Sam Baron

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.

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.

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.

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.

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.

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.

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.

There has been a recent surge of interest in mathematical explanations of empirical facts. A number of putative cases of such explanation have been identified, and used to provide support for an explanatory version of the indispensability argument for mathematical platonism. In this paper, I consider the prospects for developing a metaphysically light-weight theory of mathematical explanations by appealing to the resources currently available in existing work on applied mathematics and scientific explanation. I argue that new resources must be marshalled to handle the mathematical case, and sketch out one option for doing so.

The present paper advances an analogy between cases of extra-mathematical explanation and cases of what might be termed ‘extra-logical explanation’: the explanation of a physical fact by a logical fact. A particular case of extra-logical explanation is identified that arises in the philosophical literature on time travel. This instance of extra-logical explanation is subsequently shown to be of a piece with cases of extra-mathematical explanation. Using this analogy, we argue extra-mathematical explanation is part of a broader class of non-causal explanation. This has important implications for extra-mathematical explanation, for time travel and for theories of explanation more generally.

Truthmaker theory is commonly thought to pose a challenge for presentism. Presentism seems to lack the ontological and ideological resources required to adequately underwrite the truth of propositions concerning the past. That is because if presentism is true, then the past does not exist. According to the standard response to this challenge, the truth of propositions concerning the past supervenes on surrogate entities that ‘stand proxy’ for past things. I argue that in order for the standard response to the truthmaker challenge to succeed these surrogate entities must stand in necessary connections to the past. I go on to argue that because the standard response is already committed to denying the existence of cross-temporal modal connections of this kind, by its own lights that response is in error.1.