Enlarging the possibility space for scientific model-based explanation

Two prominent views in the scientific explanation literature are: (1) that scientific explanations should be ontic or track causal or constitutive relations between the explanans and explanandum; (2) Idealizations in scientific models can be either epistemically dispensable or indispensable in principle. (1) manifests in the requirements which proponents of that view hold for scientific models to be deemed explanatory. Per these advocates, scientific models must not only track causal or constitutive relations but must include some mapping from the model components to the target system. (2) represents something like the current state of play for understanding the place of idealizations in scientific models and involves the longstanding issue of intertheoretic reduction. Idealizations can either be epistemically indispensable (that is not derivable from or reducible to) the relevant micro-level theory or epistemically dispensable in principle. The following project aims to rebut both of these views, thereby seeking to enlarge the possibility space for scientific explanation. For this reason, this project gestures towards and develops new dimensions for scientific model-based explanation. Pace (1), there are many scientific models which do not track ontic or causal relations but are nevertheless explanatory. The first chapter considers a cognitive dynamical model --the HKB model of bimanual coordination-- which fails these requirements for explanation but is one which I claim can still be shown to be explanatory. This represents a promising bit of evidence which can be marshalled and directed against this commitment. Along the lines of (1), proponents of this requirement claim that scientific models must be ontic or risk facing a problematic "directionality problem." The second chapter provides a route of response for the advocate of non-ontic scientific explanations, demonstrating how this problem can be resolved along pragmatic lines. Finally, the partition of the possibility space for understanding the role of idealizations in scientific models encapsulated in (2) is challenged in the third chapter. Therein, a certain species of idealization -continuum idealizations- are discussed and a pragmatic and deflationary approach to the issue of intertheoretic reduction is argued for. These chapters all serve to demonstrate countervailing considerations which, if successful, act as important challenges for the veracity of both (1) and (2). Rather than achieving a mere refutation of these commitments, the success of this project calls for a re-imagining and enlargement of the possibility space for scientific model-based explanations.Includes bibliographical references

Mathematical Explanation: Examining Approaches to the Problem of Applied Mathematics

The problem of applied mathematics is to account for the ’unreasonable effectiveness’ of mathematics in empirical science. A related question is, are there mathematical explanations of scientific facts, in the same way there are empirical explanations of scientific facts? Philosophers are interested in the problem of applied mathematics for two main reasons. They are interested in whether the use of mathematics in empirical science is sufficient to motivate ontological conclusions. The indispensability argument suggests that the widespread application of mathematics obligates us to accept mathematical entities into our ontology. The second primary philosophical question concerns the details of the applications of mathematics. Philosophers are interested in what sort of relationship between mathematics and the physical world allows mathematics to play the role that it does. In this thesis, I examine both areas of literature in detail. I begin by examining the details of the indispensability argument as well as some significant critiques of the argument and the methodological conclusions that it gives rise to. I then examine the work of those philosophers who debate whether the widespread application of mathematics in science motivates accepting mathematical entities into our ontology. This debate centers on whether there are mathematical explanations of scientific facts, which is to say, scientific explanations which have an essential mathematical component. Both sides agree that the existence of mathematical explanations would motivate realism, and they debate the acceptability of various examples to this end. I conclude that there is a strong case that there are mathematical explanations. Next I examine the work of the philosophers who focus on the formal relationship between mathematics and the physical world. Some philosophers argue that mathematical explanations obtain because of a structure preserving ’mapping’ between mathematical structures and the physical world. Others argue that mathematics can play its role without such a relationship. I conclude that the mapping view is correct at its core, but needs to be expanded to account for some contravening examples. In the end, I conclude that this second area of literature represents a much more fruitful and interesting approach to the problem of applied mathematics

Predictive success, partial truth and skeptical realism

Realists argue that mature theories enjoying predictive success are approximately and partially true, and that the parts of the theory necessary to this success are retained through theory-change and worthy of belief. I examine the paradigmatic case of the novel prediction of a white spot in the shadow of a circular object, drawn from Fresnel's wave theory of light by Poisson in 1819. It reveals two problems in this defence of realism: predictive success needs theoretical idealizations and fictions on the one hand, and may be obtained by using different parts of the same theory on the other hand. I maintain that these two problems are not limited to the case of the white spot, but common features of predictive success. It shows that the no-miracle argument by itself cannot prove more than a \textit{skeptical realism}, the claim that we cannot know which parts of theories are true. I conclude by examining if Hacking's manipulability arguments can be of any help to go beyond this position

Predictive success, partial truth and skeptical realism

Realists argue that mature theories enjoying predictive success are approximately and partially true, and that the parts of the theory necessary to this success are retained through theory-change and worthy of belief. I examine the paradigmatic case of the novel prediction of a white spot in the shadow of a circular object, drawn from Fresnel's wave theory of light by Poisson in 1819. It reveals two problems in this defence of realism: predictive success needs theoretical idealizations and fictions on the one hand, and may be obtained by using different parts of the same theory on the other hand. I maintain that these two problems are not limited to the case of the white spot, but common features of predictive success. It shows that the no-miracle argument by itself cannot prove more than a \textit{skeptical realism}, the claim that we cannot know which parts of theories are true. I conclude by examining if Hacking's manipulability arguments can be of any help to go beyond this position

A role for mathematics in the physical sciences

Abstract Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics

The Applicability of Mathematics and the Indispensability Arguments

In this paper I will take into examination the relevance of the main indispensability arguments (Quine’s and Colyvan’s, Putnam’s, and explanatory indispensability argument) for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability problems as subordinate to ontological ones: no ontological stance on mathematical entities (or truths) can offer an easy road to the comprehension of the applicability of mathematics

Idealizations and analogies: Explaining critical phenomena

The “universality” of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions in unifying a large class of phenomena, regardless of microscopic constitution. They argue for an essential explanatory role for “commonalities” rather than that of idealizations. Building on Batterman’s insight, this article aims to show that assessing the differences between the universality of critical phenomena and two paradigmatic cases of “commonality strategy”—the ideal gas model and the harmonic oscillator model—is necessary to avoid the objections raised by Lange and Reutlinger. Taking these universal explanations as benchmarks for critical phenomena reveals the importance of the different roles played by analogies underlying the use of the models. A special combination of physical and formal analogies allows one to explain the epistemic autonomy of the universality of critical phenomena through an explicative loop

Explaining Universality: Infinite Limit Systems in the Renormalization Group Method

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable

Indispensability Without Platonism

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage

Regulative Idealization: A Kantian Approach to Idealized Models

Scientific models typically contain idealizations, or assumptions that are known not to be true. Philosophers have long questioned the nature of idealizations: Are they heuristic tools that will be abandoned? Or rather fictional representations of reality? And how can we reconcile them with realism about knowledge of nature? Immanuel Kant developed an account of scientific investigation that can inspire a new approach to the contemporary debate. Kant argued that scientific investigation is possible only if guided by ideal assumptions—what he calls “regulative ideas”. These ideas are not true of objects of nature, and yet they are not heuristic tools or fictional represen- tations. They are necessary rules governing the construction and assessment of scientific explanations. In this paper, I suggest that some idealizations can be interpreted as having necessary regulative value and as being compatible with scientific realism. I first analyze the puzzle of the nature of idealization and present the main approaches to this topic in the literature. Second, I reconsider the puzzle vis-a-vis a restricted, Kantian definition of idealization and a novel characterization of the relation between idealization and truth. Finally, I discuss in detail an example of idealization (the Hardy-Weinberg equilibrium) along the suggested Kantian lines