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.

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.

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.

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.

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.

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). 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.

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.

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). 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?

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.

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.