected by direct representationalists on account of the apparent “explosion of the content of the fictional world” (Toon, 2016, p. 456). It is considered problematic for the fictional world of Sherlock Holmes to include the fact that World War 2 occurs in 1939; there is a bloating of the fictional universe. Is the direct representationalist not making use of this same heresy if they contend that the real world is contained in the imagination of someone using a Newtonian model of the solar system? To reject the former (the reality principle) surely entails the rejection of the latter (the ‘real world plus fictional qualities in the imagination’). Acceptance of the latter warrants the question, what is wrong with the former? A response to this could state that we are not actually reincarnating the reality principle here. Instead, the world of which the model is a component is the real world, not the fictional ‘like-our-own’ world of which Sherlock Holmes is a member. The model then seems to have an identity with the real world. Arturo Rosenbluth and Norbert Wiener (1945) take on the notion of a model having a one-to-one identity with the real world, in the way the direct representationalist may be guilty of claiming. They contend that an imagination of such complexity would be self-defeating in the sense that the scientist would not need to model anything if they could comprehend the real world in such a manner (Rosenbluth, 1945, p. 320) and that such a rich comprehension is in fact closed off from us. Thus, it is incoherent to speak of the scientist imagining the real world as it really is; when modelling, you must fictionalise the whole world if you fictionalise some of it.
What then of the other direct representationalist avenue? Does claiming that the scientist modelling is actually just imagining the added (or subtracted) qualities redeem the direct representationalist view? Simply put, no. Claiming that scientists only hold imagined qualities about the real world in their head is non-sensical. The notion of qualities distinct from the possessors of those qualities is contrived. Our direct representationalist must make use of some version of Plato’s forms in order to argue that we can shear qualities from the things to which they pertain. The claim that I can hold the smoothness of a surface in my mind without also having to imagine the object of which that surface is a component – or even the surface itself – is counter intuitive. In order to avoid reincarnating Plato’s forms, the direct representationalist may well claim that the perfect sphere, or the frictionless plane, are held in our comprehension when doing modelling. Once again though, our direct representationalist is committing heresy as they are building up a model system which they claimed needing discarding. The moment our scientist is conjuring up an idealised sphere in their mind, they are bringing into existence a model system of the kind the indirect representationalist expounded. The foundations of the direct representationalist position seem rotten, and certainly cannot be explained away without regressing into the very position they oppose.
My attack upon direct representationalism should not be misconstrued as discounting the analogy used by Toon to explain what scientists do when they engage with models. The incoherence I target within direct representationalism says nothing of the utility of Toon’s analogy. It is instead my belief that Toon’s notion of scientists engaging with models being akin to children engaging in games of make-believe with dolls is a fruitful one; for example, the apparent conflation of the model with reality done by the scientists is a valuable insight. Where Toon’s analogy is limited however, is in regard to the ‘learning’ aspect of modelling and the scripted nature of children playing with dolls. I shall expand upon these criticisms now before arguing that the analogy of tabletop roleplaying can overcome these issues.
Toon claims that, just as the child learns something about what it is to look after a baby through their games of make-believe, so too does the scientist learn about the real-world through engagement with the model. I do not think though that we would say that knowledge of caring has been generated by the process of playing with dolls. Whilst the doll may look like a baby and the child engaging with it will treat it as if it is a baby, the similarity between the doll and real baby is exactly that, a matter of appearance. Even a matter as simple as putting on clothing, for the doll requires the child to do things which are markedly different from trying to put a coat on a real baby. When clothing the doll, one can rotate the stiff plastic arms at will and slot them through the sleeves of the coat, all whilst being able to easily handle and manoeuvre the whole doll. When trying to put clothes on a baby (even the most placid baby) the whole practice is more delicate, careful and constrained with a whole host of difficulties that playing with doll does not inform a child of. The analogy breaks down here; the model is not similar enough to its real-world counterpart for exploration of one to inform about the other. Further, the child playing with dolls needs to know about babies and what interacting with them is like in order to use the doll for games of make-believe. By contrast, the scientist does not seem to have to bring with them the same level of understanding in order to engage with their model. This may sound a peculiar claim, as naturally a scientist will have years of training in the sciences when they do modelling, but they do not have to be intimately aware of the model they engage with. Certainly, the example Toon himself uses is of scientists being taught new things about molecule structure and motions. The scientist modelling is merely informed by their background knowledge of the subject matter; the interaction of a child with its doll is entirely shot through with all that they know of babies. Toon’s analogy of scientific modelling being akin to children playing with dolls then seems incapable of accounting for how modelling can generate real-world knowledge as the two practices are so thoroughly divorced from one another, in this regard.
