Fabrizio Li
email: fabrizio_livigni@hotmail.com

Regimes of evidence in complexity sciences

Keywords: Complexity sciences, Santa Fe Institute, epistemic argumentative regimes, ontological views, Science e. dynamical systems, statistical physics, agent-based models, network simulations, cellular automata, genetic algorithms, spin glasses, Big Data statistics, etc. Like

Since their inception in the 1980s, complexity sciences have been described as a revolutionary new domain of research. By describing some of the practices and assumptions of its representatives, the present article shows that this field is an association of subdisciplines laying on existing disciplinary footholds. The general question guiding us here is: On what basis do complexity scientists consider their inquiry methods and results as valuable? To answer it, I describe five "epistemic argumentative regimes," namely the ways in which complexity scientists argue the credibility of their research, and five "ontological views," that is the ways in which they interpret the material and formal causes of their study objects and models. Finally, the article proposes the term of "regime of evidence" to designate the specific combination of one ontological view with one or more epistemic argumentative regimes.

Introduction

From 1982 to 1984, a group of senior physicists from the Los Alamos National Laboratory, the University of Illinois, Princeton, and Caltech gathered regularly in order to discuss about their common objective of founding an interdisciplinary research institution. In 1984 they decided to establish a private research center called the "Santa Fe Instite" (SFI) in Santa Fe, New Mexico (Li Vigni 2020c). At the same time, they launched the "science of complexity" conceived of as an overarching theory of all complex adaptive systems (Cowan et al. 1994).

considered "complexity" as a "revolution in science as a whole" (p. 327). British sociologist John Urry has talked about a "complexity turn" in knowledge [START_REF] Urry | The Complexity Turn[END_REF]) and claimed that "complexity sciences seem to provide the means to overcome [the] divisions between nature and society and between the natural/physical sciences and the social sciences" (Urry 2006, p. 115). Historians [START_REF] Schweber | Complex Systems, Modelling and Simulation[END_REF] have also written that, thanks to the computer, sciences have underwent a "Ian Hacking revolution," which has transformed scientific practices of several disciplines, created new scientific institutions and vehiculated a new feel to the world. In their article, Schweber and Wächter have focused on one of the components of such a revolution, what they call the "complex systems computer modelling and simulation revolution." While computer simulation gives a "new perception of the notion of scientific model" by allowing an interactive and visual character (p. 606), the SFI is, according to them, "perhaps the paradigmatic institutional manifestation" of such a revolution (p. 588). 1 As a reviewer of this article has suggested.

Today only very few complexity scientists believe in the actual or yet-to-come unity of a science of complexity. They are generally scientific entrepreneurs who struggle for the institutionalization of the field (e.g. Bourgine and Johnson 2006;Weisbuch 2007). But the vast majority of complexity practitioners and observers do agree on its internal socioepistemic heterogeneity. As for the novelty of complexity on the contrary, there seems to be less discussion and critique. In the light of a careful analysis, observers' descriptions about the revolutionary power of this domain seem to echo complexity founders' (often grandiloquent) promises and claims according to which, because of its anti-reductionist, anti-deterministic, post-Newtonian and holistic approach [START_REF] Mitchell | Complexity. A Guided Tour[END_REF], complexity science (in the singular) was going to be the "science of the XXI century" (SFI 2009;[START_REF] Ixxi | Communiqué de presse. L'Institut rhônalpin des systèmes complexes au coeur de la recherche du 21 ème siècle![END_REF]. Nevertheless, if we adopt a pragmatist and Science & Technology Studies (STS) approach based on the empirical analysis of scientists' practices, we are soon brought to confirm the intrinsic heterogeneity and looseness of complexity as well as to contest its radical novelty. Its representatives rather adopt a multiplicity of ways to accumulate scientific credibility in a plurality of subdisciplines gathering together intermittently, in visiting institutes and conferences, under the generic term of complex systems. Some of these subfields existed before the birth of the SFI, some others have appeared afterwards but have mutualized epistemic tools, styles and frameworks from established disciplines.

While several normative articles exist about complexity epistemology, works on what complexity scientists actually do are rarer (e.g. [START_REF] Varenne | La reconstruction phénoménologique par simulation : vers une épaisseur du simulat[END_REF][START_REF] Varenne | Théories et modèles en sciences humaines[END_REF]. This article offers to fill the gap by proposing the concept of regimes of evidence as the articulation between one or more epistemic argumentative regimes with one ontological view. The first term refers to the ensemble of numerical, narrative, material and visual arguments that scientists mobilize in order to increase the credibility of their research, by claiming the solidity of their methods or by establishing an evidence. Five of these are described: the parsimony, the toy model, the mathematical, the statistical and the proof of concept. The term of ontological view refers to the conception of the essence that scientists have of their study objects, of the simulations supposed to study them, and of the articulation between the two. Five of these are described: the dualist, the agnostic, the homomorphic, the vitalist and the monist. Such categorizations are the result of an inductive empirical and analytical work presented in the following pages.

The theoretical positions and the social groups of complexity scientists preexist the analysis, while the analytical terms proposed to apprehend them come after it.

The general question of this article is epistemological: On what basis do complexity scientists consider their inquiry methods and results as valuable? The method chosen to answer the question is sociological: Based on empirical material, I propose to describe what complexity scientists actually do instead of prescribing them what they should do. In the following, some extracts of interviews, scientific texts and archives are gathered in order to show the methodological practices of complexity scientists, and to deconstruct the claim of their novelty. The second section presents the materials and methods, the third and the fourth are dedicated respectively to expound the five epistemic argumentative regimes and the five ontological views that operate within the subdisciplines gathered around the label of complexity. The fifth section briefly discusses the concept of regime of evidence and in particular the question of the possible postures that scientists can have in extra-academic activities. Three configurations are thus described: the heuristic, the productive and the consulting. The conclusion summarizes the main contributions of the article.

Materials and methods

The materials which this article is based upon are composed by 115 interviews with complexity scientists from the US and Europe and some dozens texts of two types: scientific publications and institutional archives.

Interviews were semi-structuredpartly open and individualized, and partly following a general framework. Such framework contained a dozen questions about personal pathway, view of complexity sciences, main epistemological practices and methods, personal and disciplinary ontological positions, definition of computer modeling and simulation, as well as relation with policy makers, NGOs and private actors. In order to bring the interviewees to make their epistemic argumentative regimes explicit, the questions focused essentially on the way they validate models and conceive error. Similarly to what linguists and sociologists of argumentation do when they classify arguments into general categories (assertoric, apodictic, hypothetical, epistemic, normative, etc.), our take here is to propose some categories of the ways in which complexity scientists defend their inquiry practices and results. In order to dig up their metaphysical assumptions and to describe their ontological views, the questions convoked Aristotle's distinction between formal and material causes. If very few interviewees were familiar with the Stagirite's terms, all of them had either one or another of the five postures described in section four. The categorizations proposed here were built along the way of the fieldwork research, since the meetings with the scientists were dialogic experiences in which to formulate and test hypotheses with the interviewees; the writing and outreach phases have refined such categorizations. Now one may ask: What is the causal relationship between the epistemological and the ontological levels? Science and Technology Studies scholars show that epistemic, moral, material, technical and political questions always imply ontological ones, and that holding an ontological view of an object always brings about epistemic, moral, material, technical and political questions about it (e.g. [START_REF] Vermeulen | Bio-Objects[END_REF]. In other words, it is impossible to establish the priority of epistemology over ontology or vice versa, for they are coevolutive and multifactorial constituents of the work of scientists.

Interviewed researchers were mostly confirmed ones, but roughly a third were either PhD or postdoctoral. Among the scientists, about two thirds were men. The interviews lasted two hours and a half on average (few were ≤ one hour long and ≥ four hours long), they were always recorded and have been conducted most of the time in face-to-face settings within the researcher's lab, more rarely elsewhere (classrooms, cafes or private houses), and in a dozen cases by telephone or video-conference. The bulk of the interviews was determined by the choice of the pivotal institutions taken as study objectsthe SFI and the Parisian Complex Systems Institute which depends from the French Centre National pour la Recherche Scientifique (CNRS)in order to explore the hub of the American and international community on one side, and the hub of the French community (one of the largest in the world) on the other side. The rest of the actors come from other laboratories inscribed in complexity sciences: These institutions will be mentioned along with the disciplinary belonging of the people cited. Other interviewees were contacted at conferences, seminars and through the snowball effect, in order to have the widest diversity of disciplines, countries, career degrees and institutions.

As for the texts, the scientific publications mentioned in the rest of the paper have been chosen for their representativeness to illustrate the matter of each section. Secondary literature can also be cited, when a specific subdiscipline or group of complexity specialists has already been studied by other social scientists. Philosophical literature is mentioned to reinforce the findings presented here, which can sometimes permit to interpret the former. As for the archives, a support is particularly of help here: the SFI main outreach document. From 1986 to 2014, the American institute published 40 issues of its Bulletin. The articles it contained were written by SFI staff members, resident scientists and freelance journalists. It was addressed to the members of the Board of Trustees, the research officers, the SFI advisors, the scientists, the donors (past and potential), as well as to university, industrial and governmental directors. Its aim was to inform such a public about the scientific and administrative programs of the institute. The Bulletin was published once to twice per year. Printed in 5000 copies, it was available for free upon request. Later, its publication became uniquely electronical and old issues were digitalized. In the mid-2010s, the bulletin was suppressed because it was considered too expensive and less efficient than other supports. The Bulletins are an excellent material in order to explore some of the main research projects, tools, frameworks and protagonists of the American (and in some part international) complexity community.

