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## Über dieses Buch

This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning.

## Inhaltsverzeichnis

### 1. The Ontology of Models

The term scientific model picks out a great many things, including scale models, physical models, sets of mathematical equations, theoretical models, toy models, and so forth. This raises the question of whether a general answer to the question What is a model? is even possible. This chapter surveys a number of philosophical approaches that bear on the question of what, in general, a scientific model is. While some approaches aim for a unitary account that would apply to models in general, regardless of their specific features, others take as their basic starting point the manifest heterogeneity of models in scientific practice. This chapter first motivates the ontological question of what models are by reflecting on the diversity of different kinds of models and arguing that models are best understood as functional entities. It then provides some historical background regarding the use of analogy in science as a precursor to contemporary notions of scientific model. This is followed by a contrast between the syntactic and the semantic views of theories and models and their different stances toward the question of what a model is. Scientists, too, typically operate with tacit assumptions about the ontological status of models: this gives rise to what has been called the folk ontology of models, according to which models may be thought of as descriptions of missing (i. e., uninstantiated) systems. There is a close affinity between this view and recent philosophical positions (to be discussed in the penultimate section) according to which models are fictions. This chapter concludes by considering various pragmatic conceptions of models, which are typically associated with what may be called mixed ontologies, that is, with the view that any quest for a unitary account of the nature of models is bound to be fruitless.

Axel Gelfert

### 2. Models and Theories

Both the received view (RVreceived view (RV)) and the semantic view (SVsemantic view (SV)) of scientific theories are explained. The arguments against the RV are outlined in an effort to highlight how focusing on the syntactic character of theories led to the difficulty in characterizing theoretical terms, and thus to the difficulty in explicating how theories relate to experiment. The absence of the representational function of models in the picture drawn by the RV becomes evident; and one does not fail to see that the SV is in part a reaction to – what its adherents consider to be an – excessive focus on syntax by its predecessor and in part a reaction to the complete absence of models from its predecessor’s philosophical attempt to explain the theory–experiment relation. The SV is explained in an effort to clarify its main features but also to elucidate the differences between its different versions. Finally, two kinds of criticism are explained that affect all versions of the SV but which do not affect the view that models have a warranted degree of importance in scientific theorizing.

Demetris Portides

### 3. Models and Representation

Models are of central importance in many scientific contexts. We study models and thereby discover features of the phenomena they stand for. For this to be possible models must be representations: they can instruct us about the nature of reality only if they represent the selected parts or aspects of the world we investigate. This raises an important question: In virtue of what do scientific models represent their target systems? In this chapter we first disentangle five separate questions associated with scientific representation and offer five conditions of adequacy that any successful answer to these questions must meet. We then review the main contemporary accounts of scientific representation – similarity, isomorphism, inferentialist, and fictionalist accounts – through the lens of these questions. We discuss each of their attributes and highlight the problems they face. We finally outline our own preferred account, and suggest that it provides the most promising way of addressing the questions raised at the beginning of the chapter.

Roman Frigg, James Nguyen

### 4. Models and Explanation

Detailed examinations of scientific practice have revealed that the use of idealized models in the sciences is pervasive. These models play a central role in not only the investigation and prediction of phenomena, but also in their received scientific explanations. This has led philosophers of science to begin revising the traditional philosophical accounts of scientific explanation in order to make sense of this practice. These new model-based accounts of scientific explanation, however, raise a number of key questions: Can the fictionsfiction and falsehoods inherent in the modeling practice do real explanatory work? Do some highly abstract and mathematical modelsmathematicalmodel exhibit a noncausal form of scientific explanation? How can one distinguish an exploratory how-possiblyhow-possibly model explanation from a genuine how-actuallyhow-actually model explanation? Do modelers face tradeoffstradeoff such that a model that is optimized for yielding explanatory insight, for example, might fail to be the most predictively accurate, and vice versa? This chapter explores the various answers that have been given to these questions.

Alisa Bokulich

### 5. Models and Simulations

In this chapter we present some of the central philosophical issues emerging from the increasingly expansive and sophisticated roles computational modeling is playing in the natural and social sciences. Many of these issues concern the adequacy of more traditional philosophical descriptions of scientific practice and accounts of justification for handling computational science, particularly the role of theory in the generation and justification of physical models. However, certain novel issues are also becoming increasingly prominent as a result of the spread of computational approaches, such as nontheory-driven simulationsnontheorydriven simulation, computational methods of inference, and the important, but often ignored, role of cognitive processes in computational model building.Most of the philosophical literature on models and simulations focuses on computational simulation, and this is the focus of our review. However, we wish to note that the chief distinguishing characteristic between a model and a simulation (model) is that the latter is dynamic. They can be run either as constructed or under a range of experimental conditions. Thus, the broad class of simulation models should be understood as comprising dynamic physical models and mental models, topics considered elsewhere in this volume.This chapter is organized as follows. First in Sect. 5.1physics-based simulation we discuss simulation in the context of well-developed theory (usually physics-based simulations). Then in Sect. 5.2 we discuss simulation in contexts where there are no over-arching theories of the phenomena, notably agent-based simulations and those in systems biology. We then turn to issues of whether and how simulation modeling introduces novel concerns for the philosophy of science in Sect. 5.3. Finally, we conclude in Sect. 5.4cognition by addressing the question of the relation between human cognition and computational simulation, including the relationship between the latter and thought experimenting.

Nancy J. Nersessian, Miles MacLeod

### 6. Reorienting the Logic of Abduction

Abduction, still a comparatively neglected kind of premiss-conclusion reasoning, gives rise to the questions I want to consider here. One is whether abduction’s epistemic peculiarities can be accommodated happily in the mainline philosophical theories of knowledge. The other is whether abduction provides any reason to question the assumption that the goodness of drawing a conclusion from premisses depends on an underlying relation of logical consequence. My answer each time is no. I will spend most of my time on the first. Much of what I’ll say about the second is a promissory note.

John Woods

### 7. Patterns of Abductive Inference

This article understands abductive inference as encompassing several special patterns of inference to the best explanation whose structure determines a promising explanatory conjecture (an abductive conclusion) for phenomena that are in need of explanation (Sect. 7.1patternof abductive inference). A classification of different patterns of abduction is given in Sect. 7.2selective abductionpossible explanation, which is intended to be as complete as possible. A central distinction is that between selective abductions, which choose an optimal candidate from a given multitude of possible explanations (Sects. 7.3 and 7.4creativeabduction), and creative abductions, which introduce new theoretical models or concepts (Sects. 7.5–7.7). While the discussion of selective abduction has dominated the literature, creative abductions are rarely discussed, although they are essential in science. This paper introduces several kinds of creative abduction, such as theoretical model abduction, common-cause abduction, and statistical factor analysis. A demarcation between scientifically fruitful abductions and speculative abductions is proposed, by appeal to two interrelated criteria: independent testability and explanatory unification. Section 7.8inferenceto the best explanation (IBE) presents applications of abductive inference in the domains of belief revision and instrumental/technological reasoning.

