According to a number of approaches in theoretical physics, spacetime does not exist fundamentally. Rather, spacetime exists by depending on another, more fundamental, non-spatiotemporal structure. A prevalent opinion in the literature is that this dependence should not be analyzed in terms of composition. We should not say, that is, that spacetime depends on an ontology of non-spatiotemporal entities in virtue of having them as parts. But is that really right? On the contrary, we argue that a mereological approach to dependent (...) spacetime is not only viable, but promises to enhance our understanding of the physical situation. (shrink)

We develop a new version of the causal theory of spacetime. Whereas traditional versions of the theory seek to identify spatiotemporal relations with causal relations, the version we develop takes causal relations to be the grounds for spatiotemporal relations. Causation is thus distinct from, and more basic than, spacetime. We argue that this non-identity theory, suitably developed, avoids the challenges facing the traditional identity theory.

It has been hypothesized that our believing that, or its seeming to us as though, the world is in some way dynamical partially explains (and perhaps rationalizes) future-bias. Recent work has, in turn, found a correlation between future-bias and near-bias, suggesting that there is a common explanation for both. Call the claim that what partially explains our being both future- and near-biased is our believing/it seeming to us as though the world is dynamical, the dynamical explanation. We empirically test two (...) versions of the dynamical explanation. The first is the moving ego explanation—according to which it is our belief that the ego moves, or our phenomenology as of the ego moving, that jointly (partially) explains future- and near-bias. The second is the moving time explanation—according to which it is our belief that time robustly passes, or our phenomenology as of robust passage, which jointly (partially) explain future- and near-bias. We found no evidence in favour of either explanation. (shrink)

This paper offers a new account of metaphysical explanation. The account is modelled on Kitcher’s unificationist approach to scientific explanation. We begin, in Sect. 2, by briefly introducing the notion of metaphysical explanation and outlining the target of analysis. After that, we introduce a unificationist account of metaphysical explanation before arguing that such an account is capable of capturing four core features of metaphysical explanations: irreflexivity, non-monotonicity, asymmetry and relevance. Since the unificationist theory of metaphysical explanation inherits irreflexivity and non-monotonicity (...) directly from the unificationist theory of scientific explanation that underwrites it, we focus on demonstrating how the account can secure asymmetry and relevance. (shrink)

Many philosophers have thought that our folk, or pre-reflective, view of persistence is one on which objects endure. This assumption not only plays a role in disputes about the nature of persistence itself, but is also put to use in several other areas of metaphysics, including debates about the nature of change and temporal passage. In this paper, we empirically test three broad claims. First, that most people (i.e. most non-philosophers) believe that, and it seems to them as though, objects (...) persist by enduring rather than perduring. Second, that most people have a view of change on which enduring but not perduring objects count as changing. Third, that one reason why the folk represent time as dynamical is because it seems to them, and they believe that, they endure through time. We found no evidence to support these claims. While there are certainly plenty of ‘folk’ endurantists in the population we tested, there are also plenty of ‘folk’ perdurantists. We did not find robust evidence that a majority of people believed that, or it seemed to them as though, objects endure rather than perdure. We conclude that many arguments in favour of endurantism that appeal to folk beliefs about, or experiences of, persisting objects and change rest on views about those beliefs and experiences that are empirically unsupported. There is no evidence to suggest that endurantism is the folk friendly view of persistence, and so we should stop treating it as such without argument. (shrink)

A number of philosophers have argued in favour of extended simples on the grounds that they are needed by fundamental physics. The arguments typically appeal to theories of quantum gravity. To date, the argument in favour of extended simples has ignored the fact that the very existence of spacetime is put under pressure by quantum gravity. We thus consider the case for extended simples in the context of different views on the existence of spacetime. We show that the case for (...) extended simples based on physics is far more complex than has been previously thought. We present and then map this complexity, in order to present a much more textured picture of the argument for extended simples. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...) appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)

Much current debate in the metaphysics of time is between A-theorists and B-theorists. Central to this debate is the assumption that time exists and that the task of metaphysics is to catalogue time’s features. Relatively little consideration has been given to an error theory about time. Since there is very little extant work on temporal error theory the goal of this paper is simply to lay the groundwork to allow future discussion of the relative merits of such a view. The (...) paper thus develops a conceptual framework from within which to evaluate claims about the actual existence, or not, of temporality as that notion appears in folk discourses about time, and from there to examine claims about the counterfactual existence, or not, of temporality so conceived. We subsequently apply this framework to three extant positions drawn from physics and metaphysics that deny the existence of time. We show that only one of these positions is a folk temporal error theory; that is, a view that denies the existence of time as that notion is operative in our everyday thought and talk. (shrink)

