Abstraction as Strategy for WorldmakingJulia Sánchez-Dorado

1. Introduction

Contemporary scientists are invested in the study of a range of highly complex natural phenomena. One of the most pervasive investigative tools they exploit to learn about those phenomena are models. Scientific models, despite their variety in form, style, and materiality, seem to share a fundamental epistemic function, namely, they are representational devices, designed to stand for and depict the behaviour of specific target systems in the world.11The conception of models as representations gained predominance in the second half of the twentieth century, under the semantic view within the philosophy of science. Classic semantic view works include: Patrick Suppes, ‘A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences’, Synthese, 12 (1960), pp. 287–301 <https://doi.org/10.1007/BF00485107>; Bas C. van Fraassen, The Scientific Image (Oxford: Oxford University Press, 1980) <https:/​/​doi.org/​10.1093/​0198244274.001.0001>; and Ronald Giere, Explaining Science: A Cognitive Approach (Chicago: University of Chicago Press, 1988) <https:/​/​doi.org/​10.7208/​chicago/​9780226292038.001.0001>. Following these works, in the 1990s and 2000s, more pragmatic approaches to the understanding of scientific models were advanced, such as the ‘models as mediators’ perspective, according to which models are still treated as representational devices, but more attention is given to the plurality of epistemic functions that they serve in practice. See Models as Mediators, ed. by Mary S. Morgan and Margaret Morrison (Cambridge: Cambridge University Press, 1999) <https:/​/​doi.org/​10.1017/​CBO9780511660108>. In recent years, the imbricate relationship between models and representation has been openly challenged by scholars. See, for instance, Tarja Knuuttila, ‘Epistemic Artifacts and the Modal Dimension of Modeling’, European Journal for Philosophy of Science, 11.65 (2021) <https://doi.org/10.1007/s13194-021-00374-5>; and Guilherme Sanches de Oliveira, ‘Representationalism Is a Dead End’, Synthese, 198 (2018), pp. 209–35 <https://doi.org/10.1007/s11229-018-01995-9>, who emphasize above all the ‘artefactual’ nature of models. However, the conception of models as representations has given rise to a dilemma in recent philosophy of science: on the one hand, partly thanks to the role played Beginning of page[p. 48] by models, contemporary science has achieved numerous accurate descriptions of nature which, in turn, have facilitated effective world interventions. On the other hand, as soon as one approaches the study of scientific models with an analytic eye, one notices that models are notorious for their partial, simplifying, and distorting character, with respect to the very same objects they aim to represent. So, if models misrepresent (that is, simplify and distort) the objects they attempt to bring to light, how can one assert that they provide accurate descriptions of them? Even more pressing is the question of whether it is justified to implement certain policies and practical interventions based on model results, given the kinds of misrepresentation they entail. Responding to these questions involves more than solving an epistemological conundrum; it goes to the heart of the role that philosophers, especially in collaboration with historians of science, can aspire to play in informing scientists’ practices, by making manifest and assessing the epistemic and social consequences of the insertion of misrepresentations in their modelling work.22For a discussion on the role that historians and philosophers of science can play in informing scientists’ practices, see Hasok Chang’s account of ‘complementary science’, that is, the practice of knowledge production based on the systematic historical and philosophical re-examination of scientific questions that are excluded from current specialist science. See Hasok Chang, Inventing Temperature: Measurement and Scientific Progress (Oxford: Oxford University Press, 2004), chapter 6, pp. 235–50 <https:/​/​doi.org/​10.1093/​0195171276.003.0006>.

This essay is dedicated to discussing one specific cognitive strategy that scientists make use of in their modelling practices, namely abstraction, and the implications it has for the dilemma of misrepresentation. Abstractions, this essay argues, can be enormously useful in the construction of epistemically successful models, even if, at the same time, they are a form of misrepresentation, insofar as abstracting involves the selection and isolation of presumably relevant features of the natural phenomenon studied, and the imaginative superimposition of relationships connecting those features to form a coherent whole (that Beginning of page[p. 49] is, a functioning model). Section two introduces the most common characterization of abstraction in the contemporary modelling literature in philosophy of science, which identifies it with the ‘omission’ of certain features of the phenomenon represented. This characterization is then partially criticized, in sections three and four, using an illustrative example taken from oceanography, namely, Marie Tharp’s practice of abstraction during the construction of her physiographic maps of the ocean floor. The aim is to highlight the (insufficiently recognized) creative potential of abstractions in science. To do so, section five incorporates some insights from the philosophy and history of art, fields where there is a longer and richer tradition of discussion about the creative roles of abstraction. Finally, to tackle the dilemma of misrepresentation for the specific case of abstraction, section six suggests that one needs to think of modelling practices not only as practices of representing but also as practices of worldmaking. In his 1978 book Ways of Worldmaking, Nelson Goodman identified several ways in which cognitive agents engage in practices of worldmaking through the manipulation of their symbol systems.33Nelson Goodman, Ways of Worldmaking (Hassocks: The Harvester Press, 1978) <https:/​/​doi.org/​10.5040/​9781350928558>. Among these, Goodman hinted at, but did not explicitly talk about, abstraction. Thus, this essay concludes by suggesting that we should think of abstraction as a worldmaking strategy as well, as much in science as in art, but that we should also reflect on the potential consequences, including the possible epistemic and social harms, that its worldmaking capacity might entail.