In addition to this is the fact that the interactions between the child and doll are scripted by the child alone. What the doll ‘does’ in games of make-believe is entirely dictated by the imaginings and actions of the child playing with it; even when the child reports that the doll is ‘upset’ or presents some sort of challenge to the child playing with it, these developments in the game of make-believe are entirely generated by the child. The scientist who twists their molecule model and finds that it cannot rotate in the way they would like plainly does not script the interaction. It would be more accurate to say that the scientist engages with the model as a different entity to them, where the child playing with the doll seems to be one entity – a child playing – with no process of action, response, reaction occurring in their games of make-believe. One may attempt to defend Toon’s thesis on the basis that the doll does exert a kind of agency with which the child must negotiate and so the game of make- believe is not determined solely by the child. An appeal to Andrew Pickering’s (2005) concept of ‘dances of agency’ could be made here in order to mount such a defence. Thechild playing with the doll is in a dance of agency with it: the material nature of the doll, what it physically can and cannot do and the responses its appearance (if not its actions, as it cannot perform actions) generate in the child construct the game of make-believe, not just the child.
Even if we take the notion of non-human agency to be a credible one, as I do, it still does not mean that the analogy is redeemed with respect to the allegation that the child’s play is scripted and the modelling is not. The child has more influence and more control over the game of make-believe – even if the doll does also exert some contrary agency which the child must negotiate or overcome – than the scientist modelling. The vast majority of the creative control of the game of make-believe is in the hands of the child, whereas the scientist appears to be on more of an equal footing with the model in terms of what is produced through their interactions. The scientist does not seem capable of scripting the outcome of this engagement with a model (provided the scientist is using their model for the purpose of discovery), but the child does seem capable of easily contriving its engagement to produce the results it wishes. It is precisely because the scientist has so little control over the model that they can generate knowledge through engaging with models, whereas the child does not generate knowledge because it is so in control of the interaction.
Two fundamental aspects of scientific modelling thus seem absent from Toon’s analogy. Filling this vacuum motivates my belief that modelling should be considered as analogous to people playing tabletop roleplaying games. When scientists engage with a model they learn something by exploring a fictional world (or webs of imaginings) that pertains to the real- world. This kind of exploration is exactly what is done through the course of playing a tabletop roleplaying game. Players take on the role of characters who know some things about the world and then, through the course of the game, come to know more about it. They ‘visit’ new places and ‘meet’ new people, deepening and enriching their understanding of the fictional world. This is almost identical to the scientist who takes on the role of a privileged observer viewing the motions of the planets in the solar system and then through the process of engaging with the model, discovers that orbits are elliptical. Further, just as the scientist’s engagement with the model system tells them something about the real-world system it is a simplified version of, so too does the simplified, fictionalised world players enter into in games of D&D teach them something of the real world. In having to roleplay interacting with people that are not other player’s characters – non-player characters performed by the gamemaster – the player learns about social interactions in our real world, they learn about how to talk and interact with real people through their roleplaying. Further, logical puzzles, tactics and strategy, creativity, artistry, problem-solving and mathematical skills are all gained, developed and trained by those playing tabletop roleplaying games. Thus, it seems that the analogy can cogently inform us about scientists learning through modelling practice.