Gerhard Schurz

### 8. Forms of Abduction and an Inferential Taxonomy

In recent years, the Peircean concept of abduction has been differentiated into different forms and made fruitful in a variety of contexts. However, the very notion of abduction still seems to be in need of clarification. The present contribution takes very seriously Peirce’s claim (1) that there are only three kinds of reasoning, that is, abduction, deduction, and induction, and (2) that these are mutually distinct. Therefore, the fundamental features of the three inferences canvassed, in particular as regards inferential subprocesses and the validity of each kind of reasoning. It is also argued that forms of abduction have to be distinguished along two dimensions: one concerns levels of abstraction (from elementary embodied and perceptual levels to high-level scientific theorizing). The other concerns domains of reasoning such as explanatory, instrumental, and moral reasoning. Moreover, Peirce’s notion of theorematic deduction is taken up and reconstructed as inverse deduction. Based on this, inverse abduction and inverse induction are introduced as complements of the ordinary forms. All in all, the contribution suggests a taxonomy of inferential reasoning, in which different forms of abduction (as well as deduction and induction) can be systematically accommodated. The chapter ends with a discussion on forms of abduction found in the current literature.

Gerhard Minnameier

### 9. Magnani’s Manipulative Abduction

Despite the extensive research in logic, cognitive science, artificial intelligence, semiotics, and philosophy of science, there is no sure proof that we have better or deeper understanding of abduction than its modern founder, Charles S. Peirce. In this sense, one of the most important developments in recent studies on abduction is Lorenzo Magnani’s discovery of manipulative abductionmanipulative abduction. In this paper, I shall examine in what ways Magnani goes with and beyond Peirce in his views on manipulative abduction. After briefly introducing his distinction between theoretical and manipulative abduction (Sect. 9.1diagrammatic reasoning), I shall discuss how and why Magnani counts diagrammatic reasoning in geometry as the prime example of manipulative abduction (Sect. 9.2theorematic reasoning). Though we can witness an increasing interest in the role of abduction and manipulation in what Peirce calls theorematic reasoning, Magnani is unique in equating theorematic reasoning itself as abduction. Then, I shall discuss what he counts as some common characteristics of manipulative abductions (Sect. 9.3practicalreasoning), and how and why Magnani views manipulative abduction as a form of practical reasoning (Sect. 9.4eco-cognitivemodel of abductionfallacyanimalabduction). Ultimately, I shall argue that it is manipulative abduction that enables Magnani to extend abduction to all directions to develop the eco-cognitive model of abduction. For this purpose, fallacies and animal abduction will be used as examples (Sect. 9.5).

Woosuk Park

### 10. The Logic of Abduction: An Introduction

In this chapter, the focus will be on formal models of hypothetical reasoningreasoninghypothetical, in particular on those concerned with abductive reasoning.In Sect. 10.1abductioninduction, the chapter offers a brief history of the notion of abduction, starting with an attempt to distinguish it from its closest neighbor, induction. Charles Peirce’s original conception of abduction is then presented and followed by an overview of abduction in the cognitive sciences, together with some paradigmatic examples of the kind that will be dealt with in the chapters to follow. Sect. 10.2abductionargumentabductioninference to the best explanation presents two main approaches to abduction in philosophy, as argument and as inference to the best explanation (IBEinferenceto the best explanation (IBE)), something which sets the ground to put forward a general logical taxonomy for abduction. Sect. 10.3 goes deeper into three logic-based classical characterizations of abduction found in the literature, namely as logical inference, as a computational process, and as a process for epistemic change.Hypothetical reasoning is understood here as a type of reasoning to explanations. This type of reasoning covers abductive as well as inductive inferences. As for the latter, in this handbook part, the concern will be limited to enumerative inductioninductionenumerative and will leave its full presentation to the corresponding chapter (Chap. 11).

Atocha Aliseda

### 11. Qualitative Inductive Generalization and Confirmation

Inductive generalization is a defeasible type of inference which we use to reason from the particular to the universal. First, a number of systems are presented that provide different ways of implementing this inference pattern within first-order logic. These systems are defined within the adaptive logics framework for modeling defeasible reasoning. Next, the logics are re-interpreted as criteria of confirmation. It is argued that they withstand the comparison with two qualitative theories of confirmation, Hempel’s satisfaction criterion and hypothetico-deductive confirmation.

Mathieu Beirlaen

### 12. Modeling Hypothetical Reasoning by Formal Logics

In this chapter, it is discussed to which extent hypothetical reasoning can be modeled by formal logics. It starts by exploring this idea in general (Sects. 12.1 and 12.2), which leads to the conclusion that in order to model this kind of reasoning formally, a more fine-grained classification of reasoning patterns should be in order. After such a classification is provided in Sect. 12.3, a formal framework that has proven successful to capture some of these patterns is described (Sects. 12.4 and 12.6) and some of the specific problems for this procedure are discussed (Sect. 12.5). The chapter concludes by presenting two logics for hypothetical reasoning in an informal way (Sects. 12.7 and 12.8hypotheticalreasoning) such that the nontechnically skilled reader can get a flavor of how formal methods can be used to describe hypothetical reasoning.

Tjerk Gauderis

### 13. Abductive Reasoning in Dynamic Epistemic Logic

This chapter proposes a study of abductive reasoning addressing it as an epistemic process that involves both an agent’s information and the actions that modify this information. More precisely, this proposal presents and discusses definitions of an abductive problem and an abductive solution in terms of an agent’s information (her knowledge and beliefs) and the involved epistemic actions (observation and belief revision). The discussion is then formalized with tools from dynamic epistemic logic; under such framework, the properties of the given definitions are studied, an epistemic action representing the application of an abductive step is introduced, and an illustrative example is provided. A number of the most interesting properties of abductive reasoning (those highlighted by Peirce) are shown to be better modeled within this approach.

Angel Nepomuceno-Fernández, Fernando Soler-Toscano, Fernando R. Velázquez-Quesada

### 14. Argumentation and Abduction in Dialogical Logic

This chapter advocates for a reconciliation of argumentation theory and formal logic in an agent-centered theory of reasoning, that is, a theory in which inferences are studied as human activities. First, arguments in favor of a divorce between the two fields are presented. Those arguments are not so controversial. However, rather than forcing a radical separation, they urge logicians to rethink the object of their studies. Arguments cannot be analyzed as objects independent from human activity, whether it is dealt with deductive or nondeductive reasoning. The present analysis naturally takes place in the context of dialogical logic in which the proof process and the semantics are conceived in terms of argumentative games, which involve the agents, their commitments and their actions. This work focuses first on deductive reasoning and then takes abduction as a case of nondeductive reasoning. By relying on some relevant ideas of the Gabbay–Woods (GW) schema of abduction and Aliseda’s approach, a new dialogical explanation of abduction in terms of concession-problem is proposed. This notion of concession problem will be defined thereafter. With respect to the topics of the model-based sciences, the question of the specificity of the speech act by means of which a hypothesis is conjectured is set more specifically.