2. Abstraction as Omission

The two most common strategies that philosophers of science have identified as introducing misrepresentations in modelling practices are abstractions and idealizations. Typical definitions of abstraction in recent modelling debates state that abstracting is the act of omitting those aspects of a natural system that are deemed irrelevant during the process of constructing a model. Meanwhile, idealization is the purposeful introduction of falsehoods, such as when economists work with models that assume subjects to be perfectly rational, when ecologists Beginning of page[p. 50] include an infinite population in their mathematical simulations, or when physicists resort to frictionless planes in their modelling. An abstract model, then, presents an incomplete, detail-poor image of a target, while an idealized model offers a partially false image of that target. This distinction can be found, among other places, in the works of Nancy Cartwright, Martin Jones, Hans Radder, Peter Godfrey-Smith, and Arnon Levy.44See Nancy Cartwright, The Dappled World: A Study of the Boundaries of Science (Cambridge: Cambridge University Press, 1999) <https://doi.org/10.1017/CBO9781139167093>; Martin Jones, ‘Idealization and Abstraction: A Framework’, in Idealization XII: Correcting the Model; Idealization and Abstraction in the Sciences, ed. by Nancy Cartwright and Martin Jones (Amsterdam: Rodopi, 2005), pp. 173–217 <https:/​/​doi.org/​10.1163/​9789401202732_010>; Hans Radder, The World Observed/The World Conceived (Pittsburgh: Pittsburgh University Press, 2006) <https:/​/​doi.org/​10.2307/​j.ctt6wrcvz>; Peter Godfrey-Smith, ‘Abstractions, Idealizations, and Evolutionary Biology’, in Mapping the Future of Biology: Evolving Concepts and Theories, ed. by Thomas Pradeu and others (Dordrecht: Springer Netherlands, 2009), pp. 47–56 <https://doi.org/10.1007/978-1-4020-9636-5>; and Arnon Levy, ‘Idealization and Abstraction: Refining the Distinction’, Synthese, 198 (2018), pp. 5855–72 <https://doi.org/10.1007/s11229-018-1721-z>. Abstraction, Jones says, ‘is a matter of complete silence’ about the features of a certain target that are left out of the model.55Jones, ‘Idealization and Abstraction’, p. 175. Similarly, Godfrey-Smith argues that an abstract model entails the ‘description of a system [that] leaves out a lot’, ‘but […] is not intended to say things that are literally false’. Meanwhile, an idealized model ‘fictionalizes in the service of simplification’, and so is not a literally true description of an aspect of the world.66Godfrey-Smith, ‘Abstractions, Idealizations, and Evolutionary Biology’, p. 48.

While abstraction remains scarcely discussed in current debates in philosophy of science, there is an extensive and growing literature on idealized models.77Two insightful accounts of idealization in the current literature in philosophy of science are Angela Potochnik, Idealization and the Aims of Science (Chicago: University of Chicago Press, 2017) <https:/​/​doi.org/​10.7208/​chicago/​9780226507194.001.0001>; and Collin Rice, Leveraging Distortions: Explanation, Idealization, and Universality in Science (Cambridge, MA: MIT Press, 2021) <https:/​/​doi.org/​10.7551/​mitpress/​13784.001.0001>. This seems motivated by the thought that, if abstracting only means omitting the irrelevant features of a target system, then there is not much of epistemological interest to be said about it, beyond the observation that it requires researchers to leave out unnecessary details when creating their representations. In contrast, idealizations would pose particularly interesting and challenging Beginning of page[p. 51] questions, insofar as they demand that philosophers make sense of how falsehoods can be dealt with or their epistemic value explained. In fact, it seems that the motivation of some scholars to maintain the idealization–abstraction distinction might consist in their attempt to find a strategy to minimize the dilemma of misrepresentation, by making abstraction an innocuous form of misrepresentation that does not really obstruct accurate representation. Thus, the dilemma would be channelled exclusively into the effects of idealization.88This reading of the motivations for sustaining the idealization–abstraction distinction in current philosophy of science, as well as a critique of the idea that models can be de-idealized, can be found in Rice, Leveraging Distortions, pp. 120–21.

However, a closer look at actual modelling practices reveals that to account for the epistemic value of abstractions requires revising and going beyond the standard definition of abstraction as ‘omission’. In a recent article, Natalia Carrillo and Sergio Martínez precisely criticize the understanding of abstraction as omission, which has become the ‘orthodox view’ in the modelling debate, with the unfortunate consequence of turning abstraction into a mere issue concerning the ‘level of detail’ with which a target system is described.99Natalia Carrillo and Sergio Martínez, ‘Scientific Inquiry: From Metaphors to Abstraction’, Perspectives on Science, 31.2 (2023), pp. 233–61 (p. 237) <https://doi.org/10.1162/posc_a_00571>. Similar critiques are found in an essay by Sergio Gallegos Ordorica, and in a recent collective volume on abstraction edited by Chiara Ambrosio and myself.1010See Sergio Armando Gallegos Ordorica, ‘The Explanatory Role of Abstraction Processes in Models: The Case of Aggregations’, Studies in History and Philosophy of Science Part A, 56 (2016), pp. 161–67 <https://doi.org/10.1016/j.shpsa.2015.10.002>; and Abstraction in Science and Art: Philosophical Perspectives, ed. by Chiara Ambrosio and Julia Sánchez-Dorado (London: Routledge, 2024). But, if not exclusively in terms of omission, how should one conceptualize the activity of abstracting in modelling practices? I will briefly introduce a historical case in oceanography to exemplify how scientists can fruitfully employ abstractions in their work. This example shows that omission is one of the aspects involved in practices of abstraction. At the same time, however, a creative ordering process is fundamentally entailed in the very same practices.1111Similar views on abstractions have been previously defended by Gallegos Ordorica, who refers to a form of ‘aggregative abstraction’ to indicate that this practice is not just about omitting features but about adding new elements to the process as well. See Gallegos Ordorica, ‘The Explanatory Role of Abstraction Processes in Models’, p. 162. Michael Stuart and Anatolii Kozlov, similarly, talk about a form of ‘generative abstraction’ in contrast to a mere ‘subtractive abstraction’. See Michael Stuart and Anatolii Kozlov, ‘Moving Targets and Models of Nothing: A New Sense of Abstraction for Philosophy of Science’, in Abstraction in Science and Art, ed. by Ambrosio and Sánchez-Dorado, pp. 118–42 (p. 121).Beginning of page[p. 52]