The approach followed here is mixed. With regard to the general question addressed, the matter is clearly epistemological, for it deals with the conditions of validity of statements, models and theories. In what concerns the data collection and interpretation, the method is sociological. Each quote relates to scientists' declarations of intent and methodological practices or to their metaphysical views and assumptions. In both cases, citations have been chosen in order to show the way complexity specialists defend the idea that their science is heuristic and that it deserves credit. The answer to the epistemological questioning provided here is pragmatic and interpretive. Pragmatist and STS approaches in sociology, which are historically deeply intertwined, refer to "following the actors," to "taking the actors seriously" and to "take the scientists as informers about whom to doubt" [START_REF] Latour | Science in action: how to follow scientists and engineers through society[END_REF][START_REF] Latour | Petites leçons de sociologie des sciences[END_REF]Boltanski, 1990). In France, American pragmatist philosophers (such as William James, John Dewey, Charles Peirce and George Mead) have inspired an entire sociological familyalternative to the hegemonic Pierre Bourdieu's onewhich, according to two of its representatives, follows a series of maxims such as: The "primacy of experience;" the processual and gradual "dynamics of arguments formation" through abduction, experience and controversy; the "primacy of reasoning through consequences" (for example, it is today cogent to study conspiracy theorists and followers not because their theories are true, but because they do have tangible social effects); the "orientation toward action" instead of privileging intellectual essentializations; and the theoretical and political "pluralism" (Chateauraynaud and Debaz 2017, pp. 604-606; see also [START_REF] Barthe | Sociologie pragmatique: mode d'emploi[END_REF] for another presentation of pragmatic sociology). These maxims do not imply the withdrawal of philosophical, sociological, political and ethical critiques, but they do bring the social scientist to privilegeat least in the first placemore a comprehensive than a normative approach to the study object. While philosophers of science aspire to be "hybrids" and to contribute to the endeavor, practice and advancement of knowledge (Grüne-Yanoff 2014), here the posture is descriptive and empirical. The aim is to explicit and categorize the often implicit or unconscious ways in which scientists fabricate the credibility of their academic internal and public work, starting by what they actually do and say. As Chateauraynaud has efficaciously synthetized, pragmatist sociology "consists in taking seriously the situations, devices and processes in which people act and think, by taking a close look at their resources and constraints" (2003, p. 26, my translation). In this sense our approach here resembles to what some philosophers now practice and call the "philosophy of science-in-practice," in which thinkers "use empirical methods drawn from the historical or social sciences (such as archival research, ethnographies or interviews) to acquire insights into and evidence of scientists' research behaviour" (Boumans and Leonelli 2013, p. 260). One of the drawbacks of such approaches is that they often step aside from the epistemological debate about complexity (or any other subject), for they do not aim at adding another set of prescriptive tenets to the discussion. On the other side, their advantages are to inform philosophers and social scientists about what scientists think and practice on the ground and, by this very fact, to pave the way both to classical normative epistemological debates and to the "philosophy-of-science in practice" approach, which consists of being "directly engaged with scientific research through interaction with scientists about philosophical problems […] which often result[s] in joint publications and the organisation of joint events" (ibid., pp. 259-260).

Epistemic argumentative regimes

such regimes may overlap logically does not constitute a problem for the analysis, since this one aims at establishing the presence, within the different subgroups of complexity sciences, of different hegemonic styles of epistemic argumentation: Some put the accent more on the development of the simplest model, others on the mathematical elegance of their theories, others yet on the cumulation of statistical results. These regimes can also characterize one subdiscipline more than another. It is in this sense that complexity is far from being a scientific revolution, since it does not really propose a thoroughly new set of methodological standards. These can be either very general principles in science like the parsimony regime, or very old scientific practices such as the toy model and the mathematical regimes, or modern practices linked to the statistical regime, which has at least three sub-regimes (the goldstandard, the Popperian corroboration and the backcasting), or engineering and industrial tools like the proof of concept, which is also present in economics, design, and so forth.

The following list does not pretend to be exhaustive but to show the internal diversity of this interdisciplinary domain 2 and the preexisting nature of such frameworks and practices as they belong to well established disciplines.

The parsimony regime

The Ockham razoranother name for parsimonyis admitted as a general principle of all sciences, comes from medieval Christian philosophy and has been widely studied by philosophers of science who have proposed different methodological criteria for a fruitful usage of it [START_REF] Hoffmann | Ockham's razor and chemistry[END_REF][START_REF] Huemer | When is parsimony a virtue?[END_REF][START_REF] Sober | Ockham's Razors. A User's Manual[END_REF]. This general epistemological principle is found at the basis of all modeling activity and consists in explaining a phenomenon by invoking the smallest possible number of causes. If it is implicitly and explicitly mentioned in basically any kind of "scientific" text, it becomes a constant worry for many complex systems modelers, who often ask how much complexity they are supposed to insert into their models to make them at the same time reliable and manageable (e.g. Pumain 1997; [START_REF] Batty | Modelling complexity: The limits to prediction[END_REF]. Such principle is often convoked along with logical, esthetical and pragmatical corollary arguments such as "simplicity," "elegance" and "efficacity" (e.g. [START_REF] Holland | Hidden Order. How Adaptation Builds Complexity[END_REF].

A computer scientist from the Parisian Complex Systems Institute illustrates the principle as follows: "with very few mechanisms, I have to explain something which seems very complex to apprehend. […] the least mechanisms you have, the most you simplify the process, and the more -I think -you can understand it" (interview, 13.02.17). As a bio-informatician from the 2 One of the most important contributions of STS is the deconstruction of the positivistic account of science as a unitary approach to knowledge. Science pluralism has been variously apprehended by STS scholars through concepts like "epistemic communities" [START_REF] Haas | Do regimes matter? Epistemic communities and Mediterranean pollution control[END_REF], "epistemic cultures" (Knorr-Cetina 1999), "ways of knowing" [START_REF] Pickstone | Ways of Knowing[END_REF], "styles of knowledge" [START_REF] Kwa | Styles of Knowing. A New History of Science from Ancient Times to the Present[END_REF] and "epistemic commitments" [START_REF] Granjou | Epistemic Commitments: Making Relevant Science in Biodiversity Studies[END_REF]. Fewer works exist about interdisciplinary fields and their internal diversity. This article can also be seen as a contribution to the exploration of diversity in interdisciplinary fields of study such as complexity sciences. (interview, 15.08.15). The approach of these researchers consists in eliminating any non-indispensable hypothesis for the production of a pattern or behavior that resembles the patterns and behaviors of the target system. Some researchers from the same institute develop a platform or meta-model which, of specific models, "in the end says: this parameter is useless. Or it's useful, but only between this and this value" (interview with a computer scientist, 13.02.17). What fascinates complexity specialists as for the practical effects of such principle is its explicative power: "the phantasy we have is to be able to say […] that, if we leave out that parameter, it is compensated by other explicative parameters which lead to the same dynamics" (ibid.). In other words, simplicity is both a method and an end on the way toward efficient and reliable models.

Nevertheless, the frequency with which the Ockham razor is cited by researchers depends on the situation. A group of computational epidemiologists from Paris based at the French national health institute (INSERM) qualify parsimony as a contextual choice [START_REF] Ajelli | Comparing large-scale computational approaches to epidemic modeling: Agent-based versus structured metapopulation models[END_REF]. Depending on the aims of a given research and on the data available, scientists choose to apply a simulation approach instead of another. For example, agent-based modeling (ABM) is very precise, for it can model a territory street by street, building by building and agent by agent. But since such information is not always available everywhere and since to compute such details for the entire globe is computationally prohibitive, ABM is (for now) applicable only to a national or continental basis. It is generally privileged when the aim is to provide Northern countries policy makers with accurate prescriptions, say, about which schools to close where and when in order to avoid the spread of a contagious disease. But since network meta-population models are applicable to the entire world (for they are less coarse-grained, computationally affordable and less dependent on informational gaps), this kind of simulation is privileged when researchers wish to predict the general dynamics of a pandemics country by country (and not neighborhood by neighborhood). Interviewees generally agree on the fact that the choice of model complexification is a matter of gradations, but a fixed point remains even when the Ockham razor is not explicitly mobilized: A model which is not parsimonious is simply not considered as a functional one because, if too many mechanisms are represented into it, the scientist may become unable to distinguish which ones are the really important ones in the understanding of the target system.

The toy model regime

According to one of the most prominent members of the SFI, computer scientist Melanie Mitchell, there are four ways of doing science. Consider the following exert from one of the SFI Bulletins where the researcher is interviewed: Mitchell […] explained that there are four approaches to sciencetheory, laboratory experiments, Gedanken experiments (thought experiments), and computer experiments.

