The book Model-Based Reasoning in Scientific Discovery, aims to explain how specific modeling practices employed by scientists are productive methods of ...

In several accounts of what models are and how they function a specific view dominates. This view contains the following characteristics. First, there is a clear-cut distinction between theories, models and data and secondly, empirical assessment takes place after the model is built. This view in which discovery and justification are disconnected is not in accordance with several practices of mathematical business-cycle model building. What these practices show is that models have to meet implicit criteria of adequacy, such as satisfying (...) theoretical, mathematical and statistical requirements, and be useful for policy. In order to be adequate, models have to integrate enough items to satisfy such criteria. These items include besides theoretical notions, policy views, mathematisations of the cycle and metaphors also empirical data and facts. So, the main thesis of this chapter is that the context of discovery is the successful integration of those items that satisfy the criteria of adequacy. Because certain items are empirical data and facts, justification can be built-in. (shrink)

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

The present paper examines the role of exact results in the theory of many‐body physics, and specifically the example of the Mermin‐Wagner theorem, a rigorous result concerning the absence of phase transitions in low‐dimensional systems. While the theorem has been shown to hold for a wide range of many‐body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that the (...) models, too, are often described as approximations to the underlying ‘full’ many‐body problem. (shrink)

A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.

Recent works in epistemology show that the claim that coherence is truth conducive – in the sense that, given suitable ceteris paribus conditions, more coherent sets of statements are always more probable – is dubious and possibly false. From this, it does not follows that coherence is a useless notion in epistemology and philosophy of science. Dietrich and Moretti (Philosophy of science 72(3): 403–424, 2005) have proposed a formal of account of how coherence is confirmation conducive—that is, of how the (...) coherence of a set of statements facilitates the confirmation of such statements. This account is grounded in two confirmation transmission properties that are satisfied by some of the measures of coherence recently proposed in the literature. These properties explicate everyday and scientific uses of coherence. In his paper, I review the main findings of Dietrich and Moretti (2005) and define two evidence-gathering properties that are satisfied by the same measures of coherence and constitute further ways in which coherence is confirmation conducive. At least one of these properties vindicates important applications of the notion of coherence in everyday life and in science. (shrink)

The following article treats the 'applicational turn' of modern fluid dynamics as it set in at the beginning of the 20th century with Ludwig Prandtl's concept of the boundary layer. It seeks to show that there is much more to applying a theory in a highly mathematical field like fluid dynamics than deriving a special case from a general explanatory theory under particular antecedent conditions. In Prandtl's case, the decisive move was to introduce a model that provided a physical/causal conception (...) of viscous flow at high Reynolds numbers. It facilitated an approximate solution to the Navier-Stokes equations, which in turn gave rise to many special applications. After a detailed account of Prandtl's achievement, the article discusses the role of the physical model and its experimental and mathematical significance. It is shown that the mathematical simplification provided by the physical model greatly expanded the explanatory capacity of the theory which the Navier-Stokes equations alone could not provide. (shrink)

Models as Mediators discusses the ways in which models function in modern science, particularly in the fields of physics and economics. Models play a variety of roles in the sciences: they are used in the development, exploration and application of theories and in measurement methods. They also provide instruments for using scientific concepts and principles to intervene in the world. The editors provide a framework which covers the construction and function of scientific models, and explore the ways in which they (...) enable us to learn about both theories and the world. The contributors to the volume offer their own individual theoretical perspectives to cover a wide range of examples of modelling, from physics, economics and chemistry. These papers provide ideal case-study material for understanding both the concepts and typical elements of modelling, using analytical approaches from the philosophy and history of science. (shrink)

Morrison and Morgan argue for a view of models as 'mediating instruments' whose role in scientific theorising goes beyond applying theory. Models are partially independent of both theories and the world. This autonomy allows for a unified account of their role as instruments that allow for exploration of both theories and the world.

It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the (...) empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

This paper examines the relationship between simulation and experiment. Many discussions of simulation, and indeed the term "numerical experiments," invoke a strong metaphor of experimentation. On the other hand, many simulations begin as attempts to apply scientific theories. This has lead many to characterize simulation as lying between theory and experiment. The aim of the paper is to try to reconcile these two points of viewto understand what methodological and epistemological features simulation has in common with experimentation, while at the (...) same time keeping a keen eye on simulation's ancestry as a form of scientific theorizing. In so doing, it seeks to apply some of the insights of recent work on the philosophy of experiment to an aspect of theorizing that is of growing philosophical interest: the construction of local models. (shrink)