Cristina Barés Gómez, Matthieu Fontaine

### 15. Formal (In)consistency, Abduction and Modalities

This chapter proposes a study of philosophical and technical aspects of logics of formal inconsistency (LFIlogics of formal inconsistency (LFI)paraconsistent logicconsistencys), a family of paraconsistent logics that have resources to express the notion of consistency inside the object language. This proposal starts by presenting an epistemic approach to paraconsistency according to which the acceptance of a pair of contradictory propositions A and $$\neg A$$¬A does not imply accepting both as true. It is also shown how LFIs may be connected to the problem of abduction by means of tableaux that indicate possible solutions for abductive problems. The connection between the notions of modalities and consistency is also worked out, and some LFIs based on positive modal logics (called anodic modal logics), are surveyed, as well as their extensions supplied with different degrees of negations (called cathodic modal logics). Finally, swap structures are explained as new and interesting semantics for the LFIs, and shown to be as a particular important case of the well-known possible-translations semantics (PTSpossible-translations semantics (PTS)).

Juliana Bueno-Soler, Walter Carnielli, Marcelo E. Coniglio, Abilio Rodrigues Filho

### 16. Metaphor and Model-Based Reasoning in Mathematical Physics

The role of model-based reasoning in experimental and theoretical scientific thinking has been extensively studied. However, little work has been done on the role of mathematical representations in such thinking. This chapter will describe how the nature of mathematical expressions in physics can be analyzed using an extension of the metaphoric analysis of mathematics. In Where Mathematics Comes From, Lakoff and Núñez argued that embodied metaphors underlie basic mathematical ideas (e. g., the concept of number is based on the embodied operations of collecting objects), with more complex expressions developed via conceptual blends from simpler expressions (e. g., addition as combining collections). In physics, however, the need to represent physical processes and observed entities (including measurements) places different demands on the blending processes. In model-based reasoning, conceptual blends must often be based on immediately available embodiments as well as highly developed mathematical expressions that draw upon expert use of long term working memory. Thus, Faraday’s representations of magnetic fields as lines of force were modeled by Maxwell as vectors. In this chapter, we compare Faraday’s experimental investigation of the magnetic field within a magnet to Maxwell’s mathematical treatment of the same problem. Both can be understood by unpacking the metaphoric underpinnings as physical representations. The implications for analogical and model-based reasoning accounts of scientific thinking are discussed.

Ryan D. Tweney

### 17. Nancy Nersessian’s Cognitive-Historical Approach

Nancy NersessianNersessian raises questions about the creation of scientific concepts and proposes answers to them based on the cognitive-historical approachcognitive-historical approach. These problems are mainly about the nature of the cognitive processes involved in the generation of ideas fundamentally new in human history and the efficacy of those mechanisms in achieving successful results. In this chapter, I intend to show the epistemic virtues that make this method a useful tool for establishing the dynamic hypothesis about the creation of knowledge in science. I also point out that, compared to other methods of cognitive studies on the creation of scientific knowledge – ethnography, in vivo observation, and laboratory experiments – the cognitive-historical approach turns out to be primary. I analyze Nersessian’s idea that scientists often employ model-based reasoning, in an iterative way, in order to solve representational problems in the target domain. Additionally, I examine her claim that model-based reasoning facilitates the conceptual change. This hypothesis involves a representation of concepts illustrated by the dynamic frames theory about concepts.

Nora Alejandrina Schwartz

### 18. Physically Similar Systems - A History of the Concept

The concept of similar systemssimilarsystem arose in physics and appears to have originated with NewtonNewton in the seventeenth century. This chapter provides a critical history of the concept of physically similar systemsphysically similar system, the twentieth century concept into which it developed. The concept was used in the nineteenth century in various fields of engineering (FroudeFroude, Bertrand, ReechReech), theoretical physics (van der Waalsvan der Waals, OnnesOnnes, LorentzLorentz, MaxwellMaxwell, BoltzmannBoltzmann), and theoretical and experimental hydrodynamics (StokesStokes, HelmholtzHelmholtz, ReynoldsReynolds, PrandtlPrandtl, RayleighRayleigh). In 1914, it was articulated in terms of ideas developed in the eighteenth century and used in nineteenth century mathematics and mechanics: equations, functions, and dimensional analysis. The terminology physically similar systems was proposed for this new characterization of similar systems by the physicist Edgar BuckinghamBuckingham. Related work by VaschyVaschy, Bertrand, and RiabouchinskyRiabouchinsky had appeared by then. The concept is very powerful in studying physical phenomena both theoretically and experimentally. As it is not currently a part of the core curricula of science, technology, engineering, and mathematics (STEMsciencetechnology, engineering, and mathematics (STEM)) disciplines or philosophy of science, it is not as well known as it ought to be.

Susan G. Sterrett

### 19. Hypothetical Models in Social Science

The chapter addresses the philosophical issues raised by the use of hypothetical modeling in the social sciences. Hypothetical modeling involves the construction and analysis of simple hypothetical systems to represent complex social phenomena for the purpose of understanding those social phenomena.To highlight its main features hypothetical modeling is compared both to laboratory experimentation and to computer simulation. In analogy with laboratory experiments, hypothetical models can be conceived of as scientific representations that attempt to isolate, theoretically, the working of causal mechanisms or capacities from disturbing factors. However, unlike experiments, hypothetical models need to deal with the epistemic uncertainty due to the inevitable presence of unrealistic assumptions introduced for purposes of analytical tractability. Computer simulations have been claimed to be able to overcome some of the strictures of analytical tractability. Still they differ from hypothetical models in how they derive conclusions and in the kind of understanding they provide.The inevitable presence of unrealistic assumptions makes the legitimacy of the use of hypothetical modeling to learn about the world a particularly pressing problem in the social sciences. A review of the contemporary philosophical debate shows that there is still little agreement on what social scientific models are and what they are for. This suggests that there might not be a single answer to the question of what is the epistemic value of hypothetical models in the social sciences.

