Sam Baron

This paper draws together two strands in the debate over the existence of mathematical objects. The first strand concerns the notion of extra-mathematical explanation: the explanation of physical facts, in part, by facts about mathematical objects. The second strand concerns the access problem for platonism: the problem of how to account for knowledge of mathematical objects. I argue for the following conditional: if there are extra-mathematical explanations, then the core thesis of the access problem is false. This has implications for nominalists and platonists alike. Platonists can make a case for epistemic access to mathematical objects by providing evidence in favour of the existence of extra-mathematical explanations. Nominalists, by contrast, can use the access problem to cast doubt on the idea that mathematical objects play a substantive role in scientific explanation.

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.

Presentism faces a familiar objection from truthmaker theory. How can propositions about the past be made true if past entities do not exist? In answering this question, there are, broadly, two roads open to the presentist. The easy road to presentism proceeds by capitulating to the demands imposed by truthmaker theory and finding truthmakers for claims about the past. This road typically involves the invocation of controversial metaphysical posits that must then be defended. The hard road to presentism resists the demands of truthmaker theory by denying that all truths must be truth-made. The road is hard as it requires providing a principled restriction on the scope of truthmaker theory. In this paper, I argue that the hard road collapses back into the easy road; there is no hard road to presentism.

Enhanced indispensability arguments seek to establish realism about mathematics based on the explanatory role that mathematics plays in science. Idealizations pose a problem for such arguments. Idealizations, in a similar way to mathematics, boost the explanatory credentials of our best scientific theories. And yet, idealizations are not the sorts of things that are supposed to attract a realist attitude. I argue that the explanatory symmetry between idealizations and mathematics can potentially be broken as follows: although idealizations contribute to the explanatory power of our best theories, they do not carry the explanatory load. It is at least open however that mathematics is load-carrying. To give this idea substance, I offer an analysis of what it is to carry the explanatory load in terms of difference-making and counterfactuals

This paper motivates and develops a new theory of time: priority presentism. Priority presentism is the view according to which (i) only present entities exist fundamentally and (ii) past and future entities exist, but they are grounded in the present. The articulation of priority presentism is an exercise in applied grounding: it draws on concepts from the recent literature on ontological dependence and applies those concepts in a new way, to the philosophy of time. The result, as I will argue, is an attractive position that can do much of the same work in satisfying our intuitions about time as presentism, but without the ontological cost.

This paper offers a new way to evaluate counterfactual conditionals on the supposition that actually, there is no time. We then parlay this method of evaluation into a way of evaluating causal claims. Our primary aim is to preserve, at a minimum, the assertibility of certain counterfactual and causal claims once time has been excised from reality. This is an important first step in a more general reconstruction project that has two important components. First, recovering our ordinary language claims involving notions such as persistence, change and agency and, second, recovering enough observational evidence so that any timeless metaphysics is not empirically self-refuting. However, the project of investigating causation in a timeless setting has a greater relevance than its application to timeless physical theory alone. For, as we show, it can be used to model the assertibility conditions of causal claims more generally

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?

Priority monism (hereafter, ‘monism’) is the view that there exists one fundamental entity—the world—and that all other objects that exist (a set of objects typically taken to include tables, chairs, and the whole menagerie of everyday items) are merely derivative. Jonathan Schaffer has defended monism in its current guise, across a range of papers. Each paper looks to add something to the monistic picture of the world. In this paper we argue that monism—as Schaffer describes it—is false. To do so we develop an ‘island universe’ argument against Schaffer's monistic theory.

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

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

One of the major difficulties facing presentism is the problem of causation. In this paper, I propose a new solution to that problem, one that is compatible with intrinsic, fundamental causal relations. Accommodating relations of this kind is important because (i) according to David Lewis (2004), such relations are needed to account for causation in our world and worlds relevantly similar to our own, (ii) there is no other strategy currently available that successfully reconciles presentism with relations of this kind and (iii) resolving the problem of causation by accommodating intrinsic, fundamental causal relations provides the presentist with a far more general solution to the problem of causation than those currently on offer.

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

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

In this article I consider what it would take to combine a certain kind of mathematical Platonism with serious presentism. I argue that a Platonist moved to accept the existence of mathematical objects on the basis of an indispensability argument faces a significant challenge if she wishes to accept presentism. This is because, on the one hand, the indispensability argument can be reformulated as a new argument for the existence of past entities and, on the other hand, if one accepts the indispensability argument for mathematical objects then it is hard to resist the analogous argument for the existence of the past

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

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of the indispensability argument.

In this paper I consider the aboutness objection against standard truth-preserving presentism (STP). According to STP: (1) past-directed propositions (propositions that seem to be about the past) like , are sometimes true (2) truth supervenes on being and (3) the truth of past-directed propositions does not supervene on how things were, in the past. According to the aboutness objection (3) is implausible, given (1) and (2): for any proposition, P, P ought to be true in virtue of what P is about, and so it is upon the past that the truth of past-directed propositions ought to supervene. Although an objection along these lines has been offered previously, I press the objection in two ways. First, by providing needed support for the view that propositions ought to be true in virtue of what they are about and, second, by arguing that the two responses available to the proponent of STP fail to be compelling

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

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?

Is time necessary for causation? We argue that, given a counterfactual theory of causation, it is not. We defend this claim by considering cases of counterfactual dependence in quantum mechanics. These cases involve laws of nature that govern entanglement. These laws make possible the evaluation of causal counterfactuals between space-like separated entangled particles. There is, for the proponent of a counterfactual theory of causation, a possible world in which causation but not time exists that can be reached by ‘stripping out’ time from the actual world, leaving quantum mechanical laws intact