3. Marie Tharp: Abstracting the Ocean Floor1212This section substantially builds on the rich work that Rasmus Winther has developed on Marie Tharp’s practice of map-making, as well as the role that abstraction played in the production of her physiographic diagrams. My intention is to use this case, largely following Winther, to develop some points of his analysis that could be further spelt out, such as on the roles of omission and creative ordering, as well as on the worldmaking capacity of abstractions. I particularly draw on Rasmus Winther, ‘Mapping the Deep Blue Oceans’, in The Philosophy of GIS, ed. by Timothy Tambassi (Cham, CH: Springer Geography, 2019), pp. 99–124 <https://doi.org/10.1007/978-3-030-16829-2>; and Rasmus Winther and Marie Raffn, ‘What If?’, in Abstraction in Science and Art, ed. by Ambrosio and Sánchez-Dorado, pp. 217–49. Additional sources consulted for this section are: Bruce Heezen, Marie Tharp, and Maurice Ewing, The Floors of the Oceans: I. The North Atlantic; Text to Accompany the Physiographic Diagram of the North Atlantic, Special Paper 65 (New York: The Geological Society of America, 1959) <https:/​/​doi.org/​10.1130/​SPE65-p1>; Marie Tharp, ‘Connect the Dots: Mapping the Seafloor and Discovering the Mid-Ocean Ridge’, in Lamont-Doherty Earth Observatory: Twelve Perspectives on the First Fifty Years, 1949–1999, ed. by Laurence Lippsett (Palisades, NY: Lamont-Doherty Earth Observatory of Columbia University, 1999), pp. 31–37; reproduced as ‘Marie Tharp’s Adventures in Mapping the Seafloor, in her Own Words’, 24 July 2020 <https://news.climate.columbia.edu/2020/07/24/marie-tharp-connecting-dots/> [accessed January 2024]; Hali Felt, Soundings: The Story of the Remarkable Woman Who Mapped the Ocean Floor (New York: Picador, 2012); and Andrew K. Knoll, A Brief History of the Earth (New York: Mariner, 2021).

In the 1950s, oceanographer and geologist Marie Tharp (1920–2006), together with her colleague Bruce Heezen (1924–1977), postulated the existence of the Mid-Atlantic Ridge, a mountain chain that divides the Atlantic seafloor from the north of Iceland to the Antarctic. After centuries of considering the seafloor terra incognita, Tharp took a fundamental step in exposing its mountainous landscape formations in a clear and innovative visual manner. With the assistance of new data gathered from sonar technology (specifically, deep sea echo sounders) developed during World War II, as well as with data regarding earthquake epicentres in the ocean, Tharp constructed a series of graphs, diagrams, maps, and even some 3-D analogues of the globe, which in conjunction worked as models to help uncover the structure of the ridge. Moreover, Tharp’s models showed remarkable continuities between the Mid-Atlantic Ridge and the mountain chains on the Pacific Beginning of page[p. 53] and Indian ocean floors, indicating the presence of a global ridge system.1313See Winther and Raffn, ‘What If?’, pp. 219–23; Knoll, A Brief History of the Earth, p. 45; and Heezen, Tharp, and Ewing, The Floors of the Oceans.

The recent works of Rasmus Winther and Hali Felt offer helpful readings of the practices through which Tharp’s models led to one of the most important discoveries in twentieth-century geoscience. Near the crest of the mid-ocean ridge, Tharp observed that there was a ‘deep notch’ or rift valley.1414Tharp, quoted in Felt, Soundings, p. 99. The existence of a V-shaped rift, Tharp and Heezen knew, suggested continental drift, a hypothesis originally proposed by Alfred Wegener in the 1920s, which stated that the Earth’s surface was formed by plates that had gradually moved throughout geological time, pushing continents apart. However, continental drift was not a widely accepted theory in the 1950s. In fact, it remained scientific ‘heresy’ for some,1515Felt, Soundings, p. 100. so Tharp’s findings were vehemently rejected at first, and even Heezen dismissed them at one point as ‘girl talk’.1616See Tharp, ‘Connect the Dots’; Winther, ‘Mapping the Deep Blue Oceans’, p. 110; Felt, Soundings, p. 99. Eventually, Tharp’s graphs and maps, where the rift valley was clearly visible, became central to the exploration of the mechanisms of continental drift and the subsequent acceptance of the theory of plate tectonics by the international geoscientific community.1717Knoll, A Brief History of the Earth, pp. 45–47.

Among the various visual artefacts that Tharp produced, the physiographic diagrams of the Mid-Atlantic Ridge became the most well-known outcomes of her exploratory work (see Figure 1).1818For a review of the variety of scientific maps that Tharp produced, beyond the physiographic diagrams, see Winther and Raffn, ‘What If?’, pp. 221–22. A physiographic diagram is a type of map that represents the topographical features of an area, not just by applying simple strokes to outline the location of mountains and valleys, but, as Felt describes, by using ‘intricate nests of black lines that made the crags and ridges on the ocean floor look three-dimensional’.1919Felt, Soundings, p. 104. Tharp stated that this technique helped her to represent a terrain as if viewed ‘from a low flying plane’,Beginning of page[p. 54] adopting a forty-five-degree angle.2020Tharp, quoted in ibid., p. 104. The physiographic technique was developed by Armin Kohl Lobeck, a Columbia professor of geomorphology who aimed to produce vivid and accessible sketches of territories that could be easily read without any specialized knowledge in geology or cartography. At the Lamont-Doherty Earth Observatory, also based at Columbia University, Tharp and Heezen adopted this technique in their work, similarly motivated by the goal of producing accessible, readable representations of the vast, hitherto mysterious seafloor.2121Felt, Soundings, pp. 104, 108.