Alessandra Basso, Chiara Lisciandra, Caterina Marchionni

### 20. Model-Based Diagnosis

Diagnostic reasoning is an activity aimed at finding the causes of incorrect behavior of various technological systems. In order to perform diagnosis, a typical diagnostic system should be equipped with the expert knowledge of the domain and statistical evidence of former failures. More advanced solution combines model-based reasoning (MBRmodel-basedreasoning (MBR)model-baseddiagnosis) and abduction. It is assumed that a model of the system under investigation is specified. Such a model allows us to simulate the normal behavior of the system. It can also be used to detect incorrect behavior and perform sophisticated reasoning in order to identify potential causes of the observed failure. Such potential causes form a set of possible diagnoses. In this chapter, formal bases for the so-called model-based diagnostic reasoning paradigm are presented and application examples are discussed in detail. A method of modeling system behavior with the use of causal graphs is put forward. Then, a systematic method for discovering all the so-called conflict sets (disjunctive conceptual faults) is described. Such conflict sets describe sets of elements in such a manner that in order to explain the observed misbehavior at least one of them must be faulty. By selecting and removing such elements from all conflicts sets – for each conflict set one such element – the proper candidate diagnoses are generated. An example of the application of the proposed methods to the three-tank dynamic system is presented and some bases for on-line generation of diagnoses for dynamic systems are outlined, together with some theorems. The chapter introduces an easy and self-contained material being an introduction to modern model-based diagnosis, covering static and dynamic systems.

Antoni Ligęza, Bartłomiej Górny

### 21. Thought Experiments in Model-Based Reasoning

Thought experimentation is at least as old as Western philosophy. Scholars have made much use of it in many disciplines. For instance, philosophical discussions on ethics, morality, knowledge, and language abound with thought experiments. Likewise, great scientific developments, such as in physics and mathematics, have been achieved via thought experimentation. This is true even long before the introduction of the term, between the late seventeenth and nineteenth centuries. But what is a thought experiment? Although giving a clear answer to this question is a very complicated task, it is quite common to consider thought experiments as pieces of reasoning about imaginary cases mainly performed with the aim of increasing our knowledge or understanding of the world. In this chapter, I review the lively debate on thought experiments. First, I introduce some famous examples and detail six of them (Sect. 21.1). Second, I give some historical background (Sect. 21.2). Then, I focus on three of the main questions asked in the literature, namely: What is a thought experiment? (Sect. 21.3), What is the function of thought experiments? (Sect. 21.4), How do thought experiments achieve their function? (Sect. 21.5). These issues will lead to tackle other important points, such as the relationship between real and thought experimentation, the differences between philosophical and scientific thought experimentation, the role played by intuitions and imagination in thought experimentation.

Margherita Arcangeli

### 22. Diagrammatic Reasoning in Mathematics

The objective of the present chapter will be to review the most recent studies about diagrammatic reasoning in mathematics. Section 22.3Euclidean geometry will focus on the very much discussed topic of the role and of the features of diagrams and diagrammatic reasoning in Euclidean geometry. Section 22.4ambiguity will be devoted to the proposal of considering diagrams as representations that are introduced in support of other symbolic practices and whose power resides in their ambiguity. In Sect. 22.5, the attention will turn toward studies discussing diagrammatic reasoning in contemporary mathematics. In Sect. 22.6Euclidean geometrytheoryof numbers, computational perspectives on how to implement diagrammatic reasoning in computer programs will be introduced, both for Euclidean geometry and theory of numbers. In Sect. 22.7, it will be discussed how the study of diagrammatic reasoning can shed light onto the nature of mathematical thinking in general. Finally, in Sect. 22.8, some brief conclusions about diagrammatic reasoning in mathematics will be drawn. The choice of reviewing the research about diagrammatic reasoning along these lines is of course at least in part arbitrary. The aim of such a regrouping is to provide the reader with a map that can be helpful for exploring the various and already copious literature that has been recently produced on the subject. The ambition is that such a map will be as extensive as possible.

Valeria Giardino

### 23. Deduction, Diagrams and Model-Based Reasoning

A key piece of data in understanding mathematics from the perspective of model-based reasoning is the use of diagrams to discover and to convey mathematical concepts and proofs. A paradigmatic example of such use is found in the classical demonstrations of elementary Euclidean geometry. These are invariably presented with accompanying geometric diagrams. Great progress has been made recently with respect to the precise role the diagrams plays in the demonstrations, so much so that diagrammatic formalizations of elementary Euclidean geometry have been developed. The purpose of this chapter is to introduce these formalizations to those who seek to understand mathematics from the perspective of model-based reasoning.The formalizations are named FG and Eu. Both are based on insights articulated in Ken Manders’ seminal analysis of Euclid’s diagrammatic proofs. The chapter presents these insights, the challenges involved in realizing them in a formalization, and the way FG and Eu each meet these challenges. The chapter closes with a discussion of how the formalizations can each be thought to prespecify a species of model-based reasoning.

John Mumma

### 24. Model-Based Reasoning in Mathematical Practice

The nature of mathematical reasoning has been the scope of many discussions in philosophy of mathematics. This chapter addresses how mathematicians engage in specific modeling practices. We show, by making only minor alterations to accounts of scientific modeling, that these are also suitable for analyzing mathematical reasoning. In order to defend such a claim, we take a closer look at three specific cases from diverse mathematical subdisciplines, namely Euclidean geometry, approximation theory, and category theory. These examples also display various levels of abstraction, which makes it possible to show that the use of models occurs at different points in mathematical reasoning. Next, we reflect on how certain steps in our model-based approach could be achieved, connecting it with other philosophical reflections on the nature of mathematical reasoning. In the final part, we discuss a number of specific purposes for which mathematical models can be used in this context. The goal of this chapter is, accordingly, to show that embracing modeling processes as an important part of mathematical practice enables us to gain new insights in the nature of mathematical reasoning.

Joachim Frans, Isar Goyvaerts, Bart Van Kerkhove

### 25. Abduction and the Emergence of Necessary Mathematical Knowledge

The prevailing epistemological perspective on school mathematical knowledge values the central role of inductioninduction and deductiondeduction in the development of necessary mathematical knowledge with a rather taken-for-granted view of abduction. This chapter will present empirical evidence that illustrates the relationship between abductive action and the emergence of necessary mathematical knowledge.Recent empirical studies on abduction and mathematical knowledge construction have begun to explore ways in which abduction could be implemented in more systematic terms. In this chapter four types of inferences that students develop in mathematical activity are presented and compared followed by a presentation of key findings from current research on abduction in mathematics and science education. The chapter closes with an exploration of ways in which students can effectively enact meaningful and purposeful abductive thinking processes through activities that enable them to focus on relational or orientation understandings. Four suggestions are provided, which convey the need for meaningful, structured, and productive abduction actions. Together the suggestions target central features in abductive cognition, that is, thinking, reasoning, processing, and disposition.

