Model checking, a prominent formal method used to predict and explain the behaviour of software and hardware systems, is examined on the basis of reflective work in the philosophy of science concerning the ontology of scientific theories and model-based reasoning. The empirical theories of computational systems that model checking techniques enable one to build are identified, in the light of the semantic conception of scientific theories, with families of models that are interconnected by simulation relations. And the mappings between these (...) scientific theories and computational systems in their scope are analyzed in terms of suitable specializations of the notions of model of experiment and model of data. Furthermore, the extensively mechanized character of model-based reasoning in model checking is highlighted by a comparison with proof procedures adopted by other formal methods in computer science. Finally, potential epistemic benefits flowing from the application of model checking in other areas of scientific inquiry are emphasized in the context of computer simulation studies of biological information processing. (shrink)

This paper surveys three controversial new directions in research about the nature of science and briefly summarizes both the intellectual and sociological impact of this work. A bibliographic introduction to the major literature is provided and some fruitful directions for future research are proposed. Philosophers of science are also exhorted to perform 'community service' by correcting misunderstandings of the methods of science fostered by these new approaches.

Philosophers have usually offered a number of ways of describing hypotheses generation, but all aim at demonstrating that the activity of generating hypotheses is paradoxical, illusory or obscure, and then not analysable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. The “computational turn” gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows (...) us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. Creativity and discovery are no more seen as a mysterious irrational process, but, thanks to constructive accounts, as a complex relationship among different inferential steps that can be clearly analysed and identified. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Scientific representation is a currently booming topic, both in analytical philosophy and in history and philosophy of science. The analytical inquiry attempts to come to terms with the relation between theory and world; while historians and philosophers of science aim to develop an account of the practice of model building in the sciences. This article provides a review of recent work within both traditions, and ultimately argues for a practice-based account of the means employed by scientists to effectively achieve representation (...) in the modelling sciences. (shrink)

Philosophers of science today by and large reject the cataclysmic and irrational interpretation of the scientific enterprise claimed by Kuhn. Many computational models have been implemented to rationally study the conceptual change in science. In this recent tradition a key role is played by the concept of abduction as a mechanism by which new explanatory hypotheses are introduced. Nevertheless some problems in describing the most interesting abductive issues rise from the classical computational approach. It describes a cognitive process (and so (...) abduction) by the manipulation of internal symbolic representations of external world. This view assumes a discrete set of representations fixed in discrete time jumps, and cannot adequately account for the issue of anticipation and causation of a new hypothesis. An integration of the traditional computational view with some ideas developed inside the so-called dynamical approach can suggest some important insights. The concept of attractor is very significant. It permits a description of the abductive generation of new hypotheses in terms of a catastrophic rearrangement of the parameters responsible for the behavior of the system. (shrink)

Epistemologists have debated at length whether scientific discovery is a rational and logical process. If it is, according to the Artificial Intelligence hypothesis, it should be possible to write computer programs able to discover laws or theories; and if such programs were written, this would definitely prove the existence of a logic of discovery. Attempts in this direction, however, have been unsuccessful: the programs written by Simon's group, indeed, infer famous laws of physics and chemistry; but having found no new (...) law, they cannot properly be considered discovery machines. The programs written in the Turing tradition, instead, produced new and useful empirical generalization, but no theoretical discovery, thus failing to prove the logical character of the most significant kind of discoveries. A new cognitivist and connectionist approach by Holland, Holyoak, Nisbett and Thagard, looks more promising. Reflection on their proposals helps to understand the complex character of discovery processes, the abandonment of belief in the logic of discovery by logical positivists, and the necessity of a realist interpretation of scientific research. (shrink)

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and combinatoric (...) spaces; (5) Gottfried Leibniz’s development of compositional analysis and synthesis as a general modelling method and a paradigm for ars inveniendi; (6) Fritz Zwicky’s revival of the morphological method of analysis and construction, and its subsequent computerised applications. (shrink)

