Sam Baron

The counterfactual approach to explainable AI (XAI) seeks to provide understanding of AI systems through the provision of counterfactual explanations. In a recent systematic review, Chou et al. (Inform Fus 81:59–83, 2022) argue that the counterfactual approach does not clearly provide causal understanding. They diagnose the problem in terms of the underlying framework within which the counterfactual approach has been developed. To date, the counterfactual approach has not been developed in concert with the approach for specifying causes developed by Pearl (Causality: Models, reasoning, and inference. Cambridge University Press, 2000) and Woodward (Making things happen: A theory of causal explanation. Oxford University Press, 2003). In this paper, I build on Chou et al.’s work by applying the Pearl-Woodward approach. I argue that the standard counterfactual approach to XAI is capable of delivering causal understanding, but that there are limitations on its capacity to do so. I suggest a way to overcome these limitations.

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.

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.

I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where consistency may be required. Second, the argument has implications for the debate over scientific realism. Many scientific theories appear to be inconsistent. The best argument for scientific realism, however, appeals to IBE. My argument thus shows that a certain kind of realist faces a threat from inconsistent theories. Third, the argument is important for dialetheism. Dialetheists maintain that some contradictions are true. Many of the arguments in favour of dialetheism appeal to explanatory considerations. What I say here provides support for defending dialethism using an IBE-based methodology.

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.

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.

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.

The existence and fundamentality of spacetime has been questioned in quantum gravity where spacetime is frequently described as emerging from a more fundamental non-spatiotemporal ontology. This is supposed to lead to various philosophical issues such as the problem of empirical coherence. Yet those issues assume beforehand that we actually understand and agree on the nature of spacetime. Reviewing popular conceptions of spacetime, we find that there is substantial disagreement on this matter, and little hope of resolving it. However, we argue that this should not trouble us as these issues, which seem to suggest the need for an account of spacetime in quantum gravity, can be addressed without one.

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.

Recent work on quantum gravity suggests that neither spacetime nor spatiotemporally located entites exist at a fundamental level. The loss of both brings with it the threat of empirical incoherence. A theory is empirically incoherent when the truth of that theory undermines the empirical justification for believing it. If neither spacetime nor spatiotemporally located entities exist as a part of a fundamental theory of QG, then such a theory seems to imply that there are no observables and so no way that the theory can be confirmed. The threat of empirical incoherence can be addressed by treating spacetime and spatiotemporally located entities as emergent. The question then arises as to what the metaphysical nature of this emergence might be. In this paper, I explore a functionalist approach to this kind of emergence in the context of loop quantum gravity. I begin by rehearsing the spacetime functionalist’s account of emergence, clarifying the view along the way. I proceed to sketch out a functionalist treatment of spatiotemporally located entities and combine the two forms of functionalism into a double functionalism, according to which both spacetime and matter have the same functional realisers.

Several approaches to quantum gravity signal the loss of spacetime at some level. According to spacetime functionalism, spacetime is functionally realised by a more fundamental structure. According to one version of spacetime functionalism, the spacetime role is specified by Ramsifying general relativity. In some approaches to QG, however, there does not appear to be anything that exactly realises the functional role defined by a Ramsey sentence for GR. The spacetime role is approximately realised. It is open to the spacetime functionalist to adopt a ‘near enough is good enough’ attitude to functional realisation, and maintain that spacetime is functionally realised nonetheless. In this paper I present a challenge for such an ‘approximate’ spacetime functionalism. The challenge, in brief, is to provide an account of how ‘close’ is close enough for approximate realisation to occur. I canvass a range of options for spelling out a similarity relation of the relevant kind, and argue that none are successful. In light of the challenge, I recommend giving up on the functional realisation of spacetime. I argue, however, that even if spacetime as a whole is not functionally realised, some of the functions of spacetime may still be performed.

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.

A number of philosophers uphold a metaphysical symmetry between time and hypertime, in this sense: in so far as hypertime exists, the nature of hypertime should agree with the nature of time. Others allow that we can mix and match the metaphysics of time and hypertime. Thus, it may be that time really passes, but hypertime does not or vice versa. In this paper, we provide a preliminary defense of the mix and match approach. We outline a number of arguments for the claim that time and hypertime must share a common nature and find them all wanting.

Consider the following pair of theses: all fundamental physical objects are spatiotemporal and all non-fundamental physical objects are ultimately composed of fundamental objects. Work on the physics of quantum gravity suggests that spacetime is a non-fundamental, emergent phenomenon and thus that thesis is false. The fundamentals are non-spatiotemporal in nature. This paper will argue against on the grounds that non-fundamental spatiotemporal objects cannot be composed of fundamental non-spatiotemporal objects. So, assuming that spacetime is emergent, new metaphysical resources are needed to explain the relationship between the fundamental objects posited by quantum gravity and spacetime.

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.

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.

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.

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.

We argue that explanations appealing to logical impossibilities are genuine explanations. Our defense is based on a certain picture of impossibility. Namely, that there are impossibilities and that the impossibilities have structure. Assuming this broad picture of impossibility we defend the genuineness of explanations that appeal to logical impossibilities against three objections. First, that such explanations are at odds with the perceived conceptual connection between explanation and counterfactual dependence. Second, that there are no genuinely contrastive why-questions that involve logical impossibilities and, third, that explanations appealing to logical impossibilities rule nothing out.

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

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.

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.

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.

In this articleIconsider what it would take to combine a certain kind of mathematicalPlatonism with serious presentism.Iargue 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.

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.

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.

Work in quantum gravity suggests that spacetime is not fundamental. Rather, spacetime emerges from an underlying, non-spatiotemporal reality. After clarifying the type of emergence at issue, I argue that standard conceptions of emergence available in metaphysics won’t work for the emergence of spacetime. I go on to consider spacetime functionalism as a way to make sense of spacetime emergence. I argue that a functionalist approach to spacetime modelled on mental state functionalism is not a viable alternative to the standard conception of emergence in metaphysics. I go on to consider an alternative: ‘partial’ functionalism, whereby certain aspects of spacetime are functionalised, rather than spacetime as a whole.