Ferdinand Rivera

### 26. Vision, Thinking, and Model-Based Inferences

Model-based reasoning refers to the sorts of inferences performed on the basis of a knowledge context that guides them. This context constitutes a model of a domain of reality, that is, an approximative and simplifying to various degrees representation of the factors that underlie, and the interrelations that govern, the behavior of this domain.This chapter addresses both the problem of whether vision involves model-basedmodel-based inferences and, if yes, of what kind; and the problem of the nature of the context that acts as the model guiding visual inferences. It also addresses the broader problem of the relation between visual processing and thinkingthinking. To this end, the various modes of inferences, the most predominant conceptions about visual perception, the stages of visual processing, the problem of the cognitive penetrabilitycognitivepenetrability (CP) of perception, and the logical status of the processes involved in all stages of visual processing will be discussed and assessed.The goal of this chapter is, on the one hand, to provide the reader with an overview of the main broad problems that are currently debated in philosophy, cognitive science, and visual science, and, on the other hand, to equip them with the knowledge necessary to allow them to follow and assess current discussions on the nature of visual processes, and their relation to thinking and cognition in general.

Athanassios Raftopoulos

### 27. Diagrammatic Reasoning

Diagramsdiagram figure prominently in human reasoning, especially in science. Cognitive science research has provided important insights into the inferences afforded by diagrams and revealed differences in the reasoning made possible by physically instantiated diagrams and merely imagined ones. In scientific practice, diagrams figure prominently both in the way scientists reason about data and in how they conceptualize explanatory mechanisms.To identify patterns in data, scientists often graph it. While some graph formats, such as line graphs, are used widely, scientists often develop specialized formats designed to reveal specific types of patterns and not infrequently employ multiple formats to present the same data, a practice illustrated with graph formats developed in circadian biologycircadian biology. Cognitive scientists have revealed the spatial reasoningspatialreasoning and iterative search processes scientists deploy in understanding graphs.In developing explanations, scientists commonly diagram mechanisms they take to be responsible for a phenomenon, a practice again illustrated with diagrams of circadian mechanisms. Cognitive science research has revealed how reasoners mentally animate such diagrams to understand how a mechanism generates a phenomenon.

William Bechtel

### 28. Embodied Mental Imagery in Cognitive Robots

This chapter is focused on discussing the concept of mental imagery as a fundamental cognitive capability to enhance the performance of cognitive robotscognitiverobot. Indeed, the emphasis will be on the embodied imagery mechanisms applied to build artificial cognitive models of motor imagerymotorimagery and mental simulation to control complex behaviors of humanoid platforms, which represent the artificial body.With the aim of providing a panorama of the research activity on the topic, first we give an introduction on the neuroscientific and psychological background of mental imagery in order to help the reader to contextualize the multidisciplinary environment in which we operate. Then, we review the work done in the field of artificial cognitive systemscognitivesystem and roboticsrobotic to mimic the process behind the human ability of creating mental images of events and experiences, and to use this process as a cognitive mechanism to improve the behavior of complex robots. Finally, we report the detail of three recent empirical studies in which mental imagery approaches were modelled trough artificial neural networks (ANNartificialneural network (ANN)cognitiverobotembodied cognitions) to enable a cognitive robot with some human-like capabilities. These empirical studies exemplify how the proprioceptive information can be used by mental imagery models to enhance the performance of the robot, giving evidence of the embodied cognition theories in the context of artificial cognitive systems.

Alessandro Di Nuovo, Davide Marocco, Santo Di Nuovo, Angelo Cangelosi

### 29. Dynamical Models of Cognition

Models of cognition address properties of the mind by formulating cognitive processes such as memory, perception, inference, and comprehension of language. Dynamical models of cognition ascribe importance to time and complexity, both of which bring context to behavior. Temporal processes bring into the moment the possibility of memory, feedback, the effects of nonlinear recursion, and the generation of expectation. Complexity brings the possibility of stable patterns of coordination emerging from interaction of subprocesses.In some models, time and complexity have provided a bridge between thought and action, a basis by which to characterize thought and action as inextricably combined. These models hold that action is a component of perception, or that thought and action are inseparable, or that thought and action act in concert, two sides of the same coin serving to reduce the uncertainty about the nature of events.This chapter provides a review of several models of cognition in terms of their dynamical features, including models not generally included in the dynamical tradition, such as ART and ACT-R. It focuses on the manner in which each model treats time and complexity, thought, and action. It provides a glimpse into the methods of model development and analysis associated with the various approaches to modeling cognitive processes.

Mary Ann Metzger

### 30. Complex versus Complicated Models of Cognition

As humans, we continuously adapt our behavior to changes in our environment, and our cognitive abilities continuously develop over time. A major question for scientists has been to discover the (cognitive) mechanism that underlies the control of human behavior in real time, as well as cognitive development in the long term. This chapter will discuss two kinds of general approaches, which we shall refer to as the reductionist approach and the complex dynamic systems (CDScomplexdynamic systems (CDS)) approach. Roughly speaking, the reductionist approach assumes that separate cognitive components, such as brain areas or processing mechanisms, are primarily responsible for behavior and development, by processing (and responding to) specific environmental cues. The CDS approach assumes that cognition and thereby the control of behavior and development are distributed over the brain, body, and environment, which continuously interact over time. The aim of this chapter is to compare the two approaches in terms of their assumptions, research strategies, and analyses. Furthermore, we will discuss the extent to which current research data in the cognitive domain can be explained by the two different approaches. Based on this review, we conclude that the CDS approach, which assumes a complex rather than a complicated model of cognition, provides the most plausible approach to cognition.

Ruud J.R. Den Hartigh, Ralf F.A. Cox, Paul L.C. Van Geert

### 31. From Neural Circuitry to Mechanistic Model-Based Reasoning

Model-based reasoning in science is often carried out in an attempt to understand the kinds of mechanical interactions that might give rise to particular occurrences. One hypothesis regarding in-the-head reasoning about mechanisms is that scientist rely upon mental models that are like scale modelsscalemodel in crucial respects. Behavioral evidence points to the existence of these mental models, but questions remain about the neural plausibility of this hypothesis.This chapter will provide an overview of the psychological literature on mental models of mechanisms with a specific focus on the question of how representations that share the distinctive features of scale modelsscalemodel might be realized by neural machinations. It is shown how lessons gleaned from the computational simulationsimulation of mechanisms and from neurological research on mental maps in rats can be applied to make sense of how neurophysiological processes might realize mental models.The goal of this chapter is to provide readers with a general introduction to the central challenge facing those who would maintain that in-the-head model-based reasoning about mechanisms in science is achieved through the use of scale-model-like mental representations.