Abstraction, understood as omission, was indeed a key strategy employed in the production of Tharp’s physiographic diagrams. Winther has made this point with regard to the ‘simplifications’ required to streamline the most valuable information necessary to produce a Beginning of page[p. 56] readable map of the ocean floor.2222Winther, ‘Mapping the Deep Blue Oceans’, p. 106. Here I try to further spell out Winther’s point about omission in the physiographic diagrams. Many features were omitted in the representation of the Mid-Atlantic Ridge, since, from the overwhelming amount of data collected during ocean sounding expeditions and brought to the laboratory, Tharp left out all that which did not appear directly relevant to the study of the morphology of the landscape formations postulated, such as the V-shape valley profile of the ridge.2323Ibid., p. 110. Yet, the omission of one notable feature is especially conspicuous in her maps: the Atlantic ridge is depicted as if the water in the ocean basin was completely subtracted from it. As Tharp remarked: ‘There is only one proper way to sketch or to contour the ocean floor and that is to present it as it actually exists as it would be seen if all the water were drained away.’2424Marie Tharp, ‘Mapping the Ocean Floor: 1947–1977’, in The Ocean Floor: Bruce Heezen Commemorative Volume, ed. by R. A. Scrutton and M. Talwani (New York: Wiley, 1982), quoted in Winther and Raffn, ‘What If?’, p. 219. Once water was omitted, Tharp could depict the seafloor as viewed from above, employing shading in her drawing to indicate the different heights of the mountains, as if the sun was projecting their shadows onto the ground.2525Winther, ‘Mapping the Deep Blue Oceans’, pp. 107, 116. She used a type of sketching called hachuring, consisting in the accumulation of (thin or thick) lines to indicate the orientation and length of the slopes, while emphasizing the flatness of the abyssal plains.2626Felt, Soundings, p. 109. Also, Tharp and Heezen decided that the vertical scale used to represent the ridge profile needed to be exaggerated, in order to facilitate the recognition of the rift running along it. They used a strong geometric distortion of 40:1; that is, the mountain height was reduced by considerably less — by a factor of forty — in the scaling process than the ocean width and length (horizontal scales). Winther explains how ‘she had to do this in order to show the Mid-Atlantic Ridge profile in a meaningful and memorable way. Otherwise, the profile would have nearly disappeared into a solid line barely crawling along the ocean bottom.’2727Winther, ‘Mapping the Deep Blue Oceans’, p. 107. See also Felt, Soundings, p. 97.Beginning of page[p. 57]

Two observations regarding abstraction can be made from this case, developing points already hinted at by Winther.2828Winther also makes additional points about Marie Tharp’s practice of abstraction that I do not address here, regarding, for instance, the role of her selection of scale and projection in the production of her maps, and the types of modal reasoning (‘what-if thinking’) that abstraction allowed Tharp to perform. See Winther, ‘Mapping the Deep Blue Oceans’, pp. 103–05; and Winther and Raffn, ‘What If?’, p. 223. Firstly, Tharp’s practice of abstraction, understood as the omission of either irrelevant or obstructing features (such as the ocean water), was central to her construction of memorable maps. At the same time, one can see that Tharp’s omissions and her parallel acts of exaggerating the profiles of the mountains and introducing fictional shading are hardly separable from one another. That is, the omission of features permitted the insertion of idealizations, while the possibility of idealizing the look of the ridge in a fertile manner motivated the omission of certain features of the ocean instead of others.

Secondly, Tharp’s practice of abstraction involved more than omission, not only in the sense that idealizations were intertwined with the omissions she introduced, as I have just pointed out, but in a stronger sense. Abstraction here involved ordering and the establishment of connections between features in order to impose a pattern onto previously disjointed sets of data. As I will develop in section five, this entailed an imaginative, creative activity. In their 1959 article, Tharp, together with Heezen and Maurice Ewing, commented on how preparing a marine physiographic diagram ‘requires the author to postulate the patterns and trends of the relief on the basis of cross sections and then to portray this interpretation in the diagram’.2929Heezen, Tharp, and Ewing, The Floors of the Oceans, p. 3, my emphasis. See also Winther, ‘Mapping the Deep Blue Oceans’, p. 4. Patterns on the ocean floor that were previously unseen are now brought to the fore by the practice of abstraction, facilitating the production of diagrams that could advance hypotheses about the morphology of the ocean floor and, in turn, help examine its implications for the theory of continental drift.

More specifically, Tharp and her colleagues had to proceed through a series of steps to produce the physiographic diagrams (see Figure 2). These successive steps exemplify how abstraction here involved ordering, together with omission, and the establishment of Beginning of page[p. 58] connections between features to form a coherent, readable map.3030The following description of these steps is taken from Heezen, Tharp, and Ewing, The Floors of the Oceans, p. 3; Tharp, ‘Connect the Dots’; Felt, Soundings; and Winther and Raffn, ‘What If?’. First, they produced simple, flat diagrams with the plotted lines of soundings, using data collected from ships tracking across the ocean with fathometers (labelled ‘b’ in Figure 2). Here the vertical scale distortion was already inserted, in order to help visualize the location of the V-shaped rift. These first diagrams were then transformed into sketches of the mountain profiles of the seafloor, highlighting the succession of peaks and valleys observed (‘c’). Then, using these scattered sketches, Tharp drew the mountains onto the maps with a three-dimensional appearance, in such a way that the ‘entire pattern’ of the ocean would appear to the eye.3131Felt, Soundings, p. 97. Tharp, Heezen, and Ewing filled the areas for which no sounding data was available by way of extrapolation from nearby areas and interpolation from general trends inferred (‘d’). ‘In other words’, they explained, ‘we made educated guesses to fill in the dataless gaps.’3232Heezen, Tharp, and Ewing, The Floors of the Oceans, p. 3; Tharp, ‘Connect the Dots’. Abstraction, understood as a dynamic combination of omission and the imaginative, resourceful ordering of previously disconnected features as an intelligible whole, was a fundamental part of the process required to move from diagrams to profile drawings, and then to three-dimensional maps. As Tharp stated, the study of the succession of peaks and valleys in the profiles plotted during the preparation of the physiographic diagram ‘revealed the existence of morphological features and morphological provinces not previously delineated’.3333Heezen, Tharp, and Ewing, The Floors of the Oceans, p. 3. These newly revealed structures were then accentuated and vividly displayed by the three-dimensional drawings on the maps. Winther comments that Tharp ‘possessed powerful capacities to see all the parts of a system in a holistic, dynamic, and interactive manner’, skills that went hand in hand with her mastery of abstraction in the drafting practice here illustrated.3434Winther, ‘Mapping the Deep Blue Oceans’, p. 109.

This historical episode suggests that, on the one hand, abstraction as omission is important for modelling practices, as it concerns the Beginning of page[p. 60] fundamental activity of singling out, simplifying, and distinguishing the relevant from irrelevant features of a represented target system. On the other hand, a closer look at the process of abstraction in Tharp’s mapmaking practices reveals that more than omission is required in order to account for the value of abstraction as a cognitive strategy; that is, this demands the inclusion of an element of ordering and the imaginative superimposition of connections between the features included in the representation.