The anglophone philosophy profession has a well-known problem with gender equity. A sig-nificant aspect of the problem is the fact that there are simply so many more male philoso-phers than female philosophers among students and faculty alike. The problem is at its stark-est at the faculty level, where only 22% - 24% of philosophers are female in the United States (Van Camp 2014), the United Kingdom (Beebee & Saul 2011) and Australia (Goddard 2008).<1> While this is a result of the (...) percentage of women declining at each point through-out the standard career trajectory, recent large-scale studies in the United States (Paxton et al. 2012) and Australia (Goddard et al. 2008) have identified a key drop-off point as the transi-tion between taking introductory classes and majoring in philosophy. So why do dispropor-tionately few female students choose to major in philosophy? (shrink)

What distinguishes causation from grounding? One suggestion is that causation, but not grounding, occurs over time. Recently, however, counterexamples to this simple temporal criterion have been offered. In this paper, we situate the temporal criterion within a broader framework that focuses on two aspects: locational overlapping in space and time and the presence of intermediaries in space and time. We consider, and reject, the idea that the difference between grounding and causation is that grounding can occur without intermediaries. We go (...) on to use the fact that grounding and causation both involve intermediaries to develop a better temporal criterion for distinguishing causation from grounding. The criterion is this: when a cause and effect are spatially disjoint, there is always a chain of causal intermediaries between the cause and the effect that are extended in time. By contrast, when the grounds and the grounded are spatially disjoint, there is always a chain of grounding intermediaries, but the chain need not be extended in time, it can be purely spatial. The difference between grounding and causation, then, is that causation requires time for chaining in a way that grounding does not. (shrink)

Philosophical accounts denying that temporal passage is an objective feature of reality face an explanatory challenge with respect to why it appears to us as though time passes. Recently, two solutions have surfaced. Cognitive illusionism claims that people experience the passage of time due to their belief that time passes. Cognitive error theory claims that we do not experience the passage of time, but hold the belief that we do, which we have acquired through making an inference from the prior (...) belief that time passes. These approaches suppose that belief and passage experience are explanatorily connected, and they depend on the claims that people who experience the passage of time or at least believe that they do also believe that time passes. To test these claims, we probed the beliefs of populations of individuals with depression and schizotypy, thus conditions that are strongly associated with alterations in temporal phenomenology. Depression was assessed with the Beck Depression Inventory (BDI) and schizotypy with the short Oxford-Liverpool Inventory of Feelings and Experiences (O-LIFE). While cognitive illusionism and inferentialist cognitive error theory would predict a strong association between BDI and O-LIFE scores and beliefs about time passage, our study found no such association. The experience of passage does not seem to be explanatorily connected to beliefs about the passage of time. (shrink)

Why is there female under-representation among philosophy majors? We survey the hypotheses that have been proposed so far, grouping similar hypotheses together. We then propose a chronological taxonomy that distinguishes hypotheses according to the stage in undergraduates’ careers at which the hypotheses predict an increase in female under-representation. We then survey the empirical evidence for and against various hypotheses. We end by suggesting future avenues for research.

Surface presentism is the combination of a general relativistic physics with a presentist metaphysics. In this paper, we provide an argument against this combination based on black holes. The problem focuses on the notion of an event horizon. We argue that the present locations of event horizons are ontologically dependent on future black hole regions, and that this dependence is incompatible with presentism. We consider five responses to the problem available to the surface presentist, and argue that none succeed. Surface (...) presentism thus faces the prospect of refutation based on evidence that confirms the existence of black holes. (shrink)

The anglophone philosophy profession has a well-known problem with gender equity. A sig-nificant aspect of the problem is the fact that there are simply so many more male philoso-phers than female philosophers among students and faculty alike. The problem is at its stark-est at the faculty level, where only 22% - 24% of philosophers are female in the United States (Van Camp 2014), the United Kingdom (Beebee & Saul 2011) and Australia (Goddard 2008).<1> While this is a result of the (...) percentage of women declining at each point through-out the standard career trajectory, recent large-scale studies in the United States (Paxton et al. 2012) and Australia (Goddard et al. 2008) have identified a key drop-off point as the transi-tion between taking introductory classes and majoring in philosophy. So why do dispropor-tionately few female students choose to major in philosophy? (shrink)