I propose an approach that expands philosophical views of scientific change, on the basis of an analysis of contemporary biomedical research and recent developments in the philosophy of scientific change. Focusing on the establishment of the exposome in epidemiology as a case study and the role of data as a context for contrasting views on change, I discuss change at conceptual, methodological, material, and social levels of biomedical epistemology. Available models of change provide key resources to discuss this type of (...) change, but I present the need for an approach that models transfer, alignment, and influence as key processes of change. I develop this as a pragmatic approach to scientific change, where processes might change substantially depending on specific circumstances, thus contributing to and complementing the debate on a crucial epistemological issue. (shrink)

Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show (...) how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided. (shrink)

This paper provides a review of Raymond Turner’s book Computational Artefacts. Towards a Philosophy of Computer Science. Focus is made on the definition of program correctness as the twofold problem of evaluating whether both the symbolic program and the physical implementation satisfy a set of specifications. The review stresses how these are not two separate problems. First, it is highlighted how formal proofs of correctness need to rely on the analysis of physical computational processes. Secondly, it is underlined how software (...) testing requires considering the formal relations holding between the specifications and the symbolic program. Such a mutual dependency between formal and empirical program verification methods is finally shown to influence the debate on the epistemological status of computer science. (shrink)

The Epistemology Of Computer Simulation has developed as an epistemological and methodological analysis of simulative sciences using quantitative computational models to represent and predict empirical phenomena of interest. In this paper, Executable Cell Biology and Agent-Based Modelling are examined to show how one may take advantage of qualitative computational models to evaluate reachability properties of reactive systems. In contrast to the thesis, advanced by EOCS, that computational models are not adequate representations of the simulated empirical systems, it is shown how (...) the representational adequacy of qualitative models is essential to evaluate reachability properties. Justification theory, if not playing an essential role in EOCS, is exhibited to be involved in the process of advancing and corroborating model-based hypotheses about empirical systems in ECB and ABM. Finally, the practice of evaluating model-based hypothesis by testing the simulated systems is shown to constitute an argument in favour of the thesis that computer simulations in ECB and ABM can be put on a par with scientific experiments. (shrink)

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on (...) to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

Recently, some philosophers of science (e.g., Gürol Irzik, Michael Friedman) have challenged the ‘received view’ on the relationship between Rudolf Carnap and Thomas Kuhn, suggesting that there is a close affinity (rather than opposition) between their philosophical views. In support of this argument, these authors cite Carnap and Kuhn’s similar views on incommensurability, theory-choice, and scientific revolutions. Against this revisionist view, I argue that the philosophical relationship between Carnap and Kuhn should be regarded as opposed rather than complementary. In particular, (...) I argue that a consideration of the fundamentally disparate nature of the broader philosophical projects of Carnap (logic of science) and Kuhn (providing a theory of scientific revolutions)renders the alleged similarities between their views superficial in comparison to their fundamental differences. In defense of the received view, I suggest that Carnap and Kuhn are model representatives of two contrasting styles of doing philosophy of science, viz., logical analysis and historical analysis respectively. This analysis clarifies the role played by Kuhn’s Structure of Scientific Revolutions in the demise of logical empiricism in the second half of the twentieth-century. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as Aristotelian (...) abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

Critics of contemporary metaphysics argue that it attempts to do the hard work of science from the ease of the armchair. Physics, not metaphysics, tells us about the fundamental facts of the world, and empirical psychology is best placed to reveal the content of our concepts about the world. Exploring and understanding the world through metaphysical reflection is obsolete. In this paper, I will show why this critique of metaphysics fails, arguing that metaphysical methods used to make claims about the (...) world are similar to scientific methods used to make claims about the world, but that the subjects of metaphysics are not the subjects of science. Those who argue that metaphysics uses a problematic methodology to make claims about subjects better covered by natural science get the situation exactly the wrong way around: metaphysics has a distinctive subject matter, not a distinctive methodology. The questions metaphysicians address are different from those of scientists, but the methods employed to develop and select theories are similar. In the first section of the paper, I will describe the sort of subject matter that metaphysics tends to engage with. In the second section of the paper, I will show how metaphysical theories are classes of models and discuss the roles of experience, common sense and thought experiments in the construction and evaluation of such models. Finally, in the last section I will discuss the way these methodological points help us to understand the metaphysical project. Getting the right account of the metaphysical method allows us to better understand the relationship between science and metaphysics, to explain why doing metaphysics successfully involves having a range of different theories, to understand the role of thought experiments involving fictional worlds, and to situate metaphysical realism in a scientifically realist context. (shrink)