### 32. Computational Aspects of Model-Based Reasoning

Computational models and toolscomputationaltool provide increasingly solid foundations for the study of cognition and model-based reasoning, with knowledge generationknowledgegeneration in different types of cognizing agents, from the simplest ones like bacteria to the complex human distributed cognition. After the introduction of the computational turn, we proceed to models of computation and the relationship between information and computation. A distinction is made between mathematical and computational (executable) modelscomputational(executable) model, which are central for biology and cognition. Computation as it appears in cognitive systems is physical, natural, embodied,physical, natural, embodied computation and distributed computation, and we explain how it relates to the symbol manipulationsymbolmanipulation view of classical computationalismclassicalcomputationalism. As present day models of distributed, asynchronous, heterogeneous, and concurrent networksdistributed, asynchronous, heterogeneous, and concurrent networks are becoming increasingly well suited for modeling of cognitive systems with their dynamic properties, they can be used to study mechanisms of abduction and scientific discovery. We conclude the chapter with the presentation of software modeling with computationally automated reasoning and the discussion of model transformations and separation between semantics and ontology.

Gordana Dodig-Crnkovic, Antonio Cicchetti

### 33. Computational Scientific Discovery

Computational scientific discovery is becoming increasingly important in many areas of science. This chapter reviews the application of computational methods in the formulation of scientific ideas, that is, in the characterization of phenomena and the generation of scientific explanations, in the form of hypotheses, theories, and models. After a discussion of the evolutionary and anthropological roots of scientific discovery, the nature of scientific discovery is considered, and an outline is given of the forms that scientific discovery can take: direct observational discovery, finding empirical rules, and discovery of theories. A discussion of the psychology of scientific discovery includes an assessment of the role of induction. Computational discovery methods in mathematics are then described. This is followed by a survey of methods and associated applications in computational scientific discovery, covering massive systematic searchsystematic search within a defined space; rule-based reasoning systems; classification, machine vision, and related techniques; data mining; finding networks; evolutionary computation; and automation of scientific experiments. We conclude with a discussion of the future of computational scientific discovery, with consideration of the extent to which scientific discovery will continue to require human input.

Peter D. Sozou, Peter C.R. Lane, Mark Addis, Fernand Gobet

### 34. Computer Simulations and Computational Models in Science

Computational sciencesciencecomputational and computer simulations have significantly changed the face of science in recent times, even though attempts to extend our computational capacities are by no means new and computer simulations are more or less accepted across scientific fields as legitimate ways of reaching results (Sect. 34.1). Also, a great variety of computational models and computer simulations can be met across science, in terms of the types of computers, computations, computational models, or physical models involved and they can be used for various types of inquiries and in different scientific contexts (Sect. 34.2). For this reason, epistemological analyses of computer simulations are contextual for a great part. Still, computer simulations raise general questions regarding how their results are justified, how computational models are selected, which type of knowledge is thereby produced (Sect. 34.3), or how computational accounts of phenomena partly challenge traditional expectations regarding the explanation and understanding of natural systems (Sect. 34.4). Computer simulations also share various epistemological features with experiments and thought experiments; hence, the need for transversal analyses of these activities (Sect. 34.5). Finally, providing a satisfactory and fruitful definition of computer simulations turns out to be more difficult than expected, partly because this notion is at the crossroads of difficult questions like the nature of representation and computation or the success of scientific inquiries (Sect. 34.6). Overall, a pointed analysis of computer simulations in parallel requires developing insights about the evolving place of human capacities and humans within (computational) science (Sect. 34.7).

Cyrille Imbert

### 35. Simulation of Complex Systems

Understanding and managing complex systems has become one of the biggest challenges for research, policy and industry. Modeling and simulation of complex systems promises to enable us to understand how a human nervous system and brain not just maintain the activities of a metabolism, but enable the production of intelligent behavior, how huge ecosystems adapt to changes, or what actually influences climatic changes. Also man-made systems are getting more complex and difficult, or even impossible, to grasp. Therefore we need methods and tools that can help us in, for example, estimating how different infrastructure investments will affect the transport system and understanding the behavior of large Internet-based systems in different situations. This type of system is becoming the focus of research and sustainable management as there are now techniques, tools and the computational resources available. This chapter discusses modeling and simulation of such complex systems. We will start by discussing what characterizes complex systems.

Paul Davidsson, Franziska Klügl, Harko Verhagen

### 36. Models and Experiments in Robotics

This chapter surveys the practices that are being employed in experimentally assessing the special class of computational models embedded in robots. The assessment of these models is particularly challenging mainly due to the difficulty of accurately estimating and modeling the interactions between the robots and their environments, especially in the case of autonomous robots, which make decisions without continuous human supervision. The field of autonomous robotics has recognized this difficulty and launched a number of initiatives to deal with it. This chapter, after a conceptual premise and a broad introduction to the experimental issues of robotics, critically reviews these initiatives that range from taking inspiration from traditional experimental practices, to simulations, benchmarking, standards, and competitions.

Francesco Amigoni, Viola Schiaffonati

### 37. Biorobotics

Starting from a reflection on the various roles played by simulations in scientific research, this chapter provides an overview of the biorobotic strategy for testing mechanistic explanations of animal behavior. After briefly summarizing the history and state of the art of biorobotics, it also addresses some key epistemological and methodological issues that need to be taken into serious consideration when setting up and performing biorobotic experiments. These issues mainly concern the relationship between the biorobot and the theoretical model under investigation, the choice of criteria for comparing animal and robotic behaviors, and the pros and cons of computer versus robotic simulations.

Edoardo Datteri

### 38. Comparing Symmetries in Models and Simulations

Computer simulationscomputer simulation brought remarkable novelties to knowledge construction. In this chapter, we first distinguish between mathematical modeling, computer implementations of these models and purely computational approaches. In all three cases, different answers are provided to the questions the observer may have concerning the processes under investigation. These differences will be highlighted by looking at the different theoretical symmetries of each frame. In the latter case, the peculiarities of agent-based or object oriented languages allow to discuss the role of phase spaces in mathematical analyses of physical versus biological dynamics. Symmetry breaking and randomness are finally correlated in the various contexts where they may be observed.

Giuseppe Longo, Maël Montévil

### 39. Experimentation on Analogue Models

Analogue models are actual physical setups used to model something else. They are especially useful when what we wish to investigate is difficult to observe or experiment upon due to size or distance in space or time; for example, if the thing we wish to investigate is too large, too far away, takes place on a time scale that is too long, does not yet exist or has ceased to exist. The range and variety of analogue models is too extensive to attempt a survey. In this chapter, I describe and discuss several different analogue model experiments, the results of those model experiments, and the basis for constructing them and interpreting their results. Examples of analogue models for surface waves in lakes, for earthquakes and volcanoes in geophysics, and for black holes in general relativity, are described, with a focus on examining the bases for claims that these analogues are appropriate analogues of what they are used to investigate. A table showing three different kinds of bases for reasoning using analogue models is provided. Finally, it is shown how the examples in this chapter counter three common misconceptions about the use of analogue models in physics.