In this paper we confront a challenge to truthmaker theory that is analogous to the objections raised by deflationists against substantive theories of truth. Several critics of truthmaker theory espouse a ‘deflationary’ attitude about truthmaking, though it has not been clearly presented as such. Our goal is to articulate and then object to the underlying rationale behind deflationary truthmaking. We begin by developing the analogy between deflationary truth and deflationary truthmaking, and then show how the latter can be found in (...) the work of Dodd, Hornsby, Schnieder, Williamson, and others. These philosophers believe that the ambitions of truthmaker theory are easily satisfied, without recourse to ambitious ontological investigation—hence the analogy with deflationary truth. We argue that the deflationists’ agenda fails: there is no coherent deflationary theory of truthmaking. Truthmaking, once deflated, fails to address the questions at the heart of truthmaking investigation. Truthmaking cannot be had on the cheap. (shrink)

Strong non-maximalism holds that some truths require no ontological ground of any sort. Strong non-maximalism allows one to accept that some propositions are true without being forced to endorse any corresponding ontological commitments. We show that there is a version of truthmaker theory available—anti-aboutness truthmaking—that enjoys the dialectical benefits of the strong non-maximalist’s position. According to anti-aboutness truthmaking, all truths require grounds, but a proposition need not be grounded in the very thing(s) that the proposition is about. We argue that (...) if strong non-maximalism can be defended, then so can anti-aboutness truthmaking on the very same basis; one can enjoy the benefits of strong non-maximalism without giving up on the idea that truth is always grounded in being. (shrink)

Many prominent critiques of philosophical methods proceed by suggesting that some method is unreliable, especially in comparison to some alternative method. In light of this, it may seem natural to conclude that these (comparatively) unreliable methods should be abandoned. Drawing upon work on the division of cognitive labour in science, we argue things are not so straightforward. Rather, whether an unreliable method should be abandoned depends heavily on the crucial question of how we should divide philosophers’ time and effort between (...) different methods, in order to maximise our prospects of achieving epistemic success. We show that, in a range of cases, even a (comparatively) unreliable method deserves to be allocated some of these resources. (shrink)

Skow ([2007]), and much more recently Callender ([2017]), argue that time can be distinguished from space due to the special role it plays in our laws of nature: our laws determine the behaviour of physical systems across time, but not across space. In this work we assess the claim that the laws of nature might provide the basis for distinguishing time from space. We find that there is an obvious reason to be sceptical of the argument Skow submits for distinguishing (...) time from space: Skow fails to pay sufficient attention to the relationship between the dynamical laws and the antecedent conditions required to establish a complete solution from the laws. Callender’s more sophisticated arguments in favour of distinguishing time from space by virtue of the laws of nature presents a much stronger basis to draw the distinction. By developing a radical reading of Callender’s view we propose a novel approach to differentiating time and space that we call temporal perspectivalism. This is the view according to which the difference between time and space is a function of the agentive perspective. (shrink)

Presentism faces a serious challenge from truthmaker theory. Standard solutions to the truthmaker objection against presentism proceed in one of two ways. Easy road presentists invoke new entities to satisfy the requirements of truthmaker theory. Hard road presentists, by contrast, flatly refuse to give in to truthmaker demands. Recently, a third way has been proposed. This response seeks to address the truthmaking problem by tensing our truthmaker principles. These views, though intuitive, are under-developed. In this paper, I get serious about (...) a fundamentally tensed approach to truthmaking by sketching out the underlying ontological picture needed to make sense of tensed truthmaker theory. (shrink)

It is a common criticism of presentism – the view according to which only the present exists – that it errs against truthmaker theory. Recent attempts to resolve the truthmaker objection against presentism proceed by restricting truthmaker maximalism (the view that all truths have truthmakers), maintaining that propositions concerning the past are not made true by anything, but are true nonetheless. Support for this view is typically garnered from the case for negative existential propositions, which some philosophers contend are exceptions (...) to truthmaker maximalism. In this article, we argue that a ‘no truthmakers’ approach to the truthmaker objection is critically flawed. (shrink)

In this paper, we explore locative grounding harmony, according to which the location of the grounds mirrors the location of the grounded. We proceed in three stages. First, we clarify the notion of locative harmony and describe different locative harmony principles. Second, we offer two arguments for the claim that grounding between physically located entities obeys principles of locative harmony. Third, we consider and respond to a range of cases that seem to show that grounding relations between physically located entities (...) do not obey such principles. We conclude that grounding between such entities obeys locative harmony. (shrink)

Current debate in the metaphysics of time ordinarily assumes that we should be realists about time. Recently, however, a number of physicists and philosophers of physics have proposed that time will play no role in a completed theory of quantum gravity. This paper defends fictionalism about temporal thought, on the supposition that our world is timeless. We argue that, in the face of timeless physical theories, realism about temporal thought is unsustainable: some kind of anti-realism must be adopted. We go (...) on to provide an argument against eliminativism about temporal thought. While it doesn't follow from this argument that fictionalism about temporal thought is true, we suggest that this nonetheless shows that fictionalism should be regarded as the preferred view. (shrink)