In this paper I propose an account of representation for scientific models based on Kendall Walton’s ‘make-believe’ theory of representation in art. I first set out the problem of scientific representation and respond to a recent argument due to Craig Callender and Jonathan Cohen, which aims to show that the problem may be easily dismissed. I then introduce my account of models as props in games of make-believe and show how it offers a solution to the problem. Finally, I demonstrate (...) an important advantage my account has over other theories of scientific representation. All existing theories analyse scientific representation in terms of relations, such as similarity or denotation. By contrast, my account does not take representation in modelling to be essentially relational. For this reason, it can accommodate a group of models often ignored in discussions of scientific representation, namely models which are representational but which represent no actual object. (shrink)

This paper argues that, for a prospective philosophical analysis of models and simulations to be successful, it must accommodate an account of mathematically rigorous results. Such rigorous results are best thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results often provide new indirect ways of assessing the success of computer simulations of individual models. This is most obvious in cases where rigorous results map different models on to one (...) another. Not only does this allow for the transfer of warrant across different models, it also puts constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling. Rigorous results and relations can thus come to be seen as giving cohesion and stability to actual practices of scientific modelling. (shrink)

According to the hierarchy of models account of scientific experimentation developed by Patrick Suppes and elaborated by Deborah Mayo, theoretical considerations about the phenomena of interest are involved in an experiment through theoretical models that in turn relate to experimental data through data models, via the linkage of experimental models. In this paper, I dispute the HoM account in the context of present-day high-energy physics experiments. I argue that even though the HoM account aims to characterize experimentation as a model-based (...) activity, it does not involve a modeling concept for the process of data acquisition, and it thus fails to provide a model-based characterization of the theory-experiment relationship underlying this process. In order to characterize the foregoing relationship, I propose the concept of a model of data acquisition and illustrate it in the case of the ATLAS experiment at CERN’s Large Hadron Collider, where the Higgs boson was discovered in 2012. I show that the process of data acquisition in the ATLAS experiment is performed according to a model of data acquisition that specifies and organizes the experimental procedures necessary to select the data according to a predetermined set of selection criteria. I also point out that this data acquisition model is theory-laden, in the sense that the underlying data selection criteria are determined by considering the testable predictions of the theoretical models that the ATLAS experiment is aimed to test. I take this sense of theory-ladenness to indicate that the relationship between the procedures of the ATLAS experiment and the theoretical models of the phenomena of interest is first established, prior to the formation of data models, through the data acquisition model of the experiment, thus not requiring the intermediary of other types of models as suggested by the HoM account. I therefore conclude that in the context of present-day HEP experiments, the HoM account does not consistently extend to the process of data acquisition so as to include models of data acquisition. (shrink)

Review essay of How to do science with models. A philosophical primer. Springer briefs in philosophy, Axel Gelfert., 129, Price € 49,99 softcover, ISBN: 978-3-319-27954-1.

The purpose of this study is to gain a better understanding of the role of abstraction and idealization in Galileo’s scientific inquiries into the law of free falling motion, and their importance in the history of science. Because there is no consensus on the use of the terms “abstraction” and “idealization” in the literature, it is necessary to distinguish between them at the outset. This paper will argue for the importance of abstraction and idealization in physics and the theories and (...) laws of physics constructed with abduction from observations and that these theoretical laws of physics should be tested with deduction and induction thorough quasi-idealized entities rather than empirical results in the everyday world. Galileo’s work is linked to thought experiments in natural science. Galileo, using thought experiments based on idealization, persuaded others that what had been proven true for a ball on an inclined plane would be equally true for a ball falling through a vacuum. (shrink)