Someone may believe they can here discern a fatal flaw in my analogy – this teaching capacity of tabletop roleplaying games entirely depends on the gamemaster, after all they create the world and ultimately mediate the actions of those within it. Players only learn because they are being told things by the gamemaster. Even worse, the practice of playing tabletop roleplaying games appears to be the kind of scripted activity – the gamemaster is after all ‘master’ of the game – I criticised as a fatal to Toon’s analogy. Such a criticism is to misunderstand the nature of tabletop roleplaying games. Firstly, the gamemaster is also one of those people who learns through the course of playing tabletop roleplaying games – their understanding and knowledge of social interactions is developed, their maths skills and creativity are expanded. It is not them leading the course of the game that causes the players to learn; it is the interaction of gamemaster and player – this seems remarkably akin to the scientists learning through the interaction between them and their models. Furthermore, the game is not scripted. To say as much would be like saying that a tennis player scripts the course of the point they are about to play when they serve. Yes, a tennis player dictates where the ball goes at the start of the point but from then onwards anything could happen. So too is this the case with a tabletop roleplaying game. A gamemaster can describe a scenario but they do not know what will occur because of the players exerting their agency, they could perceive options and courses of action unaccounted for by the gamemaster and so new developments occur, wholly unscripted.
This goes even deeper: gamemasters will often say through the course of a game, when asked about some obscure bit of lore in their world, or the name of a character, or even what a character they control will do, that they simply do not know. It is not that the players are embedded in a fictional world which, although they do not understand, the gamemaster has complete mastery over. The world is generated through the course of their interactions, its borders expanded in ways that the gamemaster themselves neither fully knows nor has hegemonic control over. They too are exploring this world. The world has a life of its own which everyone playing the game is interacting with and facilitating, but not controlling. This, again, seems to bear striking similarities with scientists modelling; exploring and facilitating but neither controlling, nor determining the outcome in a scripted manner.
Just as scientists modelling treat models as if they are real, identical with that which they model, so too do players in a tabletop roleplaying game ascribe things to, speak of and engage with their games as if they were real (Budra, 2012, pp. 12-13). Player’s will often consider seriously the ethical decisions they are forced to make and are deeply emotionally affected by the traumas visited upon their characters, even in the often fantastical, ridiculous settings they plan in. It is worth noting that a game of D&D is not just matching the children playing with their dolls in this aspect of being analogous to scientists modelling, it is going further. Children playing with dolls may well be callous of their doll when they are distracted by something else, and certainly most children grow out of playing with dolls and so give up any concern and investment they once had in their doll. By contrast, players in a game of D&D are likely to always value the game they played and certainly continue to treat the experiences they had within the game as significant – if they once felt them to be significant, they are likely to continue deeming to be so. This element of the practice seems more akin to the scientists who are invested in their models; the image of the scientists fascinated and enthralled by the ‘beauty’ of a model is something we can easily conjure. This is clearly echoed by the role-players in a way not present with the children playing with dolls, or indeed any other analogy of modelling practice. I think the greatest boon offered by the use of the tabletop roleplaying game analogy is the fact that it allows us to speak of modelling as a practice embedded within paradigms. I
favour Kuhn’s (1962) account of science being broken into paradigms which have their own internal vocabularies, with unique explanations of phenomena and which are adhered to by scientists irrationally. Though there are sound reasons for favouring one paradigm over another, there is no fundamental logical reason to discount one; ultimately, taste determines a person’s subscription to a paradigm. Paradigms in science dictating the kinds of modellingscientists conduct is akin to editions of tabletop roleplaying games constraining the ways people play. One edition of a game can be radically different to another, emphasizing and facilitating different kinds of gameplay. There is no logical reason to use one and not the other, just the individual tastes of those playing in any given game. Whilst there are still many who take issue with Kuhn’s account of science as proceeding by paradigm, if you take it to be true, then the analogy of tabletop roleplaying is more insightful as it can include this aspect of scientific practice. Further, the analogy is not reliant upon Kuhn’s ideas, such that, if you reject Kuhn, you need take no issue with the analogy I am offering. This addition to our analysis of modelling is one that has not been done before in talk of modelling in science and certainly cannot be accounted for in either Toon’s analogy or the fiction analogy. It is evident to us that there are no paradigms, editions or otherwise at play in children’s games of make-believe with dolls; the types of things they do with dolls may be somewhat socially dependent but this dependence is not linked to play in a rich and codified way sufficient for it to be analogous with scientific paradigms determining modelling practice. By that same token, genre in fiction cannot be appealed to as analogous to paradigms in science. This is because the borders of genres are permeable; what distinguishes a murder mystery from a thriller from a drama, etc., is ephemeral. Paradigms in science do not blend into one another, they have clear differences, not least amongst which is the fact that they deal with wholly different worlds. Only the editions within the tabletop roleplaying games seems to get at the nature of paradigms and how they affect modelling practice.