A great deal has been written about 'would' counterfactuals of causal dependence. Comparatively little has been said regarding 'would' counterfactuals of ontological dependence. The standard Lewis-Stalnaker semantics is inadequate for handling such counterfactuals. That's because some of these counterfactuals are counterpossibles, and the standard Lewis-Stalnaker semantics trivializes for counterpossibles. Fortunately, there is a straightforward extension of the Lewis-Stalnaker semantics available that handles counterpossibles: simply take Lewis's closeness relation that orders possible worlds and unleash it across impossible worlds. To apply the (...) extended semantics, an account of the closeness relation for counterpossibles is needed. In this paper I offer a strategy for evaluating 'would' counterfactuals of ontological dependence that understands closeness between worlds in terms of the metaphysical concept of grounding. (shrink)

Despite their centrality to medicine, drugs are not easily defined. We introduce two desiderata for a basic definition of medical drugs. It should: (a) capture everything considered to be a drug in medical contexts and (b) rule out anything that is not considered to be a drug. After canvassing a range of options, we find that no single definition of drugs can satisfy both desiderata. We conclude with three responses to our exploration of the drug concept: maintain a monistic concept, (...) or choose one of two pluralistic outcomes. Notably, the distinction between drugs and other substances is placed under pressure by the most plausible of the options available. (shrink)

In this chapter we argue that our concept of time is a functional concept. We argue that our concept of time is such that time is whatever it is that plays the time role, and we spell out what we take the time role to consist in. We evaluate this proposal against a number of other analyses of our concept of time, and argue that it better explains various features of our dispositions as speakers and our practices as agents.

Why does female under- representation emerge during undergraduate education? At the University of Sydney, we surveyed students before and after their first philosophy course. We failed to find any evidence that this course disproportionately discouraged female students from continuing in philosophy relative to male students. Instead, we found evidence of an interaction effect between gender and existing attitudes about philosophy coming into tertiary education that appears at least partially responsible for this poor retention. At the first lecture, disproportionately few female (...) students intended to major. Further, at the first lecture, female students were less interested in philosophy, were less self-confident about philosophy, and were less able to imagine themselves as philosophers. Similarly, female students predicted they would feel more uncomfortable in philosophy classes than male students did. Further study with a control is warranted to determine whether this interaction effect is peculiar to philosophy, or whether it is indicative of a more general gendered trend amongst first year undergraduate students. (shrink)

The Triviality Argument against presentism maintains that we should reject presentism because there is no way to define the view that is not either trivially true or obviously false. We suggest that this style of argument over-emphasises purely linguistic means of representing a philosophical thesis. We argue that there is no reason to suppose that all philosophical theses must be linguistically representable, and thus that the failure to linguistically represent presentism is no big deal. It certainly shouldn’t lead us to (...) reject the view. We offer a more general moral for philosophy, and that is to look beyond purely linguistic methods of representing philosophical views and embrace a wider range of representational media. (shrink)

I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...) of noneism-the view according to which non-existent entities possess properties and stand in relations-is true. The argument thus forces a choice between nominalism without noneism, intra-mathematical explanation and a backing conception of explanation. You can have any two, but not all three. (shrink)

There is an old meta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in (...) much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that pure mathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well. (shrink)

Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis would (...) not have liked. The explanation is an obvious one but controversial, so it is defended against all the objections that can be mustered. (shrink)

We defend two claims: (1) if one is attracted to a strong non-maximalist view about truthmaking, then it is natural to construe this as the view that there exist fundamental truths; (2) despite considerable aversion to fundamental truths, there is as yet no viable independent argument against them. That is, there is no argument against the existence of fundamental truths that is independent of any more specific arguments against the ontology accepted by the strong non-maximalist. Thus there is no argument (...) that the strong non-maximalist herself will find dialectically motivating. (shrink)

According to dialetheism, there are some true contradictions. According to the A-theory, the passage of time is a mind-independent feature of reality. On some A-theories, the passage of time involves the movement of the present. I show that by appealing to dialetheism one can explain why the present moves. I then argue that A-theorists should adopt this explanation. To do this, I defend two claims. First, that the dialetheic explanation is an improvement on the only other explanation available for why (...) the present moves and, second, that adopting the explanation is better than leaving the motion of the present unexplained. Assuming that A- theorists should adopt the best available version of their view, it follows that they should adopt a dialetheic explanation of why time passes. (shrink)