"It is difficult not to notice a curious unrest in the philosophic atmosphere of the time, a loosening of old landmarks, a softening of oppositions, a mutual borrowing from one another on the part of systems anciently closed, and an interest in new suggestions, however vague, as if the one thing sure were the inadequacy of extant school-solutions. The dissatisfactions with these seems due for the most part to a feeling that they are too abstract and academic. Life is confused (...) and superabundant, and what the younger generation appears to crave is more of the temperament of life in its philosophy, even though it were at some cost of logical rigor and formal purity." - William James (1904). -/- Abstract: The study of model-based reasoning (MBR) is one of the most interesting recent developments at the intersection of psychology and the philosophy of science. Although a broad and eclectic area of inquiry, one central axis by which MBR connects these disciplines is anchored at one end in theories of internal reasoning (in cognitive science), and at the other, in C.S. Peirce’s semiotics (in philosophy). In this paper, we attempt to show that Peirce’s semiotics actually has more natural affinity on the psychological side with ecological psychology, as originated by James J. Gibson and especially Egon Brunswik, than it does with non-interactionist approaches to cognitive science. In particular, we highlight the strong ties we believe to exist between the triarchic structure of semiotics as conceived by Peirce, and the similar triarchic stucture of Brunswik’s lens model of organismic achievement in irreducibly uncertain ecologies. The lens model, considered as a theory of creative abduction, provides a concrete instantiation of at least one, albeit limited, interpretation of Peirce’s semiotics, one that we believe could be quite fruitful in future theoretical and empirical investigations of MBR in both science an philosophy. (shrink)

In his influential paper, 'Why Was the Logic of Discovery Abandoned?', Laudan contends that there has been no philosophical rationale for a logic of discovery since the emergence of consequentialism in the 19th century. It is the purpose of this paper to show that consequentialism does not involve the rejection of all types of logic of discovery. Laudan goes too far in his interpretation of the historical shift from generativism to consequentialism, and his claim that the context of pursuit belongs (...) to neither discovery nor justification is based on narrow interpretations of the contexts of discovery and justification. As a result, Laudan draws unwarranted conclusions concerning both the early and contemporary defenders of a logic of discovery. A methodological logic of discovery - which involves self-corrective methods of hypothesis generation that promote the long-term goals of science and which require consequential support for justification - is a type of logic of discovery that survives the shift to consequentialism. (shrink)

In several works, Ruth Millikan has developed a ‘teleosemantic’ theory of concepts. Millikan’s theory has three explicit desiderata for concepts: wide scope, non-descriptionist content, and naturalism. I contend that Millikan’s theory cannot fulfill all of these desiderata simultaneously. Theoretical concepts, such as those of chemistry and physics, fall under Millikan’s intended scope, but I will argue that her theory cannot account for these concepts in a way that is compatible with both non-descriptionism and naturalism. In these cases, Millikan’s view is (...) subject to the traditional ‘indeterminacy problem’ for teleosemantic theories. This leaves the content of theoretical concepts indeterminate between a descriptionist and non-descriptionist content. Furthermore, this problem cannot be overcome without giving up the naturalism desideratum. I suggest that the scope of Millikan’s theory should be limited. At best, the theory will be able to attribute naturalistic, non-descriptionist content to a smaller range of concepts. (shrink)

Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large number of (...) comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations. (shrink)

We argue that abduction does not work in isolation from other inference mechanisms and illustrate this through an inference scheme designed to evaluate multiple hypotheses. We use game theory to relate the abductive system to actions that produce new information. To enable evaluation of the implications of this approach we have implemented the procedures used to calculate the impact of new information in a computer model. Experiments with this model display a number of features of collective belief-revision leading to consensus-formation, (...) such as the influence of bias and prejudice. The scheme of inferential calculations invokes a Peircian concept of ‘belief’ as the propensity to choose a particular course of action. (shrink)