4. Three Criticisms of Accounts of Abstraction as Omission

Based on the foregoing analysis, three specific criticisms of traditional accounts of abstraction as mere omission can be formulated. A first criticism points to the difficulty of drawing a clean distinction between abstraction and idealization in practice. When Tharp removed the water from the representation of the ocean basin, she inevitably had to idealize the look of the seafloor, for instance by including fictional shading, since the visual depiction of the mountain chains, for which only sounding data was available, required her to imagine their appearance, as well as how shadows would be projected, in analogy with visible mountains above sea level. More generally, abstractions and idealizations are not easily distinguishable from one another because there are often causal dependencies between the different features constituting a system, so that by omitting some of them, the relations between the features included in the representation and those left out become lost. Collin Rice has recently argued that ‘the abstraction of certain features would almost always insert distortions with respect to other features. For instance, leaving out environmental features distorts how genetics contributes to development.’3535Rice, Leveraging Distortions, p. 4. The example Rice uses is taken from Helen Longino, Studying Human Behavior: How Scientists Investigate Aggression and Sexuality (Chicago: Chicago University Press, 2013) <https:/​/​doi.org/​10.7208/​chicago/​9780226921822.001.0001>. The difficulties of distinguishing idealization from abstraction are also discussed in Uskali Mäki, ‘Isolation, Idealization and Truth in Economics’, in Idealization VI: Idealization in Economics, ed. by Bert Hamminga and Neil B. De Marchi, Poznań Studies in the Philosophy of the Sciences and the Humanities, 38 (Amsterdam: Rodopi, 1994), pp. 147–68 <https:/​/​doi.org/​10.1163/​9789004457379_010>; and Leif Hancox-Li, ‘Idealization and Abstraction in Models of Injustice’, Hypathia, 32.2 (2017), pp. 329–46 <https://doi.org/10.1111/hypa.12317>. Leif Hancox-Li agrees that there is Beginning of page[p. 61] no general way of unambiguously distinguishing between abstractions (understood as omission) and idealizations, unless one determines in advance that if the form of the omission one introduces is ‘harmless’ for the goals of the modelling, then it is an abstraction, whereas if it distorts, for instance by omitting a difference-maker or key feature in the identification of a mechanism, then it is an idealization.3636Hancox-Li, ‘Idealization and Abstraction in Models of Injustice’, p. 6. But, of course, whether an omission is harmless or not will depend on the particular purposes of the model and on what scientists believe to be the main features of the phenomenon under investigation at the beginning of the activity.

A possible consequence of this first criticism might be the rejection of the terminological distinction between idealization and abstraction altogether. It remains to be seen whether this conclusion must necessarily be reached, or whether it might remain a useful distinction to be drawn, in order to identify different aspects of practices of misrepresentation that are not exactly equivalent. Introducing this first criticism here has the more limited aim of calling attention to the fact that, in actual modelling practices, omitting certain features of the target under investigation most often elicits the introduction of either intentional or unintentional distortions, enriching and complementing one another.

A second criticism of accounts of abstraction as mere omission is that such accounts imply that scientists omit certain features of a target because they know from the beginning of their practice which features of the system being investigated are relevant and which are not. However, determining which features are relevant is often the result of a process of modelling with abstractions, and not the starting point. Tharp inferred certain trends from the profile diagrams that she and Heezen produced based on sounding data, and then projected those trends onto the map in the form of conspicuous visual patterns, by making ‘educated guesses’ to fill the data gaps. They wished to find out how things would look, and how things would be structured, if certain peak and valley successions were imposed on wide areas of the seafloor.Beginning of page[p. 62] They did not know with certainty, in advance, what the central aspects were of the morphology of the system they were studying. The process of abstracting facilitated the visualization of noteworthy relationships that had until then remained occluded.

A third criticism of accounts of abstraction as omission follows from the previous two. It has been frequently assumed in these accounts that abstraction is ‘harmless’, in the sense that it does not hamper accurate representation.3737Ibid. This is a questionable claim not only because something’s being harmless or not will depend on the particular modelling goals set in advance, as discussed above, but also because if we take abstraction to be harmless in general, then the contribution of abstraction to modelling will be ‘strictly passive’, that is, it will not do any serious explanatory or exploratory work.3838Rice, Leveraging Distortions, pp. 120–21. To the contrary, what Tharp’s case makes manifest is that the abstractions employed were neither passive nor innocuous. They were in fact highly creative, in the sense that they demanded scientists to engage in an active practice of ordering and establishing connections between the scattered data they possessed concerning the morphological features of the ocean floor, in conceptually and visually imaginative ways, until noteworthy patterns emerged. In a recollection of their research in the 1950s, Heezen remarked that the physiographic maps drawn by Tharp afforded an ‘abstract view of the sea floor [… which] can be seen in no other way but in the mind’s eye’.3939Bruce Heezen and Charles D. Hollister, The Face of the Deep (Oxford: Oxford University Press, 1971), p. 7, quoted in Winther and Raffn, ‘What If?’, p. 221. The mind’s eye was required to imagine the content of as-yet-unexplored areas of the deep ocean and to transform that content into a unifying material representation in the form of a map. Creativity and the systematic exercise of the imagination were fundamental to carrying out this task. An anecdote recalled by Tharp, concerning the final step of the production of the physiographic map of the Atlantic, affirms and nicely illustrates abstraction as a creative practice. At the bottom of the map, she located a large white legend (see Figure 1), partly for the purpose of covering up an area of the ocean about which almost no sounding data was available, but also — as Tharp playfully suggested to Heezen — so as to ‘include Beginning of page[p. 63] mermaids and shipwrecks’ next to it, to surreptitiously imply, ‘like the cartographers of old’, that acts of guesswork about unknown areas were fundamental to the process of constructing the map. Unfortunately, ‘Bruce [Heezen] would have none of it.’4040Tharp, ‘Connect the Dots’; Winther and Raffn, ‘What If?’.