Computer experiments, she contends, allow the scientist to incorporate theory and thought in a sort of digital laboratory. (SFI 1995, p. 4) The thought experiment or, in German, the Gedanken-Experiment has an old tradition. Using intuition, it considers a hypothesis, theory or principle for the purpose of thinking through its consequences, without the need, or in the absence of the possibility, to back it up with an empirical experiment. Historically, complexity sciences appeared when the computational power of PCs was not as performant as today. Between the beginning of the 1980s and the end of the 1990s, complex systems specialists used to work almost only on "toy models," a sort of computational instantiation of the Galilean-like thought experiment3 . [START_REF] Lenhard | Thought experiments and simulation experiments. Exploring hypothetical worlds[END_REF] distinguishes the thought experiment stricto sensu from the simulation on the basis of two criteria. Both explore hypothetical worlds, but while the first is "epistemically transparent" because it takes place in cognition, the second is "epistemically opaque" because it makes use of algorithmic procedures whose calculations are not always accessible to the modeler (Lenhard on this point bases himself on Humphreys 2004): "Simulations are not opaque because it would be unclear how one step follows from its predecessors. On the contrary, it is the multitude of interrelated steps that can render the overall process opaque" (Lenhard 2018, p. 489). Also, they lay upon two different kinds of iteration, the "convergence" and the "atlas" type: the first "is involved in cases like exploring a new pathway that eventually becomes your routine way. At the beginning, there is much uncertainty and back-and-forth, but after a couple of repetitions the pathway begins to stabilize" (ibid.); the second "works rather by exhausting the possibilities and thereby creating a compendium, or atlas. The "toy model"an expression that comes from physics, definitely the dominant discipline within complexity sciences [START_REF] Deffuant | Visions de la complexité. Le démon de Laplace dans tous ses états[END_REF][START_REF] Grauwin | Complex Systems Science: Dreams of Universality, Reality of Interdisciplinarity[END_REF]; Li Vigni 2020c)is a specific kind of model which aims at exploring the causal reasons at work in a given phenomenon in a very simplified and abstract way [START_REF] Axelrod | The Complexity of Cooperation. Agent-Based Models of Competition and Collaboration[END_REF]. It is built starting from the elements which appear to be essential to the working mechanism at the basis of a given system. Moreover, this type of models is fabricated regardless of "real world" data, and sometimes does not even have a concrete target, but only a "hypothetical" one (Weisberg 2013, p. 121). By means of this simplified procedure, scientists try to show that it is possible to seize the general principles of a given phenomenon, reason why no realistic description or prediction is ever pretended by researchers working on toy models. In the light of the typology of explanations proposed by Grüne-Yanoff and Weirich (2010), toy models serve to propose "partial explanations" which describe "the operation of some factors behind a phenomenon's occurrence" by isolating such factors (p. 38) and "potential explanations" which make "more precise the possible worlds in which [a given] conjecture holds" (p. 43). [START_REF] Ylikoski | Understanding with theoretical models[END_REF] go further in the analysis of this kind of models. They write that while the "common objection is that [toy model] is too abstract to be explanatory," they defend it for it is "a device for thinking about theoretical possibilities" (p. 21-22). The important thing for them is to consider such tools in the context of "a family of related models, not as isolated representations" and "in the context of competing theories" (p. [23][24] so to permit them to complement and correct each other. Their value would lay in the fact they allow to formulate "possible causal scenarios" which can help "narrow the space of possibilities, that is, to eliminate as many of the competing scenarios as possible" (p. 25-26), as well as "causal mechanism schemes" which can constitute the "building blocks of causal scenarios" (p. 28).

Among the first and most active epistemic communities present within complexity sciences in the 1980-90s, one can mention complexity economics [START_REF] Palmer | Artificial economic life: a simple model of a stockmarket[END_REF], the physics of materials [START_REF] Stein | Spin glasses[END_REF][START_REF] Solomon | Complexity: A science at 30[END_REF], computational social sciences [START_REF] Epstein | Growing Artificial Societies[END_REF]Dean et al. 1999), computational theoretical biology [START_REF] Kauffman | The Origins of Order. Self-Organization and Selection in Evolution[END_REF][START_REF] Holland | Hidden Order. How Adaptation Builds Complexity[END_REF], as well as Artificial Life (Langton 1997). Despite the theoretical and methodological differences between all these researchers, they share the fact they have worked, and sometimes still work, with toy models. To illustrate the philosophy behind this practice, let us consider an example from a complexity economist. The following interview extract is from an American researcher who was among the first post-doctoral students at the SFI back in the 1990s. The fragment is interesting inasmuch as the interviewee contextualizes the toy model into the larger spectrum of simulation styles in economics and compares it to the thought experiment:

Question: Is simulation a kind of experiment? Answer: Yes. Or really isn't it an extension of theory? It's a theoretical model. One of the reasons why ABM got troubles in economics is that when you turn it on a computer, simulation is the attempt to get really close to reality. Lots of people try to build realistic models. In Washington there's people doing very detailed models on tax system. In these complex models you're never going to understand what's the key detail. On the other side you got these computer experiments, much simpler, toy models, not intending to be all the reality. They try to understand the basic components. The problem with economists is they believe that models should fit very well with reality to be good. And I don't think that's right. ABMs should be treated as other pencil and paper economics models, which are sort of thought experiments. (Interview,14.09.16) In other words, for some complexity scientists the toy model is the best way to push forward the understanding of systems. Now, toy model users often mention the parsimony argument in their texts and interviews. But to think that the two regimes are always and only present together would be wrong. For example, the quantitative geographers and the computational epidemiologists encountered in France and the US aim at complexifying their models as much as possible, but they also constantly mention the need to remain parsimonious.

The mathematical regime

Within complexity sciences, the mathematical formalization is a very important tool of inquiry and, for some, an objective in itself as for the power it bears in attributing credibility to research. In one of the bulletins published by the SFI, one could read that the first president George " Cowan's vision [was] to apply the quantitative tools of the physical sciences, such as mathematics, to the social sciences" (SFI 1994, p. 3). The motivation of such mission of naturalization of social sciences lays on a positivistic conviction, condensed in Ernest Rutherford's famous sentence that Cowan cites, according to which "All science is either physics or stamp collecting" (Birks 1963). At the beginning of the 2000s, Cowan led a project of formalization of cognitive sciences (SFI 2002), while Murray Gell-Mann associated to two linguists in order to quantitatively study the genealogical tree of human tongues (SFI 2004).

In SFI's view indeed, non-mathematical social sciences are "pre-scientific," so that only numerical formalization can make of them "real science." But humanities are not the only target of this positivist project. The same attention has been given to life sciences, as it is testified by the workshops organized to transfer numerical tools to biologists (e.g. SFI 2001), as well as by the approach followed by certain complexity specialists seeking for general theories. Take the study conducted by two ecologists and one physicist about the allometric scaling of animal metabolic ratios: "They propose that the origin of this distinctive biological scaling arises from the fact that cardiovascular systems, respiratory systems, plant vascular systems, and insect tracheal tubes all exhibit the same fractal-like branching structure" (SFI 1997, p. 7). For certain complexity scientists, mathesis is definitely universalis. The mathematical regime refers to all those who believe that numbers and equations are not only working tools, but also the very structure of the cosmos, the altar of scientific evidence and at the same time the only meaningful language to tackle their study object. In other words they believe that scientists should mainly or only produce simple mathematical theories to describe systems behavior. These researchersoften physicists, mathematicians and other disciplines representatives with a strong training in numbersuse mathematics to argue the dignity of their research, and sometimes the superiority of it compared to more discursive or computational approaches.

Theoretical ecology and quantitative geography, today well represented at the SFI, inscribe in such regime. According to the tenants of these fields, mathematics are important in the context of theory. Such an aspiration comes from the physicist culture that, at one of the founding meetings of the SFI, Gell-Mann famously synthesized as follows: "Surface complexity arising out of deep simplicity" (Pines 1988, p. 3). Such way of thinking has been shared by most complexity scientists, and the international members of the Network for Ecological Theory Integration (NETI)a group of ecologists from the US, Europe, Australia and Chileare no exception. In their viewexplicitly turned toward physics -, science has to produce not only hypotheses and local models, but also general theories, where theory is defined "as a hierarchical framework that contains clearly formulated postulates, based on a minimal set of assumptions, from which a set of predictions logically follows" (Marquet et al. 2014, p. 701). According to these SFI affiliates, 1) theories "should be built on first principles," the "bedrock of science," in order to be "efficient;" 2) they should also "entail as few assumptions and free parameters as possible" (see the parsimony regime); and, above all, 3) they should be written in mathematical language:

Mathematically formulated theories are generally preferable, because the logic is more transparent, less subject to alternative interpretations, and more amenable to rigorous empirical testing. Increasing the number of imprecise, qualitative terms and meanings will do little to advance ecology, but using mathematics to reduce ambiguity will. (Ibid., p.

703)

The NETI common research efforts, embodied in several international workshops and some collective publications, aim at an integration of several mathematical theories available in ecology -such as the Fisher's sex ratio theory, the optimal foraging theory, the metabolic theory, the maximum entropy theory, and the neutral theory of biodiversity. All these bodies of concepts condense in relatively simple equations the complex dynamics of ecosystems or of parts of them. The challenge of the NETI group is to combine and unify them in an overarching general theory of ecosystems.