This paper takes part in the methodological debate concerning the nature and the justification of hypotheses about computational systems in software engineering by providing an epistemological analysis of Software Testing, the practice of observing the programs’ executions to examine whether they fulfil software requirements. Property specifications articulating such requirements are shown to involve falsifiable hypotheses about software systems that are evaluated by means of tests which are likely to falsify those hypotheses. Software Reliability metrics, used to measure the growth of (...) probability that given failures will occur at specified times as new executions are observed, is shown to involve a Bayesian confirmation of falsifiable hypotheses on programs. Coverage criteria, used to select those input values with which the system under test is to be launched, are understood as theory-laden principles guiding software tests, here compared to scientific experiments. Redundant computations, fault seeding models and formal methods used in software engineering to evaluate test results are taken to be instantiations of some epistemological strategies used in scientific experiments to distinguish between valid and non-valid experimental outcomes. The final part of the paper explores the problem, advanced in the context of the philosophy of technology, of defining the epistemological status of software engineering by conceiving it as a scientifically attested technology. (shrink)

Science is a form of distributed analysis involving both individual work that produces new knowledge and collaborative work to exchange information with the larger community. There are many particular ways in which individual and community can interact in science, and it is difficult to assess how efficient these are, and what the best way might be to support them. This paper reports on a series of experiments in this area and a prototype implementation using a research platform called CACHE. CACHE (...) both supports experimentation with different structures of interaction between individual and community cognition and serves as a prototype for computational support for those structures. We particularly focus on CACHE‐BC, the Bayes community version of CACHE, within which the community can break up analytical tasks into “mind‐sized” units and use provenance tracking to keep track of the relationship between these units. (shrink)

This paper examines the nature of model-based reasoning in the interplay between theory and experiment in the context of biomedical engineering research laboratories, where problem solving involves using physical models. These "model systems" are sites of experimentation where in vitro models are used to screen, control, and simulate specific aspects of in vivo phenomena. As with all models, simulation devices are idealized representations, but they are also systems themselves, possessing engineering constraints. Drawing on research in contemporary cognitive science that construes (...) cognition as occurring in a complex distributed system comprising people and artifacts, I argue that reasoning with model systems is a constraint satisfaction process involving co-construction, manipulation, and revision of mental and physical models. (shrink)

The thesis proposes an account of the means of scientific representation focused on similarity, or more specifically, on the notion of “creative similarity”. I first distinguish between two different questions regarding the problem of representation: the question about the constituents and the question about the means of representation (following Suárez 2003; van Fraassen 2008). I argue that, although similarity is not a good candidate for constituent of representation, it can satisfactorily answer the question about the means of representation if adequately (...) characterized. To motivate this position, I dispute the main arguments offered against similarity as means of representation, namely the arguments from variety, vagueness, and misrepresentation, and contend that similarity plays a central epistemic role in practices of representing in science. The study of the role of similarity in scientific practice, I argue, requires the analysis of the uses of judgments of similarity in the construction of scientific models. I examine the cases of the Mississippi Basin Model and the San Francisco Bay Model to illustrate how judgments of similarity are directly involved in the production of epistemically fruitful models. Informed by the practical investigation developed throughout the thesis, I finally outline what I call the creative similarity account of the means of representation. The notion of “creative similarity” helps to capture the way in which similarity, as means of representation, intervenes in actual practices of representing, namely, in the form of a productive interplay of judgments of similarity and distortions (i.e. idealizations, abstractions, simplifications), which is employed by resourceful agents with the aim of understanding aspects of the natural world. (shrink)

In part because “imagination” is a slippery notion, its exact role in the production of scientific knowledge remains unclear. There is, however, one often explicit and deliberate use of imagination by scientists that can be (and has been) studied intensively by epistemologists and historians of science: thought experiments. The main goal of this article is to document the varieties of thought experimentation, not so much in terms of the different sciences in which they occur but rather in terms of the (...) different functions they fulfil. I argue that thought experimentation (and hence imagination) plays a role not only in theory choice but in singular causal analysis and scientific discovery as well. I pinpoint, moreover, some of the rules governing the use of thought experiments in theory choice and in singular causal analysis, that is, some of the criteria they should meet in order to fulfil those functions successfully. (shrink)

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested (...) in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. (shrink)