5. Creative Abstraction in the Arts

Taking into account the three foregoing criticisms of the orthodox view of abstraction as omission, what could an alternative, revised account of abstraction in science be? Much has been advanced already, as the key seems to be to incorporate the fact that abstraction is an active, creative practice through which epistemic agents gain access to important patterns concerning the relationships between (morphological, structural, mechanistic) features operating in a system of interest. In attempting to spell out the implications of a creative account of abstraction, this section incorporates some insights from the arts, given the longer and more sophisticated tradition of discussion about the aesthetic and epistemic potential of abstraction in this field.4141One might ask to what extent this leap of argumentation, and move from the discussion of abstraction in science to abstraction in art, is justified. If one adopts a framework that accepts that the sciences and the arts are domains that share the epistemic aim of advancing understanding of the world, as, for instance, Nelson Goodman and Catherine Elgin each do, then the leap may not be that difficult to bridge. Still, even from a more traditional conception of the separation between the two domains, according to which the sciences are understood as the enterprise of producing new knowledge, while the arts are a purely aesthetic domain with no genuinely epistemic function, one could nevertheless accept that a dialogue with the arts, where the notion of abstraction has been problematized thoroughly, might yet serve as an inspiring resource for philosophers of science to examine unexplored aspects of the debate on abstraction in science. See Nelson Goodman, Languages of Art: An Approach to a Theory of Symbols (Indianapolis: The Bobbs-Merrill Company, 1968); and Catherine Elgin, True Enough (Cambridge, MA: MIT Press, 2017) <https:/​/​doi.org/​10.7551/​mitpress/​9780262036535.001.0001>. In the writings of early twentieth-century modernist artists, for instance, one finds multiple reflections on abstraction as a highly creative activity.4242Anna Moszynska, Abstract Art, 2nd edn (London: Thames and Hudson, 2020). In the theoretical as well as more practice-oriented writings of artists like Wassily Kandinsky, Hilma af Klint, Paul Klee, Piet Mondrian, Anni Albers, and Kazimir Malevich, abstract composition is rarely understood as a matter of pure omission or of the elimination of details Beginning of page[p. 64] from an initially realistic pictorial form. Here, abstraction also involves adding and supplementing, in such a way that the artist creates connections in the world that have not been seen before. Thus, abstraction is for modernist artists a ‘creative’ practice in the literal sense of the word.

More specifically, Wassily Kandinsky describes the practice of producing an abstract composition as occurring in successive steps. ‘[O]ne of the first steps into the realm of abstraction’, he writes, is the ‘rejection of the third dimension’, the perspectival core of figurative representation, to the point that the identification of everyday objects on the surface of the canvas is no longer possible.4343Wassily Kandinsky, On the Spiritual in Art [1911], ed. and trans. by Hilla Rebay (New York: Solomon R. Guggenheim Foundation, 1946), p. 77. Until this point, the process he describes seems to coincide with the conception of abstraction as the omission of features, as discussed earlier, which in this case primarily entails the omission of spatial perspective and of recognizable three-dimensional objects. Yet the key for Kandinsky is the subsequent step, in which the artist, in their continued work towards abstract composition, creates ‘an ideal surface’, with its own internal organization, existing independently of the original scene or experience that motivated the artistic creation.4444Ibid., p. 77. This new ideal plane, despite being non-figurative, is still three-dimensional for Kandinsky, since lines, shapes, and colours are here superimposed, creating the impression of depth, with some forms appearing closer to the viewer than others. Viewers are then to examine the internal configurations of the ideal plane on the canvas, and to cultivate an aptitude for the detection of relevant relationships existing among those lines, shapes, and colours.

Anni Albers, student and then teacher and workshop director at the Bauhaus school in Dessau, has a comparable creative conception of abstract composition. Weaving, Albers asserts, is an art form that uses material resources such as thread and loom operations to produce genuine abstractions (Figure 3).4545Ann Coxon, Briony Fer, and Maria Müller-Schareck, Anni Albers (London: Yale University Press and Tate, 2018). Her own ‘pictorial weavings’ are acts of creating independent abstract planes on two-dimensional textile surfaces: ‘let threads be articulate again and find a form themselves Beginning of page[p. 65] to no other end than their own orchestration.’4646Ibid., p. 13. This internal orchestration of the composition is not only the product of a practice of omission, by which figurative form is left out and only essential geometric shapes kept in, but also of a practice of creative ordering, implemented ‘out of dots, out of lines, out of a structure built of those elemental elements’ which compose the organized abstract plane in textile form.4747Ibid., p. 21.

It is not only modernist visual artists that have highlighted the creative nature of abstract composition. In contemporary aesthetics, one can also find illuminating philosophical reflections on how abstraction constitutes a creative practice. Kendall Walton, whose work on make-believe has been as crucial for philosophers of science as for philosophers of art in describing the epistemic functions of fictions, explains the role of abstraction in terms of the ‘imagined seeing’ of connections that it affords.4848Kendall Walton, Mimesis as Make-Believe: On the Foundations of the Representational Arts (Cambridge, MA: Harvard University Press, 1990). When viewers encounter an abstract artwork and recognize the various elements present in the composition (lines, shapes, colours), they can imagine seeing relationships between them and, in turn, make inferences about further relationships occurring between objects and features in the world outside of the plane, in light of the learning process that the abstract work facilitated.4949Richard Wollheim, ‘Seeing-as, Seeing-in and Pictorial Representation’, in Wollheim, Art and its Objects, 2nd edn [1980] (Cambridge: Cambridge University Press, 2015), pp. 137–51 <https://doi.org/10.1017/CBO9781316286777.009>. In comparable terms, Michael Newall has more recently referred to the ‘non-veridical perception’ that takes place in our encounters with visual abstractions.5050Michael Newall, What Is a Picture? Depiction, Realism, Abstraction (Basingstoke: Palgrave Macmillan, 2011) <https://doi.org/10.1057/9780230297531>. This is because abstract space is a ‘space other to that of our everyday experience’, where the ‘planes, lines and strokes of paint that do inhabit it appear to be ruled by different laws to those of gravity and mechanics’. As in a liberated territory, relationships between features can occur more freely, ‘according to some alternative, pictorial mechanics’.5151Ibid., p. 194. Abstractions, understood in this way, help us Beginning of page[p. 67] to freely explore and imagine possibilities within the abstract space thus created, and to eventually transfer some of the formal, visual, or material relationships perceived within the autonomous space of the artwork to aspects of the world existing outside of it.

