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We examine arguments for distinguishing between ontological and epistemological concepts of fundamentality, focusing in particular on the role that scale plays in these concepts. Using the fractional quantum Hall effect as a case study, we show that we can draw a distinction between ontologically fundamental and nonfundamental theories without insisting that it is only the fundamental theories that get the ontology right: there are cases where nonfundamental theories involve distinct ontologies that better characterize real systems than fundamental ones do. In (...) 

This paper analyses the antireductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation. 

I argue that a common philosophical approach to the interpretation of physical theories—particularly quantum field theories—has led philosophers astray. It has driven many to declare the quantum field theories employed by practicing physicists, socalled ‘effective field theories’, to be unfit for philosophical interpretation. In particular, such theories have been deemed unable to support a realist interpretation. I argue that these claims are mistaken: attending to the manner in which these theories are employed in physical practice, I show that interpreting effective (...) 

In the recent literature on causal and noncausal scientific explanations, there is an intuitive assumption according to which an explanation is noncausal by virtue of being abstract. In this context, to be ‘abstract’ means that the explanans in question leaves out many or almost all causal microphysical details of the target system. After motivating this assumption, we argue that the abstractness assumption, in placing the abstract and the causal character of an explanation in tension, is misguided in ways that are (...) 

Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...) 

This paper provides a sorelyneeded evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For nonbelievers, it contributes to a divideandconquer strategy for showing that there are no such explanations in science. My discussion also undermines the appeal (...) 

How can a reflective scientist put forward an explanation using a model when they are aware that many of the assumptions used to specify that model are false? This paper addresses this challenge by making two substantial assumptions about explanatory practice. First, many of the propositions deployed in the course of explaining have a nonrepresentational function. In particular, a proposition that a scientist uses and also believes to be false, i.e. an “idealization”, typically has some nonrepresentational function in the practice, (...) 

This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...) 

Thought: A Journal of Philosophy, EarlyView. 

Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to refocus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one. 

Call an explanation in which a nonmathematical fact is explained—in part or in whole—by mathematical facts: an extramathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extramathematical explanation is developed. The theory is modelled on a deductivenomological theory of scientific explanation. A basic DN account of extramathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...) 

A number of philosophers have recently suggested that some abstract, plausibly noncausal and/or mathematical, explanations explain in a way that is radically dif ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...) 

Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the nonexplanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...) 



I explore a challenge that idealisations pose to scientific realism and argue that the realist can best accommodate idealisations by capitalising on certain modal features of idealised models that are underwritten by laws of nature. 

© The Authors [2018]. Published by Oxford University Press. All rights reserved. For permissions, please email: [email protected] article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...In his Moby Dick, Herman Melville writes that “to produce a mighty book you must choose a mighty theme”. Marc Lange’s Because Without Cause is definitely an impressive book that deals with a mighty theme, that of noncausal explanations in the empirical sciences and in mathematics. Blending a (...) 

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The takehome message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability. 

Despite widespread evidence that fictional models play an explanatory role in science, resistance remains to the idea that fictions can explain. A central source of this resistance is a particular view about what explanations are, namely, the ontic conception of explanation. According to the ontic conception, explanations just are the concrete entities in the world. I argue this conception is ultimately incoherent and that even a weaker version of the ontic conception fails. Fictional models can succeed in offering genuine explanations (...) 

The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four (...) 

A finergrained delineation of a given explanandum reveals a nexus of closely related causal and non causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the LotkaVolterra equations. There (...) 