Inductive reasoning aims at constructing rules and models of general applicability from a restricted set of observations. Induction is a keystone in natural sciences, and it influences diverse application fields such as engineering, medicine and economics. More generally, induction plays a major role in the way humans learn and operate in their everyday life. The level of reliability that a model achieves depends on how informative the observations are relative to the flexibility of the process by which the model is (...) constructed. When the process is articulated so that the model can incorporate descriptive details and subtleties, a large set of informative observations are required to reliably tune the model, whereas models obtained from simple procedures can be tuned with fewer observations. This article introduces the concept of “dominance”, which refers to the situation in which a reduced subset of observations suffices to reconstruct the model. A mathematical framework is presented to quantify the reliability of learning procedures as a function of the size of the subset of dominant observations. Although limited in scope, we believe that our study can contribute to the understanding of some fundamental mechanisms by which knowledge is generated from observations in inductive reasoning. (shrink)

There is a demand to nurture scientific creativity in science education. This paper proposes that the relevant conceptual infrastructure with which to teach scientific creativity is often already included in philosophy of science courses, even those that do not cover scientific creativity explicitly. More precisely, it is shown how paradigm theory can serve as a framework with which to introduce the differences between combinational, exploratory, and transformational creativity in science. Moreover, the types of components given in Kuhn’s disciplinary matrix are (...) argued to indicate a further subdivision within transformational creativity that makes explicit that this most radical type of creativity that aims to go beyond and thus to transform the current paradigm can take many different directions. More generally, it is argued that there are several synergies between the topic of scientific creativity and paradigm theory that can be utilized in most philosophy of science courses at relative ease. Doing so should promote the understanding of scientific creativity among students, provide another way to signify the relevance of paradigm theory, and more strategically be a way of reinforcing the place of philosophy of science in science education. (shrink)

In some of the papers in which she develops and defends the mental modelview of thought experiments in physics, Nersessian expresses the belief that her account has implications for thought experiments in other domains as well. In this paper, I argue, firstly, that counterfactual reasoning has a legitimate place in historical inquiry, and secondly, that the mental model view can account for such "alternative histories". I proceed as follows. Firstly, I review the main accounts of thought experiments in physics and (...) point at some explanatory advantages of the mental model view. Subsequently, I argue that historians cannot dispense with counterfactual reasoning altogether and qualify a number of principled objections against the explicit use of alternative histories for theoretical purposes. Finally, I show that the mental model view can account for such thought experiments in history. (shrink)

The problem of epistemic opacity in Artificial Intelligence is often characterised as a problem of intransparent algorithms that give rise to intransparent models. However, the degrees of transparency of an AI model should not be taken as an absolute measure of the properties of its algorithms but of the model’s degree of intelligibility to human users. Its epistemically relevant elements are to be specified on various levels above and beyond the computational one. In order to elucidate this claim, I first (...) contrast computer models and their claims to algorithm-based universality with cybernetics-style analogue models and their claims to structural isomorphism between elements of model and target system. While analogue models aim at perceptually or conceptually accessible model-target relations, computer models give rise to a specific kind of underdetermination in these relations that needs to be addressed in specific ways. I then undertake a comparison between two contemporary AI approaches that, although related, distinctly align with the above modelling paradigms and represent distinct strategies towards model intelligibility: Deep Neural Networks and Predictive Processing. I conclude that their respective degrees of epistemic transparency primarily depend on the underlying purposes of modelling, not on their computational properties. (shrink)

The important role of mathematical representations in scientific thinking has received little attention from cognitive scientists. This study argues that neglect of this issue is unwarranted, given existing cognitive theories and laws, together with promising results from the cognitive historical analysis of several important scientists. In particular, while the mathematical wizardry of James Clerk Maxwell differed dramatically from the experimental approaches favored by Michael Faraday, Maxwell himself recognized Faraday as “in reality a mathematician of a very high order,” and his (...) own work as in some respects a re‐representation of Faraday’s field theory in analytic terms. The implications of the similarities and differences between the two figures open new perspectives on the cognitive role of mathematics as a learned mode of representation in science. (shrink)