Finally, my analogy includes a notion of rigour. Scientists can create models which pertain more or less closely to the real-world and, within modelling for experimental purposes, the knowledge generated by modelling can be rigorously arrived at or dubiously arrived at. Rigour is not an aspect of novels – unless we wish to argue that historical novels can be rigorous. This seems suspect as it implies a standard against which we can verify whether a historical novel is ‘correct’ or not, and thus would supervene upon a thoroughgoing defence of fictionalisations of epistemically tricky historical knowledge. Nor does rigour apply to childish games of make-believe. The children may well adhere to some rules they have devised but they are hardly playing incorrectly if they do not make use of those rules – we might be tempted to say that they are just playing a different game of make-believe. Because the rules of D&D are codified, they can be rigorously met or ignored. Those playing a tabletop roleplaying game and discarding certain rules would then be akin to scientists. Both can coherently be said to not be meeting the standards set by the community and actively breaking rules they would legitimately be expected to otherwise abide by.
This is just one of the many ways I have illustrated the utility of adopting the analogy that scientific modelling practice is akin to people playing tabletop roleplaying games. In addition to the concept of rigour which can now be introduced into the framework, so too can paradigms within science, scientists’ treatment-as-if-real of models, the unscripted nature of models and the explorative aspect of modelling practice all be coherently incorporated into our analysis. Further to this I have also highlighted what I deem to be an inherent hypocrisy within direct representational views of modelling practice in science. My analogy, firmly rooted in the indirect representational tradition, is hopefully capable of overcoming some of the issues philosophers have raised against indirect representationalism. The nature of modelling within science is indirectly representational, with scientists engaging with models being akin to people playing tabletop roleplaying games.
Bibliography
Budra, P., 2012. Roll a D20 and the Author Dies. In: P. a. B. C. Budra, ed. From Text to
Txting: New Media in the Classroom. s.l.:Indian University Press, pp. 1-14. Garding, L., 1999. Models in Science and Otherwise. Proceedings of the American
Philosophical Society, 143(1), pp. 3-11.
Godfrey-Smith, P., 2009. Models and Fictions in Science. Springer, 143(1), pp. 101-116.
Kuhn, T., 1962. The Nature and Necessity of Scientific Revolutions. In: The Structure of Scientific Revolutions. s.l.:University of Chicago Press, pp. 107-125.
Mearls, M. and Crawford. J et al., 2014, Player’s Handbook, Wizards of the Coast. Pickering, A., 2005. Asian Eels and Global Warming: A Posthuanist Perspective on Society
and the Environment. Ethics and the Environment, 10(2), pp. 29-43.
Rosenbluth, A. a. W. N., 1945. The Role of Models in Science. Philosophy of Science, 12(4),
pp. 316-321.
Toon, A., 2011. Playing with Molecules. Elsevier, 42(4), pp. 580-589.
Toon, A., 2016. Imagination in Scientific Modelling . In: A. Kind, ed. The Routledge Handbook of Philosophy of Imagination. s.l.:Routledge, pp. 451-462.