Quantitative geographyour second exampleis a "nomothetic" kind of geography, seeking to detect general laws of urban development that transcend regional particularisms (Varenne 2017, p. 30). Once again, within this community physics plays a role model (Bettencourt and West 2010). Some quantitative geographers are indeed ex-physicists that propose to do a science of cities with the tools they learned in their precedent career, many others are trained geographers with a strong inclination for quantitative tools who aim at making their discipline "more scientific" by the yardstick of formalization [START_REF] Cuyala | Analyse spatio-temporelle d'un mouvement scientifique. L'exemple de la[END_REF]. SFI researchers apply power laws to world city databases and argue macroscopic general properties of urban centers independently of the continent, such as the fact that social phenomena increase at the same path as the demographic expansion [START_REF] Bettencourt | Growth, innovation, scaling, and the pace of life in cities[END_REF]Bettencourt et al. 2010).

According to them, GDP, wages, art and patents follow the same scalar rhythm as the number of crimes. On the other side, these scientists remark that basic needs like housing, electricity or water usage stay proportionally the sameno matter the size and location of the city.

Thirdly, they highlight the fact that infrastructures increase proportionally less than the increase of population, because of economies of scale which allow more people to use the same infrastructures. Some philosophical works have commented the intrinsic, often concealed, contradictions of the complexity sciences epistemic projectofficially anti-reductionist and anti-determinist, but actually as reductionist and determinist as the "classical science" they say they wish to counter [START_REF] Israel | The science of complexity: epistemological problems and perspectives[END_REF][START_REF] Morin | Restricted complexity, general complexity[END_REF]Li Vigni 2020a). In particular Israel (2005, p. 505) wrote: there is no doubt that the mathematical-formal approach remains the heart of the theoretical elaborations of the science of complexity. And this is precisely where the ambiguity lies: since, in this way, the science of complexity runs the risk of becoming an updated version of reductionism, that is, of the attempt to subordinate every aspect of reality to the same interpretative key.

Exceptions must be noticed however. For example some researchers who inscribe in complexity sciences write books about the impossibility of "putting society into equations" [START_REF] Jensen | Pourquoi la société ne se laisse pas mettre en équations[END_REF] or criticize "the considerable influence exerted by physics in the domain of complex systems modeling" (Banos 2016, p. 45).

The statistical regime

The toy model is opposed to what we can call the simplified realistic model, which is theoretically more complex but still stylized and metaphorical [START_REF] Edmonds | From KISS to KIDS. An 'Anti-simplistic' Modelling Approach[END_REF]. Its relative realistic significance concerns the material with which it is nourishedempirical data. Yet, this type of model does not reach the morphological accuracy and the ambition of exhaustivity that some recent simulations possess. In computational epidemiology for example, complexity specialists propose accurate agent-based simulations of the entire United States in order to predict the epidemic peaks region by region. In such a case we can talk about complex realistic models, which are validated through more complicated epistemological procedures making use of statistics. [START_REF] Graebner | How to Relate Models to Reality? An Epistemological Framework for the Validation and Verification of Computational Models[END_REF] distinguishes between verification, that is testing the internal consistency of a model, and validation in the strict sense, which aims at testing whether the model reasonably represents the target system.

Statistics are important in both operations, because they are used to verify the model by doing data sensitivity analysis, compensating the absence of data or exploring the possible variations of each parameter taken alone and in interaction with other parameters, namely during "sequential modeling" (building the model block by block in the perspective of an increasing complexification); but statistics are also used to validate the model by fixing the free parameters of a simulation starting from available data or by launching several runs of the model in order to obtain a faithful representation of the target system. Today statistical operations on simulations are run up to million times thanks to international (public and private) grid computing. In general, complexity scientists using complex realistic models and statistics aspire at predicting and providing "full explanations," which entail to illustrate "why a certain fact occurred at a certain time in a certain way, either by providing its causal history or by identifying the causal relations that produced it" (Grüne-Yanoff and Weirich 2010, p.

37).

At least three sub-regimes can be identified within the statistical regime. Firstly, the goldstandard data sub-regime (an expression that comes from medicine and statistics) concerns the reliability of data: In order to establish their validity, scientists take as a comparison the best available reference test, which is thus constantly updated and amended over time. In a French laboratory of microscopic and computational embryology using ABM to simulate in silico embryos, there are two sub-teams. One is focused on the biological part (caring for the animals, leading the experiments, analyzing the data) and the other is focused on engineering (developing mathematical tools, writing code, managing the microscopes). In this context, the biological data used to feed the computer simulations must be validated upon gold-standard data which, as the director of the laboratory explained, is the perfect data set which is going to serve as a milestone, so that you can later compare the efficacity of your algorithms. Other people call it the "ground truth." This expression is in use in computer science. It's funny, because [in biology] we consider that what we can do best is with our eyes, the expert's eye. Yet, if you charge different people for building the same gold-standard, they won't agree on the result. (Interview with a biochemist from BioEmergences lab at CNRS, 24.04.15) Even if this researcher explains that in the biological community "it is customary to say that the gold-standard must be validated by two independent experts," she admits that "this is very difficult to realize for material reasons and temporal constraints" (ibid.). The manual and visual validation of a dataset indeed presupposes a long perceptual work that is extremely energy and time consuming, for embryological datasets imply, during a 24 hours' time lapse, the displacement of thousands of cells that the researchers have to track down one by one.

A second sub-regime can be called the Popperian corroboration. It is well exemplified by two computer scientists from the Paris Complex Systems Institute and one quantitative geographer from Géographie-Cités (CNRS-Sorbonne, Paris), who have developed an algorithm to fortify specific models written with different programming languages. Starting from the epistemological assessment according to which the simple corroboration of models is not sufficient to validate them (also known as equifinality [START_REF] Oreskes | Philosophical issues in model assessment[END_REF]Beven 2019]), the authors appeal to an algorithmic technique to explore the space of parameters in order to falsify models following Popper's prescriptions [START_REF] Chérel | Beyond Corroboration: Strengthening Model Validation by Looking for Unexpected Patterns[END_REF]. According to these researchers, an algorithm that can produce unexpected patterns provides a method to The process is seen as iterative. Once a model is ready, scientists can explore the space of parameters, then they can search for unexpected patterns in order to re-adjust the model, and finally the process can start over again until they get to a model considered satisfactory.

Through their genetic algorithm, conceived to produce innovation, the three researchers generate an indefinite variation of patterns in order to reinforce models by challenging them.

French sociologist of statistics Alain Desrosières used to describe statistical techniques as "things that hold" (Desrosières 1998, p. 9). Inversely, the genetic algorithm of these complexity specialists is conceived to explore the "things that do not hold" into the models.

A third sub-regime has a pattern-based validation and corresponds to what [START_REF] Graebner | How to Relate Models to Reality? An Epistemological Framework for the Validation and Verification of Computational Models[END_REF] calls the descriptive output validation, which consists of asking "to what extent the output of the model can replicate existing data." In the case of realistic models indeed, the exploration of parameters is mostly done in comparison with the target-system data. The backcasting subregime consists in considering a simulation as valid as soon as its output patterns resemble the patterns that have been established through the analysis of "real world" databases. While forecasting aims at predicting the future by means of the analysis of present data, backcasting implies to test model hypotheses over a past event of which initial and final data are available, in order to test both the "dynamical sufficiency" and the "mechanistic adequacy" of the model -that is, respectively, the "model's capacity to reproduce patterns observed in the target" and "its capacity to represent the mechanistic structure of the target" [START_REF] Graebner | How to Relate Models to Reality? An Epistemological Framework for the Validation and Verification of Computational Models[END_REF]). As [START_REF] Augusiak | Merging validation and evaluation of ecological models to 'evaludation': A review of terminology and a practical approach[END_REF] wrote, "Mechanistic modelling simplifies real-world processes to understand driving mechanisms well enough so that forecasts of a system's response to certain conditions become feasible" (p. 118). For the scientists who work on explanatory or predictive realistic modeling, this sub-regime is fundamental.

The term of backcasting appeared in the 1980s in the field of future studies, sustainable development and planning in a normative fashion [START_REF] Robinson | Energy backcasting A proposed method of policy analysis[END_REF][START_REF] Dreborg | Essence of backcasting[END_REF][START_REF] Holmberg | Backcasting. A framework for strategic planning[END_REF]. It is now used within complexity sciences by quantitative geographers and computational epidemiologists, among others, in order to validate their models [START_REF] Cottineau | L'évolution des villes dans l'espace post-soviétique[END_REF][START_REF] Van Den Broeck | The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale[END_REF]). An ex-PhD candidate in quantitative geography from Sorbonne in Paris efficaciously explained that "The meaning of backcasting is to verify whether, starting from all the data we possess, we achieve to put together and reconstruct a system of cities which is coherent from a holistic viewpoint" (interview, 13.07.15). A computational epidemiologist based at INSERM of Paris illustrates this regime with an example of model validation in epidemiological predictions:

We have done what-if tests, for example by simulating that the network is homogeneous, and we have seen that the consequences would indeed be very different. We have validated the model on the SARS epidemics in a historical manner. We have adjusted the model only with data concerning Hong Kong epidemics. With this fit we have seen whether the model was capable of reproducing the propagation at a spatial level. And it did, with a good agreement relatively to our data. It is an easy technique that we put in place with post-hoc studies, and by using already collected, confirmed, updated and validated data. (Interview,24.07.15) The match of the outcomes is not only numerical (statistical). It is also visual (graphical).