Susan G. Sterrett

### 40. Models of Chemical Structure

Models of chemical structure play dual crucial roles in organic chemistryorganic chemistry. First, they allow for the discovery and application of laws to the complex phenomena that chemists hope to understand. Second, they are a source of novel concepts that allow for the continuing development of structure theory and theoretical organic chemistry. In chemistry, therefore, the centrality and significance of models to the scientific enterprise is manifest and furthermore chemistry is a relatively clear, useful, and interesting context in which to consider more general philosophical questions about the nature and role of models in science.

William Goodwin

### 41. Models in Geosciences

The geosciences include a wide spectrum of disciplines ranging from paleontology to climate science, and involve studies of a vast range of spatial and temporal scales, from the deep-time history of microbial life to the future of a system no less immense and complex than the entire Earth. Modeling is thus a central and indispensable tool across the geosciences. Here, we review both the history and current state of model-based inquiry in the geosciences. Research in these fields makes use of a wide variety of models, such as conceptual, physical, and numerical models, and more specifically cellular automata, artificial neural networks, agent-based models, coupled models, and hierarchical models. We note the increasing demands to incorporate biological and social systems into geoscience modeling, challenging the traditional boundaries of these fields. Understanding and articulating the many different sources of scientific uncertainty – and finding tools and methods to address them – has been at the forefront of most research in geoscience modeling. We discuss not only structural model uncertainties, parameter uncertainties, and solution uncertainties, but also the diverse sources of uncertainty arising from the complex nature of geoscience systems themselves. Without an examination of the geosciences, our philosophies of science and our understanding of the nature of model-based science are incomplete.

Alisa Bokulich, Naomi Oreskes

### 42. Models in the Biological Sciences

Evolutionary theory may be understood as a set of overlapping model types, the most prominent of which is the natural selection model, introduced by Charles Darwin and Alfred Russel Wallace. Many of the most prominent models today are represented through mathematical population genetics, in which genetical representations of populations evolve over time to produce evolutionary change. I review the variety of evolutionary models – from genic to group to species selection models – and how they are confirmed through evidence today. I discuss both applications to cases where we do not know the genetics, and to animal behavior and evolution.

Elisabeth A. Lloyd

### 43. Models and Mechanisms in Cognitive Science

In this chapter, we present and discuss models in the context of cognitive sciences, that is, the sciences of the mind. We will focus on computational models, which are the most popular models used in the disciplines of the mind.The chapter has three sections. In the first section, we explain what is a computational model, give a pair of examples of it, illustrate some crucial concepts related to this kind of models (simulationsimulation, computational explanationcomputationalexplanation, functional explanationfunctionalexplanation, and mechanicismmechanicism) and introduce a class of partially alternative models: dynamical models. In the second section, we discuss a pair of difficulties faced by computational explanation and modeling in cognitive sciences: the problem raised by the constraint of modularity, and the problem of the allegedly required integration between dynamical and computational models. Finally, in the third section, we provide a short recap.

Massimo Marraffa, Alfredo Paternoster

### 44. Model-Based Reasoning in the Social Sciences

Social scientists use different types of model to reason about social objects and to study social phenomena. In this chapter, I provide an overview of various forms of model-based reasoning in social research, especially quantitative and qualitative. In the course of the chapter, I highlight differences with other variants of model-based reasoning, notably the one inherited from logical positivism, and I discuss the use of experiments and simulation in social contexts. The chapter also investigates intersections between model-based reasoning and other notions, such as explanation and causality, truth and validity.

Federica Russo

### 45. Models in Architectural Design

At one time, architects and construction specialists used to rely mainly on sketches and physical models as representations of their own cognitive design models. Today, they rely increasingly on computer models including parametric models, generative models, as-built models, building information models (BIMbuilding information model (BIM)), and so forth. Of course, processes of abstraction and the actual architectural model-based reasoning itself remain in the mind of the practitioner who is in control of the design and construction process. However, this whole new array of alternative computer-based representation models has profoundly affected decision-making in architectural design and construction. In this chapter, a brief overview is first given of the state-of-the-art in design thinking research. Following this, an outline is given of how diverse data models, such as BIM and parametric models, are currently used in architectural design and construction. An indication is then given of how these models relate to the in-mind model-based reasoning on which architectural designers and construction experts rely in decision-making and creative thinking. This outline will not only review well-known theories of design thinking and architectural design practice, it will also integrate ongoing theoretical research about analogical reasoning and about abductive, deductive, and inductive reasoning.

Pieter Pauwels

### 46. Representational and Experimental Modeling in Archaeology

I distinguish, by specificity and representational function, several different types of archaeological models: phenomenological, scaffolding, and explanatory models. These take the form of concrete, mathematical, and computational models (following Weisberg’s taxonomy), and they exemplify what Morgan describes as the double life of models; they vary significantly in the degree to which they are intended to accurately represent a particular target, or are media for experimental manipulation of idealized cultural processes. At the phenomenological end of the spectrum, representational models of data include typological constructs that selectively represent variability in archaeological data on several dimensions: formal (material), spatial, and temporal. Archaeologists also build phenomenological models of data drawn from nonarchaeological sources – cultural and natural – that are relevant for interpreting archaeological data as evidence. Assemblages of these target and source models provide the necessary scaffolding for building and evaluating more ambitious explanatory and experimental models of cultural systems and processes, actual and hypothetical.

Alison Wylie

### 47. Models and Ideology in Design

Models play a number of roles in design. Models may assist designers in the solution of technical problems. In addition, modelsmodel may assist designers in achieving ideological goals. Ideological goals of designers could include respect for cultural norms, such as the distinction between masculine and feminine, or adherence to a designdesign paradigm, such as modernism. In this latter role, design models could be compared to model citizens, that is, community members of exemplary character. Use of such models helps designers to produce solutions that fit with the prevailing norms of good design and to promote the standards of design paradigms. For example, the Ville Savoye house was designed by Le Corbusier using ships as models both to solve technical problems of accommodation but also to visibly promote the modernist design paradigm. The purpose of this chapter is to review examples of models that serve this last ideological function. Design ideologies reviewed include revivalism, modernism, industrial design, and biomimicry. Each of these paradigms is characterized by a set of values that designers seek to reflect and promote through their works. There is no finite or canonical list of design ideologies but this set is widely known and acknowledged. So, these examples illustrate how models may serve ideological functions in various design disciplines.