The ideas concerning artistic abstraction succinctly collected here can inform the debate on the epistemic value of abstraction in scientific modelling. What we seem to find in debates in the arts is a general tendency to consider the omission of irrelevant features at best the first step, and not the goal, of abstract composition. Artistic abstraction is primarily conceived as an imaginative, creative act, which produces autonomous spaces for the exploration of forms, materials, and structures, and foregrounds relevant relationships recognized between these components. Scientific modelling practices, such as the production of Tharp’s physiographic maps, should be understood as an analogous type of creative act. Thanks to abstraction, insightful relationships between previously disconnected features of a natural system, such as the ocean floor, can be brought to the fore and organized in a coherent, unifying manner. If philosophers of science were to adopt more creative conceptions of abstraction in the current modelling debate, the supposed differences between abstraction and idealization would to some extent vanish, since the two strategies would wear their active, imaginative character on their sleeves. That is to say, idealization would remain an active practice of inserting (potentially fruitful) falsehoods in a model, while abstraction would stand now as an active practice of omitting and creatively ordering features until a cogent, insightful pattern emerges.

6. Abstraction as Strategy for Worldmaking

So far, the sense of abstraction sketched here builds on omission but adds an aspect of creative ordering to it. Yet one could take this proposal a step further and admit that if abstraction has a creative nature, then abstract representations can be generative too. That is, the strongest consequence of the present account is that abstraction can be understood as a strategy for worldmaking. In Ways of Worldmaking, Nelson Goodman argues that worlds are constantly made from other worlds, which we already have at hand, through the manipulation of Beginning of page[p. 68] symbol systems.5252Goodman, Ways of Worldmaking. His thesis is that what there is in the world depends on our conceptual schemes and representational systems. As he states: ‘recognizing patterns is very much a matter of inventing and imposing them.’5353Ibid., p. 22. And abstraction, as we have seen, is especially helpful for uncovering/establishing trends and patterns in modelling practices. Goodman specifically enumerates ‘deletion’, ‘weighting’, ‘composition’, ‘decomposition’, ‘ordering’, and ‘deformation’ as strategies commonly used to build world versions, to which we could add abstraction, understood in the rich, creative sense described here (or perhaps as a systematic combination of several of the strategies listed by Goodman).5454Ibid., pp. 7–16.

The worldmaking capacity of abstraction was in fact already hinted at in early abstractionist thought. Kandinsky produced a series of prints, entitled Kleine Welten (Small Worlds), which stands as an intriguing example of the new, independent worlds that abstraction helps create.5555I thank Ross Shields for the lead to these artworks. The twelve prints of the portfolio Small Worlds (Kleine Welten) by Kandinsky, from 1922, can be seen as part of the Museum of Modern Art’s digitalized collection. See <https://www.moma.org/collection/works/portfolios/143911> [accessed December 2023]. More explicitly, Paul Klee held that ‘art does not reproduce the visible; rather, it makes visible’, so that ‘out of abstract elements a formal cosmos is ultimately created’.5656Paul Klee, ‘Creative Confession’ [1920], in Klee, Creative Confessions and Other Writings, ed. by Matthew Gale, trans. by Norbert Guterman (London: Tate, 2013), pp. 7–14 (p. 7). If the omission of irrelevant features of a target system were, at best, the first step in the practice of abstracting, ‘creating a cosmos’ would be its final, most ambitious step, that which exposes its incredibly generative potential. Not surprisingly, Winther also identifies this worldmaking potential in Marie Tharp’s work. The oceanographic community initially received the publication of her first physiographic map of the Mid-Atlantic Ridge in 1957 with scepticism, but progressively ‘Tharp’s maps became the world’.5757Winther, ‘Mapping the Deep Blue Oceans’, p. 109, italics in the original.

Of course, some philosophers committed to metaphysical realism might be dissatisfied with the idea of taking the term worldmaking too Beginning of page[p. 69] literally. They may wish to contest that nothing is really created in the practice of using abstractions in representation.5858Elgin, True Enough, p. 257. Did Tharp’s maps, Kandinsky’s and Klee’s paintings, and Albers’s fabrics really make a world? Even Goodman asked himself, rather rhetorically: ‘shouldn’t we now return to sanity from all this mad proliferation of worlds?’5959Goodman, Ways of Worldmaking, p. 20. In a sense, the relationships foregrounded by practices of abstraction, and the patterns made visible through them, are not really brought into existence by the abstractions: they were there all along, waiting to be organized and unified by the scientist or artist in question.6060This is a modified version of the argument made in Elgin, True Enough, p. 257. This is true but trivial, argues the philosopher of science and art Catherine Elgin, in line with Goodman, since we have little reason to care about the many potential relationships that exist outside of our representational practices in a non-meaningful way.6161Ibid., p. 257. Intentionally employing the resource of abstraction is an act of creating meaningful relationships, by discriminating between the myriad features that agents encounter and drawing lines (also literally in the cases of Tharp, Kandinsky, and Albers) between some of them. The novel relationships highlighted by our best artistic and scientific representations have the potential to transform our vision of the world as we conceive it. So, both for Goodman and Elgin, the prospect of an alternative metaphysical position, which rejects the worldmaking capacity of strategies like abstraction, and tries instead to search for a neutral, underlying version of the world that is not explained through our representational systems, is desolating. Such a world would be a ‘world without kinds or order […] or patterns — a world not worth fighting for or against’.6262Goodman, Ways of Worldmaking, p. 20.