It is tempting to think that, if a person's beliefs are coherent, they are also likely to be true. This truth conduciveness claim is the cornerstone of the popular coherence theory of knowledge and justification. Erik Olsson's new book is the most extensive and detailed study of coherence and probable truth to date. Setting new standards of precision and clarity, Olsson argues that the value of coherence has been widely overestimated. Provocative and readable, Against Coherence will make stimulating reading for (...) epistemologists and anyone with a serious interest in truth. (shrink)

The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, but there is a good reason (...) to except no such correlation. it is argued that there is a subjective element in the decision as to what constitutes a mathematical concept. a number of purported solutions to the mystery of the applicability of mathematics to nature are discarded, until we are left with eugene wigner's thesis that we are here confronted with a "miracle that we neither understand nor deserve.". (shrink)

Among many reasons for which contemporary philosophers take coherentism in epistemology seriously, the most important is probably the perceived inadequacy of alternative accounts, most notably misgivings about foundationalism. But coherentism also receives straightforward support from cases in which beliefs are apparently justified by their coherence. From the perspective of those against coherentism, this means that an explanation is needed as to why in these cases coherence apparently justifies beliefs. Curiously, this task has not been carried out in a serious way (...) in the anti-coherentist literature although there is no scarcity of objections to coherentism. The traditional charge has been that justification by coherence is circular. More recently the isolation problem allegedly reveals that coherentism justifies beliefs that should not be justified. Questions have also been raised with respect to the basing relation and feasibility.1 However, these objections do not explain why some beliefs appear to be justified by their coherence. This paper fills this gap in the anti-coherentist literature by offering a noncoherentist account of justification by coherence. The paper proceeds as follows. Section I delineates the framework of discussion and develops some conceptual tools needed in later analyses. Section II argues that there are genuine cases of an increase in existing empirical justification by coherence, but that it does not require coherence to generate additional justification—coherence serves as a channel of justification among beliefs, which is no more problematic than channeling of justification from basic to derived beliefs in foundationalism. Section III makes a stronger case for justification by coherence, where each of the coherent beliefs has no independent empirical justification; but Section IV argues that even in these cases coherence need not generate justification—coherence licenses the channeling of justification from outside sources.. (shrink)

The ArgumentIn its reconstruction of scientific practice, philosophy of science has traditionally placed scientific theories in a central role, and has reduced the problem of mediating between theories and the world to formal considerations. Many applications of scientific theories, however, involve complex mathematical models whose constitutive equations are analytically unsolvable. The study of these applications often consists in developing representations of the underlying physics on a computer, and using the techniques of computer simulation in order to learn about the behavior (...) of these systems. In many instances, these computer simulations are not simple number-crunching techniques. They involve a complex chain of inferences that serve to transform theoretical structures into specific concrete knowledge of physical systems. In this paper I argue that this process of transformation has its own epistemology. I also argue that this kind of epistemology is unfamiliar to most philosophy of science, which has traditionally concerned itself with the justification of theories, not with their application. Finally, I urge that the nature of this epistemology suggests that the end results of some simulations do not bear a simple, straightforward relation to the theories from which they stem. (shrink)

Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..

In this paper, I explore Larry Laudan's and Jarrett Leplin's recent claim that empirically equivalent theories may be differentially confirmed. I show that their attempt to prise apart empirical equivalence and epistemic parity commits them to two principles of confirmation that Hempel demonstrated to be incompatible.

Scientific models represent aspects of the empirical world. I explore to what extent this representational relationship, given the specific properties of models, can be analysed in terms of propositions to which truth or falsity can be attributed. For example, models frequently entail false propositions despite the fact that they are intended to say something "truthful" about phenomena. I argue that the representational relationship is constituted by model users "agreeing" on the function of a model, on the fit with data and (...) on the aspects of a phenomenon that are modelled. Model users weigh the propositions entailed by a model and from this decide which of these propositions are crucial to the acceptance and continued use of the model. Thus, models represent phenomena when certain propositions they entail are true, but this alone does not exhaust the representational relationship. Therefore, the constraints that produce the choice of the relevant propositions in a model must also be examined and their analysis contributes to understanding the relationship between models and phenomena. (shrink)

I argue against an account of scientific representation suggested by the semantic, or structuralist, conception of scientific theories. Proponents of this conception often employ the term “model” to refer to bare “structures”, which naturally leads them to attempt to characterize the relation between models and reality as a purely structural one. I argue instead that scientific models are typically “representations”, in the pragmatist sense of the term: they are inherently intended for specific phenomena. Therefore in general scientific models are not (...) (merely) structures. I then explore some consequences of this pragmatist account of representation, and argue that it sheds light upon the distinction between theories and models. I finish by briefly addressing some critical comments due to Bas Van Fraassen. (shrink)