Cameron Shelley

### 48. Restructuring Incomplete Models in Innovators Marketplace on Data Jackets

Innovators Marketplace, a market-like workshop where cards showing existing pieces of knowledge in various domains are combined to create ideas of services/products and thrown into demand-driven communication to choose practical ideas, has been extended to a setting of the market of data. This extension is called Innovators Marketplace on Data Jackets, a workshop in which each prepared card called a data jacketdatajacket (DJ) represents the digest knowledge about a dataset, that is, a kind of metadata. Data jackets are disclosed, whereas the corresponding data are not, and participants of the workshop create ideas for combining and analyzing data using the visualized correlation of data jackets. In this chapter, this workshop is described as a systematic process for reasoningreasoning on incomplete modelsincomplete model, where each data jacket is regarded as an incomplete local model in the domain of the data, and communication is launched for satisfying requirements in the market (regarded as incomplete global models) by restructuring and combining local models. The data jacket may initially include atoms and terms in the domain, not connected via complete causal relations. Via the communication, however, links including causal relations appear and are revised toward obtaining a glocal model corresponding to a solution to satisfy requirements in the marketplace. In this process, the local model corresponding to each element is also revised to obtain useful knowledge digesting the corresponding data.

Yukio Ohsawa, Teruaki Hayashi, Hiroyuki Kido

### 49. Models in Pedagogy and Education

Pedagogy is a discipline concerned with theories and practices of education. Its epistemological model is complex. It may be considered as qualified by two structural directions: pluralism and dialecticity.The pluralism of pedagogy is represented by its possible theoretical routes, by the different levels of sharing of disciplinarity and by a multiplicity of aspects. It involves empirical and experimental research, historical and philosophical dimensions, and epistemological and metatheoretical lines. The theoretical plurality of pedagogy concerns subjects, ages and places of education, languages and research methods, and actual directions and interpretative issues. The multidisciplinary plurality of pedagogy distinguishes it in pedagogical sciences, educational sciences, and educational developmental sciences. The disciplinary multiplicity of pedagogy is expressed by the diversity of pedagogical sciences that belong to general pedagogy. Even if pedagogical sciences are multiple, social pedagogy, history of pedagogy and special needs education are disciplines specifically related to the field of pedagogy.The dialecticity of pedagogy expresses its controversial nature divided between science and philosophy. The scientific approach to pedagogy evolves from systematicity to complexity. It develops, namely, in parallel with the construction and the reconstruction of the very idea of science. The systematization of educational sciences strengthens the philosophical role of pedagogy. The so-called identity crisis of pedagogy will bring it to rediscover the sense of its own reflexive intentionality. The relationship between theory and practice makes pedagogy a science of education, in particular a theory of educational development processes.

Flavia Santoianni

### 50. Model-Based Reasoning in Crime Prevention

Model-based reasoning approaches can be used to formalize and analyze (informal) theories from the field of criminology, to help gain more insight in criminological phenomena that were not clear based on just the informal theory. The analysis of the displacement of crime is an important research interest in criminological research. In this chapter, an agent-based simulation model of crime displacement is presented, which can be used not only to simulate the spatiotemporal dynamics of crime, but also to analyze and control those dynamics. Methods are used that are aimed at developing intelligent systems that monitor human-related processes and provide appropriate support. More specifically, an explicit domain model of crime displacement has been developed, and model-based reasoning techniques are applied to the domain model, in order to analyze which environmental circumstances result in which crime rates, and to determine which support measures are most appropriate. The model can be used as an analytical tool for researchers and policy makers to perform thought experiments, that is, to shed more light on the process under investigation, and possibly improve existing policies (e. g., for surveillance).

Charlotte Gerritsen, Tibor Bosse

### 51. Modeling in the Macroeconomics of Financial Markets

Since the stock price bubble of 1920 and the following 1929–1933 Great Depression, financial crises have become increasingly frequent and globalized. When in the late 2007 the Global Financial Crisis began to show the flawed characteristics of the US capitalist system while spreading throughout all other economies of the world, the ideas of the post-Keynesian School of Economics – a school of economic thought having its origins in The General Theory – and in particular, those of Hyman Minsky, became prominent. Minsky’s conception of “crisis-prone markets” has become fundamental not only to interpret the 2007 credit crunch – as well as a sort of “ignored prediction” – but also to elucidate the features of the post-modern capitalistic system and its evolution. This chapter begins with a review of Minsky’s thought on the inherently unstable nature of capitalism. It then examines Irving Fisher’s debt deflation model and its application to interpret financial crises and recessions. A reflection on the issues of finance-led capitalism in the neo-liberal era completes the first part of the chapter where it is argued that the Minskyian model, if integrated with the social structure of accumulation theory, is very relevant for interpreting the causes and the evolution of the 2007 crisis. The second part of the chapter progresses with the investigation around the constructs of risk and uncertainty, and their modeling in Economics and Business Studies.

Giovanna Magnani

### 52. Application of Models from Social Science to Social Policy

The use of models in social science is now widely acknowledged, and well beyond cosmetic or illustrative purposes. However, the details and the mechanics of their use still prove hard to pin down. Equally, the usefulness of social scientific models in social practice and intervention is often challenged by a number of contentious and recurrent issues. One of these issues is ontological: How do model descriptions and aspects of social reality relate to each other? Often the descriptions offered by models are thin and unrealistic. Can we (and how much) learn about what goes on in the real-social world by analyzing the way/s that world gets described or explained by a model? A second issue is methodological: why using models when we can design experiments in the social world that are able, with some rigor, to inform us on what works? Nowadays there is an established trend to prefer the results achieved, for example, by well-conducted randomized control trials, by many considered the golden rule to doing good and useful social science.In this chapter, we will first show some of the limitations and costs of using models in representing real-life situations, and suggest some strategies by which we can still formulate informative inferences from model to target system. We will then point out some of the virtues and benefits of using models (particularly causal models) when what is at stake is not only answering the question what works in policy terms, but also why it works – or, even more interestingly, why it does not work in given circumstances.

Eleonora Montuschi

### 53. Models and Moral Deliberation

It is clear that models embody or encode information about moral values and moral conduct that is frequently important in moral deliberation, that is, the process of solving moral problemsmoralproblem. However, there is a diversity of views on how models perform this function. In part, this diversity is due to the well-known diversity of views on the concept of model itself. Naturally, scholars with different views of what a model is produce different accounts of their place in moral deliberation. As a result, the shared involvement of models in these accounts has been largely unnoticed. The purpose of this chapter is to review the main, varying accounts of models and model-based reasoning in moral deliberation. These accounts include models as rules, as mental models, schemata, analogies, empathy, and role models. These accounts emphasize different aspects of moral deliberation. Rule-based accounts tend to emphasize morally generalized information concentrated in a set of rules and a cognitive style based on calculation. Other accounts, such as analogies, empathy and role models, tend to emphasize morally particular information spread out throughout a large set of source analogs, and reflect the emotional aspects of moral deliberation. Most accounts concentrate on information originating with the deliberators, although role models, conversely, emphasize models that originate outside the deliberators themselves. Hopefully, this chapter invites further work on the relationships among the accounts reviewed within.

Cameron Shelley

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