Philosopher Julie Jebeile has studied the way scientists draw on visual representations to explain with simulations and gave three reasons for this: 1) the synoptic view allows to have access to complex phenomena at a single glance; 2) images have a revealing power insofar that they highlight the relation between variables which the opacity of models generally conceal; 3) and they permit to single out relevant information out of lots of non-pertinent data [START_REF] Jebeile | Explaining with simulations: Why visual representations matter[END_REF]. Besides the synoptic, revealing and selective functions, there is a fourth one which can be called pattern identification function. As a computer scientist from the Parisian Complex Systems Institute explained, to ensure that his colleagues from quantitative geography validate a model it is necessary for them to see the "right plot" at the end of a simulation run (interview, 31.01.17). According to the same researcher, his geographer colleagues aim at "finding the rules which reproduce the paths they observe [in available databases]; [for them] the knowledge is in the model and not in its specific outputs" (ibid.). In both these subdisciplines, backcasting serves to validate the model, but while computational epidemiologists wish to anticipate actual disease diffusions, quantitative geographers only wish to "tell a history" based on a "theoretical foundation" (ibid.).

Nota bene: While scientists using the statistical regime employ mathematics of course, they do not try to condense the entire behavioral complexity of a system into one simple equation or set of equations. Mathematical formula are embedded into the several mechanisms included into the simulation, but in this regime what is convoked to prove the validity of a model is the statistical outputs of the simulation, not the mathematical equations producing them. It is no coincidence if in the eyes of mathematical regime tenants simulations are devalued. For example, the NETI group wrote that they see ABM "only as a stage in the process of understanding that may lead to the identification of first principles and, eventually, to the development of efficient theories" (Marquet et al. 2014, p. 707). On the other side, complexity scientists' use of simulation can be intended to overcome the impossibility of formally mathematizing certain systems. In most cases, simulation tools are meant to bypass the linearity and stationarity of equations in order to capture the non-linearity and the dynamism of complex systems. For example, in one of his books, Artificial Life founder Christopher Langton explained the interest of simulating life by agent-based models precisely because coding allows to study systems that escape the mathematical harnessing: "it would take tens to hundreds of lines of equations to express even a simple model of an organism's behavior […] and there are simply no mathematical tools for dealing with equational systems of that complexity" (Langton 1997, p. 5). In a position paper, a computational social scientist from the SFI explains that ABM can be a way to solve unsolvable equations or to replace equations at all: "there are important classes of problems for which writing down equations is not a useful activity. In such circumstances, resort to agent-based computational models may be the only way available to explore such processes systematically" [START_REF] Axtell | Why agents? On the varied motivations for agent computing in the social sciences[END_REF].

The proof of concept regime

The "proof of concept" -or the equivalent formula of "proof of principle"designates the practical realization of an idea, a method or a process in view of demonstrating its feasibility;

it "describes research in the beginning stages, at the cutting edge of new applications or technologies, and is a buzzword used to mark out scientific research as potentially extendable and/or scalable" (Kendig 2016, p. 737). Proof of concept is a common approach in industrial production, engineering and design, and is used for its relative inexpensiveness with the aim of gaining confidence in the practical potential of a hypothetical scheme.

Interestingly, while most complexity scientists are driven by theoretical research questions, some are (or collaborate with) engineers and industrials in view of the fabrication of artefacts.

In this case, they convoke the industrial or robotic feasibility of their models as an argument for their validity more than mathematics or other criteria. Let us take the example of a chemical engineer from the Center for Complex Systems and Dynamics, at the Illinois Institute of Technology in Chicago. According to his account, he could never obtain the trust of his collaborators if he considered his simulations as something more than a simple exploration of potential "regions of interest:" I collaborate with people who do experiments. I just try conditions in simulation to show how blood vessels are being formed and, based on those results, they sometimes say, "We didn't think that that could have been something of interest" and they start thinking about it. […] The only way I could convince others to collaborate with me is when I tell them that I respect the real experiments being the final judge. (Interview,16.09.16) The proof of concept regime is an empirical argumentative regime, where simulations are seen as useful forerunners, but nothing reliable in and by themselves: "if the simulation was as good as reality, many things that have been simulated and worked fine but fell apart when tried in real life shouldn't have fallen apart" (ibid.). This is a very different argumentative regime compared to the precedent ones, where mathematics or simulations are considered as having the last word: What constitutes a proof here is the material concretization of a computational model.

In the swarm robotics stream of Artificial Life, the proof of concept is a necessary step before realizing bigger developmental projects (Bonabeau et al. 1999). Artificial lifers promise a variety of "applications" of their expertise to technology, management, production and even art (Bonabeau and Théraulaz 1994). Today, the most advanced and spread implementations are to be found in machine learning algorithms, as they are employed for problem solving and decision making. If several representatives of this field patented some algorithms of this kind, few have founded a company to develop personalized consulting services for other companies with the aim of optimizing industrial production and business management. "Icosystem"founded in 2000 by French physicist Eric Bonabeau in Cambridge (MA)is one of these. Its domains of application are corporate diversity, product design, marketing, operational strategy and network analysis. The company has worked for corporations from different sectors (telecommunication, pharmacy) and for governmental agencies (defense, healthcare). In an article entitled "A More Rational Approach to New-Product Development" (Bonabeau et al. 2008), Bonabeau and his coauthors highlighted the limits of the classical new-product development that they qualify as a "monolithic process." Alternatively, they propose to split the process "into two distinct stages: a truth-seeking early stage, focused on evaluating novel products' prospects and eliminating bad bets, and a success-seeking late stage, focused on maximizing the value of products that have been cleared for development" (Bonabeau et al. 2008). In the rest of their article, the authors tell the story of a device called Chorusa unit of R&D using a computer software provided by Icosystem -, which has been used by the pharmaceutical company Eli Lilly with the objective of finding the best candidates for drugs late-stage development, "in an environment where development costs and failure rates are extremely high" and where less expensive and more traditional approaches cannot work. The Chorus genetic algorithm is conceived to create a portfolio of molecules and test their feasibility in silico. The evidence is first made with a "proof of mechanism" supposed to provide "an acceptable therapeutic index, a practical dose regimen and a manageable degree of [pharmacokinetic/pharmacodynamic] variability" (Owens et al. 2015, p. 19). Before the phase III, which is dedicated to industrial development, the phase II has to provide the proof of concept evidence: "Chorus defines 'early stage' as the work of determining proof of concept (POC) for a drug candidate. Researchers must show […] that the drug is likely to be effective and not to have obvious serious side effects" (Bonabeau et al. 2008). As sociologist Benjamin [START_REF] Raimbault | À l'ombre des biotechnologies. Reformuler la production de savoirs par la bio-ingénierie en France et aux Etats-Unis[END_REF] summarizes, "The proof of concept is not uniquely the final material realization of a project […] but a way to reason and to experiment halfway between science and industry, in which feasibility is the decisive criterion" (p. 280). Table 1 sums up the five epistemic argumentative regimes and the hegemonic disciplines/subdisciplines in each of them.

Ontological views

Philosophers of science have much debated about the relation between the world of the model and the world of the target system [START_REF] Gelfert | The Ontology of Models[END_REF]. The question they ask is, "How does working with [models] tell us anything about the world?" [START_REF] Morgan | The World in the Model. How Economist Work and Think[END_REF]. While some scholars have defended the superiority of laboratory experiments over computer simulations [START_REF] Grüne-Yanoff | The explanatory potential of artificial societies[END_REF][START_REF] Roush | The epistemic superiority of experiment to simulation[END_REF][START_REF] Symons | Epistemic Entitlements and the Practice of Computer Simulation[END_REF] and/or have defined the simulation as an "argument" [START_REF] Beisbart | How can computer simulations produce new knowledge?[END_REF], others have argued the equal epistemic dignity of digital modeling [START_REF] Humphreys | Extending Ourselves. Computational Science, Empiricism, and Scientific Method[END_REF][START_REF] Elsenbroich | Explanation in Agent-Based Modelling: Functions, Causality or Mechanisms?[END_REF] and either compared computer simulations to "mind experiments" [START_REF] Farge | L'approche numérique en physique[END_REF] or to "simulated experiments" with the same value as that of laboratory ones [START_REF] Winsberg | Simulated Experiments: Methodology for a Virtual World[END_REF]. What about the onto-epistemological assumptions of the scientists themselves? The pragmatist approach adopted here leads us to examine their reflexivity about their scientific practices and metaphysical views. Similarly to the first section, philosophers positions will be mentioned next to complexity scientists' ones.