Recent attempts to resolve the truthmaker objection to presentism employ a fundamentally tensed account of the relationship between truth and being. On this view, the truth of a proposition concerning the past supervenes on how things are, in the present, along with how things were, in the past. This tensed approach to truthmaking arises in response to pressure placed on presentists to abandon the standard response to the truthmaker objection, whereby one invokes presently existing entities as the supervenience base for (...) the truth of past-directed propositions. In this paper, I argue that a fundamentally tensed approach to truthmaking is implausible because it requires the existence of cross-temporal supervenience relations, which are anathema to presentism. (shrink)

A number of approaches to quantum gravity (QG) seem to imply that spacetime does not exist. Philosophers are quick to point out, however, that the loss of spacetime should not be regarded as total. Rather, we should interpret these approaches as ones that threaten the fundamentality but not the existence of spacetime. In this paper, I argue for two claims. First, I argue that spacetime realism is not forced by QG; spacetime eliminativism remains an option. Second, I argue that eliminativism (...) provides a useful framework for developing two existing approaches to the metaphysics of QG, involving functionalism and mereology respectively. (shrink)

The idea that time does not exist is, for many, unthinkable: time must exist. Almost every experience we have tells us so. There has been plenty of debate around what time is like, but not whether it exists. The goal of this book is to make the absence of time thinkable. Time might not exist. Beginning with an empirically flavoured examination of the 'folk' concept of time, the book explores the implications this has for our understanding of agency, and the (...) extent to which our best physics and best metaphysics are compatible with a timeless conception of reality. (shrink)

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

Recent discussion of the problem of negative existentials for truthmaker theory suggests a modest solution to the problem: fully general negative truths like do not require truthmakers, whereas partially general negative truths like do. This modest solution provides a third alternative to the two standard solutions to the problem of negative existentials: the endorsement of truthmaker gaps, and the appeal to contentious ontological posits. We argue that this modest, middle-ground position is inconsistent with certain plausible general principles for truthmaking. The (...) only stable positions are to treat all negative truths as requiring truthmakers, or admit that no negative truths require truthmakers. Along the way, we explore some previously unaddressed questions for nonmaximalist truthmaker theory. (shrink)

Mereological harmony is the idea that the mereological structure of objects mirrors the mereological structure of locations. Grounding harmony is the idea that there is a similar mirroring between the grounding structure of objects and locations. Our goal in this paper is exploratory: we introduce and then explore two notions of grounding harmony: locative and structural. We outline potential locative and structural harmony principles for grounding, and show which of these principles may entail, or be entailed by, principles of mereological (...) harmony. We then present a case study in grounding harmony, by applying it to Schaffer’s :31, 2010a) specific version of priority monism. We show that, given a strong form of grounding harmony, Schaffer-style monism is inconsistent, but that this inconsistency can be resolved by offering bespoke notions of grounding harmony. We use Schaffer’s priority monism to demonstrate a broader tension within certain packages of metaphysical views, including versions of priority pluralism. We close by briefly considering the case against structural grounding harmony. (shrink)

According to conventionalist accounts of personal identity, persons are constituted in part by practices and attitudes of certain sorts of care. In this paper, we concentrate on the most well-developed and defended version of conventionalism currently on offer (namely, that proposed by David Braddon-Mitchell, Caroline West, and Kristie Miller) and discuss how the conventionalist appears forced either (1) to accept arbitrariness concerning from which perspective to judge one's survival or (2) to maintain egalitarianism at the cost of making “transfiguring” decisions (...) such as Pascal's Wager rationally intractable. We consider three ways the egalitarian conventionalist could make these choices tractable and show that each one comes at significant cost to the view. We end the paper by considering whether accepting arbitrariness would be a better move for the conventionalist and conclude that, even here, she runs the risk of transfiguring choices being rationally intractable. (shrink)

It has seemed, to many, that there is an important connection between the ways in which some theoretical posits explain our observations, and our reasons for being ontologically committed to those posits. One way to spell out this connection is in terms of what has become known as the explanatory criterion of ontological commitment. This is, roughly, the view that we ought to posit only those entities that are indispensable to our best explanations. Our primary aim is to argue that (...) the moral nonnaturalist places herself in an invidious position if she simply accepts that the nonnatural moral facts that she posits are not explanatory. Instead, we offer the nonnaturalist an alternative strategy for dealing with moral explanations. The strategy is to retain the explanatory criterion of ontological commitment and maintain that moral properties are, in fact, explanatory. The explanations they provide are not causal explanations; instead, moral properties make a non-causal difference to the physical facts. (shrink)

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 (...) that it is possible for there to be such cases, and provide some toy examples to demonstrate this. I then identify a potential source of scientific case studies as a guide for future work. (shrink)