Leaving metaphysical worries aside, do we have reasons to be concerned about the potential of abstraction for worldmaking? It was mentioned earlier that those who support accounts of abstraction as omission assume not only that abstraction is passive but also that it is harmless. In clear contrast, to adopt a creative view on abstraction means to acknowledge that abstraction has the potential to be both a positively fruitful and a harmful cognitive strategy, insofar as it is Beginning of page[p. 70] a tool to make, remake, and transform the world. Abstraction can produce epistemic fruits as well as epistemic harms, so one should be wary of the epistemic and pragmatic consequences of adopting dubious abstractions. Pragmatist philosophers such as John Dewey and William James referred to the dangers of ‘vicious abstractionism’ with precisely this worry in mind. Winther reads the warnings of pragmatists as pointing to the effects of the ‘pernicious reification’ that abstractions can lead to.6363Rasmus Winther, ‘James and Dewey on Abstraction’, The Pluralist, 9.2 (2014), pp. 1–28 (p. 1) <https://doi.org/10.5406/pluralist.9.2.0001>. Winther applies the notion of ‘pernicious reification’ in his reading of different pragmatist works, including William James, Pragmatism [1907] (Cambridge, MA: Harvard University Press, 1979); and John Dewey, Human Nature and Conduct, 1922, ed. by Jo Ann Boydston, The Middle Works, 1899–1924, 14 (Carbondale: Southern Illinois University Press, 1983). Roughly put, pernicious reification happens when cognitive agents endorse the knowledge that results from an abstract concept or abstract visual representation but ignore the particular function that the abstraction was supposed to play, overlooking the historical conditions of the emergence of the abstraction, and disregarding its appropriate domain of application.6464In comparable terms, Alfred North Whitehead calls this the ‘fallacy of misplaced concreteness’. See Alfred North Whitehead, Science and the Modern World [1925] (New York: The Free Press, 1967), p. 51; and Alfred North Whitehead, Process and Reality: An Essay in Cosmology [1929] (New York: The Free Press, 1978), p. 93. When such aspects are not considered, the products of the abstraction are inappropriately universalized and ontologized, thus failing to operate in real life.6565Winther, ‘James and Dewey on Abstraction’, pp. 1, 9.

Other types of warnings about the risks of abstraction have come from political theory and feminist critique in recent decades. A claim commonly found in these fields is that there are no such things as value-free abstractions, as when abstract formal models of justice6666Lisa H. Schwartzman, ‘Abstraction, Idealization, and Oppression’, Metaphilosophy, 37.5 (2006), pp. 565–88 <https://doi.org/10.1111/j.1467-9973.2006.00457.x>. or general ethical principles6767Onora O’Neill, ‘Abstraction, Idealization and Ideology in Ethics’, Royal Institute of Philosophy Supplements, 22 (1987), pp. 55–69 <https://doi.org/10.1017/S0957042X00003667>. are proposed, or when the consequences of adopting certain abstract scientific representations are uncritically endorsed.6868On the presence of social and other non-epistemic values in science, see Helen Longino, Science as Social Knowledge (Princeton, NJ: Princeton University Press, 1990); Heather Douglas, Science, Policy, and the Value-Free Ideal (Pittsburgh: University of Pittsburgh Press, 2009) <https:/​/​doi.org/​10.2307/​j.ctt6wrc78>; and Potochnik, Idealization and the Aims of Science. The political philosopher Onora O’Neill Beginning of page[p. 71] has, for instance, highlighted that idealized as much as abstract theory, in aiming towards generality, can ignore the distinctive experiences of the oppressed, because the abstractions such theories entail are value-charged in ways that often exclude the social and historical features that are constitutive of human agency.6969O’Neill, ‘Abstraction, Idealization and Ideology in Ethics’, pp. 56–64. Lisa Schwartzman also points out that ‘methods of abstraction often involve the bracketing of information that is crucial to understanding the nature and sources of oppression’, adding that ‘many allegedly abstract theories actually assume a male norm’.7070Schwartzman, ‘Abstraction, Idealization, and Oppression’, p. 567. Although the conceptualization of abstraction in the work of these feminist scholars matches the definition of abstraction-as-omission more closely than the creative definition of abstraction that is endorsed here, their critical assessments reflect the attribution of a generative, worldmaking potential to abstractions, hence their critiques still hold strongly here.

Importantly, Schwartzman avers, the solution to the potential harms of abstraction ‘is not simply to do away with all abstraction’ and focus on the particularities of specific situations and individuals. The best way to approach the problem ‘may be to pay attention to the kinds of abstraction’ that a given representation employs and to disallow those that perpetuate forms of oppression.7171Ibid., p. 575. The reason why the possibility of eliminating abstractions from our representations should be rejected in general is that it would be both unfeasible and unproductive: ‘abstraction is unavoidable in all reasoning’,7272O’Neill, ‘Abstraction, Idealization and Ideology in Ethics’, p. 55. since abstract models and images help us to navigate among concrete descriptions of situations. ‘It is only when we see situations of that sort as requiring action of this type’, O’Neill says, ‘that knowledge of some description becomes action guiding.’7373Ibid., p. 64, emphasis in the original. Critical race theorist Charles Mills adds, similarly, that rejecting abstraction ‘deprives one of the apparatus necessary for making general theoretical statements’, and indeed hampers Beginning of page[p. 72] the possibility of ‘critiquing those same hegemonic misleading abstractions’ that one observes in certain forms of representation.7474Charles Mills, ‘Ideal Theory as Ideology’, Hypatia, 20.3 (2005), pp. 165–83 (p. 173) <https://doi.org/10.1111/j.1527-2001.2005.tb00493.x>.

These last remarks about the potential harms of abstraction have a much broader scope than the specific case of scientific modelling with which this chapter began. I end with them to stimulate further reflections on how the worldmaking abilities of scientists, artists, and social agents more generally, should also remind us of the limits, constraints, and risks that abstractions, among other (mis)representational strategies, impose. Amia Srinivasan has perceptively noted that ‘successful representational interventions have a Janus-faced structure’: they picture an aspect of the world ‘as it is currently constituted, and yet also picture it anew’, striking ‘a fine balance between familiarity and departure’.7575Amia Srinivasan, ‘VII — Genealogy, Epistemology and Worldmaking’, Proceedings of the Aristotelian Society, 119.2 (2019), pp. 127–56 (p. 150) <https://doi.org/10.1093/arisoc/aoz009>. It is precisely in this sense that abstract representations are creative acts. They afford understanding of a familiar, yet not fully known world, and, at the same time, they describe it in a manner that has never been thought of before. Like Tharp’s map-making world interventions, they find a balance between depicting a part of the world as it is, accurately, and constructing it anew.Beginning of page[p. 73]