Since the beginning, STS scholars have struggled to show the complexity of the sociotechnical world, the mixing up of nature and culture, science and technology, humans and non-humans, theoretical and material practices, as well as the indissolubility of epistemological, ontological and axiological spheres and dimensions [START_REF] Hackett | The Handbook of Science and Technology Studies[END_REF][START_REF] Law | The Materials of STS[END_REF][START_REF] Woolgar | The wrong bin bag: A turn to ontology in science and technology studies?[END_REF]. This does not mean that, in the STS view, social scientists have to explicitly analyze all spheres together all the time. If the epistemological and the ontological questions are often separated by philosophers, here to talk about ontology permits to better understand the different epistemological postures at presence in complexity sciences. During the fieldwork research, it became clear to me that scientists could share the same epistemic argumentative regimes, but still behave very differently as for the extraacademic applications of their models and results. The codified and the "spontaneous epistemologies" [START_REF] Althusser | Philosophie et philosophie spontanée des savants[END_REF]) of complexity specialists were not enough to explain the observed differences in what concerns their attitudes about the scientific and sociopolitical use of their simulations. This is because epistemological postures are deeply related to ontological ones. For some interviewees, the computer runs in another dimension compared to the "real world," and the digital simulation can never be a proof of anything occurring in the analogical realm. For others, the world of the computer and the world of the target system share important similarities, or are seen as ontologically coincidental.

As the whole panoply of evidence production techniques that complex systems specialists put in place comes from existing disciplines and consolidated epistemic practices, in the same way complexity sciences ontological views come from existing disciplines, except one: The vitalist view (section 4.3) in vigor within the community of Artificial Life [START_REF] Helmreich | Silicon Second Nature. Constructing Artificial Life in a Digital World[END_REF].

How many ontological postures are there? [START_REF] Hacking | Historical Ontology[END_REF] has highlighted the plurality of ontologies at work in sciences, as well as their historicity. In an article published on Social Studies of Science, [START_REF] Sismondo | Ontological turns, turnoffs and roundabouts[END_REF] has added that the ontologies at work in sciences are not individual and contextual perspectives, but world visions shared by entire communities that are the result of material and sociotechnical practices coevolution. Such an anti-platonic movement implies that the number of extant ontologies is not infinite, as Sismondo himself explains: "a focus on interwoven practices that can be described on the pages of journals like this one means that there will always be at most a handful of ontologies at issue" (ibid., p. 5).

The field of complexity scientists confirm such claims.

The dualist view

For the dualists, the digital simulation can only suggest possible lines of inquiry and help pinpoint questions to ask and questions to discard. Within this framework, simulation is purely heuristicit does not prove anything. An anthropologist from the SFI illustrates this ontology as follows: "I think [simulations a]re used in most of the cases, certainly in social sciences that I'm aware of […], to show the likelihood. And so they don't prove something but they show that a more abstract hypothesis is at least feasible on the ground" (interview, 23.09.16). The metaphysical reasoning here is based on the fact that physical, biological and social realms are very different from that of ideas and computer simulations. The sphere of symbolswhich simulations are an instantiation ofruns on a parallel and separated rail compared to that of the target system. The epistemological position that is linked to this ontological view is prudential. If the two worlds never touch or cross each other, the computer cannot say anything "true" about the system under investigation. In this sense, simulation serves to test hypotheses, but more like a game than like a "synthetic laboratory," since such hypotheses have to be confronted with in vivo experiments.

Often, those who share this view come from life and social sciences, and use toy models. An evolutionary biologist affiliated to the SFI told me he always reproaches his students when they qualify their computer simulations as "experiments:" The dualist view can also concern new entrants in the field of computational sciencesfor they lack of confidence in the digital models -, or complex systems specialists at the beginning of the history of the fieldwhen simulations were not as accurate as today's. For the latter case we can think of the many artificial lifers, computational archeologists, sociologists and economists that used to play with toy models back in the 1980s and 1990s.

I
Yet it would be a mistake to think that all toy model users are necessarily dualists. Some scientists sharing other views use very simplified models in the await for more complex and realistic ones. Some philosophers have similar conceptions of computer models (e.g. Longo 2013; Opitz 2017). According to Oreskes et al. (1994, p. 641), "Models can only be evaluated in relative terms, and their predictive value is always open to question. The primary value of models is heuristic." According to Morgan (2012)who is probably the most explicit in such matter -"by experimenting with the model, economists can gain understanding and provide explanations of how the economic world in the model works and use these in an informal way to reflect on the workings of the real economy that the model is taken to represent" (pp. 36-37). According to her view, in the case of laboratory experiments in biology for example, the deductive leap between the model species and the target species is lesser, since both share the same material ontology. Even more clearly, she affirms that "The model world is at most a parallel world. […] economic models are only representations of things in the economy, not the things themselves" (Morgan 2012, pp. 286-287).

The agnostic view

The scientists that hold this position have a pragmatic argument about the essence of the target and of the simulated systems. Such an argument consists in claiming that simulations sometimes "work," and for this very reason it is useful to employ them in different situations, no matter why they work.

Two researchers from the Los Alamos National Laboratory collaborating with computational epidemiologists show such suspension of judgement about ontological issues. One is a statistician and says that statistical results are more or less "defendable" depending on some collectively established criteria (interview, 29.09.16). He is indeed conscious of the social codes he needs to respect in order to "validate" a model in the eyes of the scientific community: "Basically the way you judge disease models is whether their assumptions seem reasonable, that's one, and then two, do they fit the data" (ibid.). Yet, what is interesting for him is to see whether the model allows the modeler to learn something: "is error sufficiently small that you can still learn something from the model? […] So if you have a specific epidemic outbreak, can you reproduce that outbreak in your simulation?" Analogously, his colleague from computer science thinks that the question of the "truthfulness" of models does not even make sense. If the model reproduces the expected pattern, this allows to continue to reflect upon the underpinning hypotheses, without asking if there is an adequatio rei intellecti between theory and target systems: Question: Yours is then a pragmatic approach: You just ask "does it work or not?" Answer: Right, exactly. So whether the model is true… I don't know if that question is even meaningful" (interview, 29.09.16).

In philosophy of science, such a position is known as "pragmatist" and claims that the "predictive power [of simulations is the] mark of success" (Symons and Alvarado 2018). Yet, compared to the laconic interviewees cited before, who strongly avoid the "truth" question, some philosophers propose a "pragmatic theory of truth and error in computer simulation," whose argumentative foundation is very loquacious and complex [START_REF] Hubig | Outlines of a pragmatic theory of truth and error in computer simulation[END_REF].

Both in complexity sciences and in philosophy, the agnostic/pragmatist position remains rare.

The homomorphic view

For the representatives of this view, the world of simulation and the world of target systems do not share the same material cause, but do share the same formal one. In this view, the ontological homology between the formal arrangement of the target system and the one of the simulated system allows researchers to go way further than dualists and agnostic in the kind of performative power they attribute to computer simulations. These are not seen just as an heuristic, for they are taken as sound proofs of what goes on in the "real" world.

A computer scientist from the Parisian Complex Systems Institute claimed that, since the target system and the simulation model share the same structure, "to work on the model means working on the real system" (interview, 03.02.17 As Israel (2005, p. 504) noticed, "The success of physics is due to the fact of having chosen as its guiding principle the Galilean approach of 'pruning the impediments' […] that is the belief in the fact that there is a mathematical order underlying nature which is simpler than it appears, and that represents the essence of phenomena." It is no coincidence if most of the homomorphic representatives, as well as the one just cited, are mainly physicists by training, no matter the subdiscipline to which they contribute in the second part of their career. This category has a considerable amount of expressive nuancessometimes the accent is on the "structure," sometimes on the "underpinning hypotheses," some others on the "formal organization." Yet, they all share the same belief about the power of the models: These can definitely explain and predict "real" systems evolution. Admittedly, homomorphic researchers trust their simulations because these "work," but they also explain why they work: In their view, the rules inscribed into the computer code "capture" the very rationales of the target systems. Some philosophers share the same ontological view as these interviewees. Computational models are described as representing "analogues" of "real" phenomena [START_REF] Sismondo | Models, simulations, and their objects[END_REF], or as having a "mimetic quality" relatively to the target systems [START_REF] Winsberg | Simulated Experiments: Methodology for a Virtual World[END_REF], or as being more or less "isomorphic" compared to them [START_REF] Suppes | Representation and invariance[END_REF][START_REF] Da Costa | Science and partial truth: A unitary approach to models and scientific reasoning[END_REF]. [START_REF] Galison | Image and Logic. A Material Culture of Microphysics[END_REF] has also distinguished between a "homologous" tradition in physics, which "make[s] statistical arguments for the existence of a particle or effect," and a "homomorphic" tradition, which "has had as its goal the representation of natural processes in all their fullness and complexitythe production of images of such clarity that a single picture can serve as evidence for a new entity or effect. These images are presented, and defended, as mimetic" (p.

19). Similarly, [START_REF] Norton | Why Atmospheric Modeling is Good Science[END_REF] assimilate (climate) computer simulations to experiences, since algorithms mimic "real" physical systems. While other examples could be given [START_REF] Elsenbroich | Explanation in Agent-Based Modelling: Functions, Causality or Mechanisms?[END_REF][START_REF] Winsberg | A Tale of Two Methods[END_REF][START_REF] Peschard | Les simulations sont-elles de réels substituts de l'expérience?[END_REF], one of the clearest endorsements to this view comes from [START_REF] Humphreys | Extending Ourselves. Computational Science, Empiricism, and Scientific Method[END_REF], who talks about the possibility that "the computational model used by S correctly represents the structure of the real system R" (p. 110).

The vitalist view

At first sight, the vitalist view seems to be a subcategory of the homomorphic, for both views share the same idea according to which the formal structure of simulation can be the same as the formal structure of the target system. But the accent that vitalists put on the very essence of their simulations distinguish them neatly from the homomorphic. Vitalists indeed push to the extreme the symmetry between the world and the model, by claiming that their simulations live in the literal meaning of the word. For vitalists, models are detached from any sake of realism and are subject to the sake of plausibility. But as soon as a digital agent is capable of feeding, defending and reproducing, we are facing a concrete instantiation of Darwinian evolution. Thus for them, simulations can be studied as real biological systems. This view is present in Artificial Life. This domain parallels Artificial Intelligence in that the distinction between hardware (matter) and software (form) is sharp and hierarchical, since the identity of an artificial being is given by its organization, not by the specific body in which it is incarnated nor by the specific combination of the two. As the founder of this field Christopher Langton once wrote, "[Artificial Life] is an attempt to abstract the principles of life from its material organization, and recreate them in other materials" (SFI 1990, p. 17). In this perspective, matter is indifferent, almost causally transparent: "The objective [of Artificial Life] is not so much to explain in particular natural phenomenon as to claim that a certain kind of phenomenon will be robustly exhibited by a broad variety of systems having a certain abstract or formal structure" (SFI 1997, p. 20). The form is the only criterion to establish life identity: "[life] is a property of the organization of matter, rather than a property of matter itself" (Langton 1988, p. 74). The conviction of artificial lifers is that, if they manage to capture the rules of life organization into computer code, the software which results out of it will not only be an imitation of living beings, but will be a silico living being.

In their view, simulations are alive for they have an autonomous existence, not in the sense that they self-program their code, but in the sense that their evolutive stages are unpredictable to the programmer.

The social scientist who has the best described artificial lifers' perspective is MIT anthropologist Stefan [START_REF] Helmreich | Silicon Second Nature. Constructing Artificial Life in a Digital World[END_REF][START_REF] Helmreich | The word for world is computer: simulating second natures in artificial life[END_REF]. One of the many things that he highlighted in his work is that, since the inception of the field, its representatives started claiming that computers are parallel worlds compared to the physical one in which we live: "Computers are candidates for being worlds, not just describing them" (Helmreich 1998, p. 103). As one of Helmreich's interviewees once told him: "After a while, the analogy between self-replicating programs and living organisms becomes so perfect that it becomes perverse to call it merely an analogy. It becomes simpler just to redefine the word organism to apply to both chemical and software creatures" (ibid., p. 123). Some philosophers have worked with artificial lifers on the philosophical foundations of their field [START_REF] Bedau | Philosophical Aspects of Artificial Life[END_REF][START_REF] Bedau | Artificial Life[END_REF]Boden 1996). Among the subjects they have dealt with, they essentially focused on the theory of evolution, on the definition of life, on the relationship between life and mind, as well as on the ontological status of the simulated living beings.

The monist view

The conviction according to which a "key property of complex adaptive systems is their ability to process informationto computein order to adapt and thrive in an environment" (SFI 2014, p. 18) is widely shared by homomorphic and vitalists. The monists differ from all the others insofar as the entire universe is seen by them as a computer or as a computational process. The term "monism" refers to the fact that the parallel rails of "real" world and simulation make one and the same thing, the material rail being completely determined by the formal one.

For one of the tenants of this viewphysicist and entrepreneur Stephen Wolframall natural and social phenomena can perfectly be reproduced and explained by a processor. If the universe is a computing process, then the simulation contained in a PC has a thorough ontological continuity with the former. Simulation hence becomes a real system or a universe into the universe, since their essence is the same. Also influenced by his personal interest for cosmology, Wolfram has come up to produce an original cosmogony: "And could it even be that underneath all the complex phenomena we see in physics there lies some simple program which, if run for long enough, would reproduce our universe in every detail?" (Wolfram 2002, p. 465). According to him, the fundamental physical laws are not that fundamental, since they are actually an emergent phenomenon of a single and simpler computational law which expresses the entire universe and all it contains. In particular, he rejects to qualify the universe as a computer, for he prefers to define it as the result of a computational process: What I would say is we have a thing that is computational, just like we can have a thing that is mathematical and, as we could say the Universe is mathematical, the Universe is computational. That means there is a computational process which is equivalent to the Universe, which reproduces the Universe. (Interview with Stephen Wolfram,13.09.16) His position does not imply to reject the importance of matter: "if you're trying to study snowflakes and you don't believe in matter, you are doing something stupid. Because snowflakes are made of ice […] there is not really a conflict or difficulty there" (ibid.). Still, computation is in this perspective the most important principle of the cosmos: if we are living in the world and we've got tables and chairs, then matter is important. But if we are trying to find a broader theory of the world, then probably mathematics is more important than the specifics of this crystalline solid or something. So similarly it is with computation, it's more important, it's a broader category of mathematics. (Ibid.)

Another monist is MIT quantum physicist Seth Lloyd, who advocates for a cosmology and a cosmogony which are similar to Wolfram's, that he knows and cites. In his book entitled Programming the Universe, he starts the narration with a Biblical-like citation: "In the beginning was the bit" (Lloyd 2006, p. IX). According to Lloyd, information is the basic principle of the cosmos next to matter and energy, for he claims that the universe "computes," "is governed by the laws of quantum mechanics" and thus is "a quantum computer" that has "compute [d] itself" (ibid., p. 3) since the "Bit Bang" (ibid., p. 46). According to Lloyd, "Energy makes physical systems do things. Information tells them what to do" (ibid., p. 40).

His monist position is even more straightforward than Wolfram's: "the universe and a quantum computer have the same information-processing power: they are essentially identical" (ibid., p. 149). The question does not focus on whether simulations can say something about the target system. The point is that if the cosmos is a computational process, then the computer simulation have all the important characteristics of the world.

Table 2 summarizes the five ontological views, the disciplines hegemonic in each of them, as well as their view of the relation model-world under the material and formal causes framework. As the table shows, the views locate over a continuum going from dualists to monists, passing through agnostic, homomorphic and vitalists.

Regimes of evidence and extra-academic activities

With the term of regime of evidence, I refer to the combination of an ontological view with one or more epistemic argumentative regimes. Such combinations are not endless.

Complexity sciences are composed by a finite number of epistemic cultures anddespite the existence of some "dialectal" variations, transient postures and exceptions within each one of themevery epistemic culture has its own prevalent regime of evidence. For this very reason, regimes of evidence can be seen as one of the components of Karin Knorr-Cetina's epistemic cultureswhich are defined as "amalgams of arrangements and mechanisms" or as the set of theoretical, practical, technical, institutional and normative practices which "make up how we know what we know" (Knorr-Cetina 1999, p. 1).

One question remains to be addressed in this last section: What are the effects of the different regimes of evidence on the way complexity scientists interface with policy makers and civil society? The degree of conviction with which researchers use their science as an expertise with practical effects for enterprises, NGOs and administrations can vary a lot (Li Vigni 2020b). Their attitudes can indeed go from a prudent approach, which considers their tools and results as a sheer heuristic way to explore theoretical questions, up to a remarkable selfconfidence with the explanatory and predictive power of their models. As for the pragmatic consequences of this, while some complexity specialists never adventure to address private and public actors to offer them expert consulting services, others do not hesitate to do so.

Many reasons can of course be adduced -a gap in scientific confidence in one's models, the lack of culture of decision making support within a given subdiscipline, as well as the specific institutional conjuncture of a scientific community in a given country at a given historical moment. But if we focus on the specific articulations between the epistemic argumentative regimes and the ontological views, at least three different positions emerge from the material presented here:

1) A merely heuristic regime of evidence, where scientists refuse to support any decision making process for the lack of confidence in their tools. It is often the case of those aligning to the dualist view and the toy model regime. In their case, models can aid research but not more, for these can neither prove a theory nor predict a given phenomenon. The dominant epistemic cultures here are life and social sciences, two domains in which researchers tend to be cautious in terms of prediction because of the remarkable complexity of their study objects. Accustomed to trial-and-error and to other qualitative inquiry techniques, biologists and social scientists who affiliate to the complexity field certainly have a strong interest in regularities detection and formalization, but tend to bring in their scientific culture traditionally suspicious of a mathesis universalis;

2) A productive regime of evidence, where scientists aligning with the vitalist and the monist views and exploiting the proof of concept regime offer to produce software and robots in view of a practical, often entrepreneurial application of their tools and models. Mostly engineers and entrepreneurs (or physicists with a strong interest in engineering and entrepreneurship), the tenants of this regime are by training turned to the material realization of artefacts. When they do not build something tridimensional, they work on simulations that they tend to consider as autonomous beings. Theory for them is not an end in itself, but a step toward something useful and/or capitalizable for society;

3) And, finally, a consulting regime of evidence, where scientists carrying a homomorphic view and laying upon the mathematical or the statistical regimeand particularly on the backcasting sub-regimedo not hesitate to offer their services to enterprises and governmental policy makers. Mostly physicists by training, the tenants of this regime practice interdisciplinarity and, often through complexity institutional spaces and networks, turn toward other disciplines and domains where they feel they can bring some theoretical and practical contribution. They may indeed predict an epidemic peak or anticipate the effect of an infrastructure implantation over an urban system in view of planning. In either case, their conviction in a mathesis universalis or, said otherwise, in the formal equivalence between the target and the simulated systems, give them the necessary confidence to use the computer modeling to claim something about "reality."

These are non-exhaustive generalizations and the analysist should avoid the charm of easy, logical correspondences between the different argumentative regimes and the different ontological views. Notable exceptions exist indeed which are explainable by taking into account, besides pure logic, also contextual and cultural facts. For example, some researchers from ecology, computer science and social sciences, who are dualists using toy models, propose to communities and administrations sophisticated devices of action research, based on serious games, debates and ABM among other tools, in order to pacify conflictual situations in the management of public natural goods [START_REF] Commod | La modélisation comme outil d'accompagnement[END_REF][START_REF] Étienne | La modélisation d'accompagnement: une forme particulière de géoprospective[END_REF]). In this case, simulations are simplified and yet expected to reproduce the interrelations linking stakeholders between them and with their environment. The reason why a toy model is, according to them, capable of modifying a sociopolitical status quo resides in the scope of these complex systems specialists, which is not predictive, but pedagogical and political. For them, the simulation plays the role of a serious game through which the different stakeholders in conflict can discuss and rethink their interactions and impact on natural resources.

Conclusion

Back in the 1980-90s, the SFI and some of its epigones in Europe launched the project of a new, unitary and revolutionary discipline with the aim of "defin[ing] the principles of a general science of complexity" (SFI Arch. #1, p. 3), but decided to abandon it after journalist John Horgan criticized, on the pages of the Scientific American, complexity science for being "flaky" and the SFI for being "fact-free" [START_REF] Horgan | From complexity to perplexity[END_REF]. Nevertheless, along the lines of the founders of this domain, some observers have argued its unity and radical novelty. But by describing complexity scientists' epistemic argumentative regimes and ontological views, this text has disconfirmed the alleged unity of complexity and minimized the claim of its radical novelty. Indeed, the five epistemic argumentative regimesparsimony, toy model, mathematical, statistical and proof of conceptand the five ontological viewsdualist, agnostic, homomorphic, vitalist and monistdraw from physics, statistics, mathematics, life sciences, as well as design and engineering. The last section has shown that the different articulations between the regimes and the views produce different postures in relation to extra-academic actors. Whether scientists show a prudential approach about their results or propose their consulting to companies, NGOs and policy makers, it depends, among other things, on their different views of the world and the kind of knowledge they think they can produce. An heuristic, a productive and a consulting regimes of evidence have thus been identified.

Interestingly, the socio-epistemic space that complexity founders have contributed to open up has produced new subdisciplines instead of a singular overarching disciplineeconophysics, Artificial Life, complex networks and computational epidemiology all stemmed from this space. Whereas [START_REF] Waldrop | Complexity. The Emerging Science at the Edge of Order and Chaos[END_REF] insisted in employing the singular "complexity science," the interlocutors featured in his book always used the plural. What is more, if until the mid-1990s some of the founders were engaged in the project of a general theory of all natural and social complex systems (Cowan et al. 1994;[START_REF] Holland | Hidden Order. How Adaptation Builds Complexity[END_REF]), other illustrious protagonists of the beginnings rather emphasized the onto-epistemic difference of the layers which physical and social nature is made of (Anderson 1972). Today very few representatives of the field believe that a science of complex systems exists or may someday exist (in my corpus, only four over the 115 interviewees and three of them have been active in the institutionalization of the field).

A remark on the limits of the present article and about its possible openings deserve to be done before concluding. Since my primary objective was to qualitatively clearing brush within the famous but poorly understood domain of complexity, the quantitative backup of the theses defended here has been left out of the picture. The fact that the agnostic and the monist views are very rare in my corpus (each being <2%) is indicative of their probable rarity in the entire complexity community. It is also possible to claim that the homomorphic view is more common than the dualist one (respectively 83 and 9% of my corpus). But the vitalist is underrepresented (<4%) because, since Artificial Life has already been studied by anthropologists and philosophers, I decided to neglect it, and this biasalong with the snowball methoddoes not permit to establish the exact ratio between homomorphic, dualists and vitalists in the complexity community. It is however easy to conceive of a short questionnaire with both closed and open questions to send to as many complexity scientists as possible in different countries, so to confirm/amend the different regimes and views identified here and to quantify them more precisely. The number of interviewees from the different epistemic cultures at presence should follow a representative logic. Lastly, the reader who may be willing to conduct such an inquiry could definitely find useful the few, but

  […] Iteration here is used for exploring a set of options under controlled variations, gathering the results and thus obtaining an overview" (p. 490). According to Lenhard, "Thought experiments are tied to the convergence type of iteration. When you perform a thought experiment, repeated execution eliminates initial intransparency or ambiguity. Simulation experiments, on the other hand, involve the atlas type of iteration. Repeated, and slightly varied, model runs do not eliminate opacity, but rather explore the space of possible model behavior" (ibid.). Nevertheless, in this text Lenhard treats simulation experiments as an indistinguished whole.

  falsify a model and at the same time to generate predictions through it. The unexpected patterns are sought by the algorithm through the stochastic perturbation of the parameter values and through the pursuit, among all possible parameters, of the different behaviors that I can have as an outcome. And if, among these different behaviors, there are some I wasn't expecting, I can say they are going to be either counter-examples, which allows us to bring down the model, or predictions of the model which I can later empirically test or compare to some database.(Interview with a computer scientist, 06.07.16)

  have a bunch of computer scientists in my group […] [At] one of our group meetings [somebody said] something like, "Last week I did this experiment." And the first thing I told him is, "Never call something you did on a computer an experiment." An experiment is something you do in the lab or in the field or in the real world. […] the reason I say this is because I want them to have the distinction between whatever they do in a computer and what they do in the lab or in the field. Because if you go talk to biology audiences and say, "This is an experiment," they'll just laugh you out of the room. (Interview, 07.10.16) Similarly, a quantitative geographer from Sorbonne in Paris claims the following: I think of [simulation] as a sort of heuristics, or in some cases even as a maieutic, for it helps you give birth to new ideas. After that, you have to throw the model away […] and you have to step to a further level. […] For me, we must avoid a reification of the models, you see? A model is simply an intermediary step toward something else. (Interview,25.04.17)

  ). But the clearest illustration of the homomorphic view comes from a computational epidemiologist based at the INSERM: [The simulation] is an abstraction of the form. If a real form exists, the form of the simulation is an abstraction of the real form. […] [In the modeling process you have to] lose some details […] some mechanisms […] that you don't consider as indispensable in the process […] What I capture with [my model] is the set of ingredients I believe have an important role within the epidemic propagation phenomenon, and they are real ingredients […] we write [mobility, gravity, diffusion] laws […] and the starting hypothesis is that these laws […] are a precise and reliable description of what's going on in reality. […]When [the simulation] works, it means that the phenomena I have captured within it are the real ones.(Interview, 09.05.17)

  Complex Systems Institute of Lyon explained, "what is important in a model is not what you put inside. It's what you leave out"

Table 1 . The epistemic argmentative regimes within the subdisciplines gathered under the label of complexity sciences Epistemic argumentative regimes Hegemonic epistemic cultures

 1

	Parsimony	All sciences, but especially life, social and computer sciences working on complex
		realistic models and validating them through statistics
	Toy model	Physics, computer science, Artificial Life, economics and other social sciences
	Mathematical	Physics, mathematics, chemistry, theoretical ecology, quantitative geography and
		computational epidemiology
	Statistical	Physics, statistics, computational life and social sciences

Table 2 . The ontological views within the subdisciplines gathered under the label of complexity sciences Ontological views Hegemonic epistemic cultures within each view Material cause in the real system and the simulation Formal cause in the real system and the simulation

 2

	Dualists	Life sciences, social sciences,	Different	Different
		engineering
	Agnostic	Statistical sciences		Whatever works	Whatever works
	Homomorphic Physics, computer science,	Different	Coincidental
		quantitative	geographers,
		computational epidemiologists
	Vitalists	Artificial	Life	(physics,	Different	Coincidental & lifelike
		computer science, theoretical
		biology)
	Monists	Physics, computer science	Coincidental	Coincidental

This is due to at least two socio-technical reasons. On the one hand, the lack of computer power and of theoretical knowledge for parallel computing; on the other, the lack of captors, efficient archival methods and statistical tools to analyze big data.

comprehensive scientometric studies that have been conducted on complexity subcommunities by some of their own representatives (Cointet and Chavalarias 2008;Grauwin et al. 2012).

Funding Not applicable.

Availability of data and material Not applicable.

Code availability Not applicable.

Bibliography

Conflict of interest

The author declares that he has no conflict of interest. Bettencourt, L.M.A., Lobo, J., Strumsky, D. and West, G. 2010