One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...) Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics. (shrink)

Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...) is ontic, the conventionalist account seems to avoid a convincing objection to other ontic accounts (Kuorikoski 2021). (shrink)

Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens under no or all conditions. In this paper, we provide a self-contained introduction to the integrated information theory of consciousness (...) (IIT). We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT-restriction to existing proposals and argue that the IIT-restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system. (shrink)

I argue that it is metaphysically necessary that: (i) every fundamental entity is conscious, and (ii) every fundamental property is a phenomenal property.

Several philosophers have suggested that some scientific explanations work not by virtue of describing aspects of the world’s causal history and relations, but rather by citing mathematical facts. This paper investigates what mathematical facts could be in order for them to figure in such “distinctively mathematical” scientific explanations. For “distinctively mathematical explanations” to be explanations by constraint, mathematical language cannot operate in science as representationalism or platonism describes. It can operate as Aristotelian realism describes. That is because Aristotelian realism enables (...) mathematics to apply to the physical world without a morphism’s mediation. (shrink)

Most physicalists believe that physicalism is a thesis that denies the existence of fundamental mentality either as a substance or as a property. Therefore, since most physicalists also endorse a posteriori physicalism, according to them, if the future physical theory posits fundamental mentality as a fundamental physical concept, then physicalism will be falsified. In contrast, there are those who believe that the core idea of physicalism is an ontological deference to science (especially physics); the idea that is usually called scientism (...) and is closely related to methodological naturalism. According to them, if physicists posit fundamental mentality as an integral part of the future fundamental physical theory, physicalism will not be falsified, and physicalists may (or should) accept fundamental mentality as a genuine physical concept. In this paper, I argue that there is some historical evidence in support of the latter understanding of physicalism. First, I give some historical evidence that seems to suggest that the historical origin of physicalism is the failure of those explanations – or pseudo-explanations – that have appealed to supernatural non-physical entities. Second, I show that in some of the initial reflections on materialism – the predecessor of physicalism – in the first half of the twentieth century, philosophers understood materialism in terms of the very historical origin. (shrink)

Extra-mathematical explanations explain natural phenomena primarily by appeal to mathematical facts. Philosophers disagree about whether there are extra-mathematical explanations, the correct account of them if they exist, and their implications (e.g., for the philosophy of scientific explanation and for the metaphysics of mathematics) (Baker 2005, 2009; Bangu 2008; Colyvan 1998; Craver and Povich 2017; Lange 2013, 2016, 2018; Mancosu 2008; Povich 2019, 2020; Steiner 1978). In this discussion note, I present three desiderata for any account of extra-mathematical explanation and argue (...) that Baron’s (2020) U-Counterfactual Theory fails to meet each of them. I conclude with some reasons for pessimism that a successful account will be forthcoming. (shrink)

An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow (...) Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory. (shrink)

A central argument for non-reductive accounts of group agency is that complex social entities are capable of exerting causal influence independently of and superseding the causal efficacy of the individuals constituting them. A prominent counter is that non-reductionists run into an insuperable dilemma between identity and redundancy – with identity undermining independent higher-level efficacy and redundancy leading to overdetermination or exclusion. This paper argues that critics of non-reductionism can manage with a simpler and more persuasive reductio strategy called mapping: allow (...) that group agents are causally efficacious in their own right and chart how their causal efficacy is carried out; how it relates to the causal efficacy of individual determiners; how it connects to the causal relevance of background structural factors. The focus exclusively on whether groups are or are not causally efficacious black-boxes implementation, while close attention to how causation is wired increases the visibility of individualist arguments and countenances structure-oriented explanations. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...) can help us make progress on the problem of induction. (shrink)

Establishing Dispositionalism as a viable theory of modality requires the successful fulfilment of two tasks: showing that all modal truths can be derived from truths about actual powers, and offering a suitable metaphysics of powers. These two tasks are intertwined: difficulties in one can affect the chances of success in the other. In this paper, I generalise an objection to Dispositionalism by Jessica Leech and argue that the theory in its present form is ill-suited to account for de re truths (...) about merely possible entities. I argue that such difficulty is rooted in a problem in the metaphysics of powers. In particular, I contend that the well-known tension between two key principle of powers ontology, namely Directedness and Independence has received an unsatisfactory solution so far, and that it is this unsatisfactory solution concerning the status of “unmanifested manifestations” that makes it hard for Dispositionalism to account for mere possibilia. I develop a novel account of the status of unmanifested manifestations and an overall metaphysics of powers which allows to better respond to Leech's objection and handle mere possibilia. The central idea of the proposal is that unmanifested manifestations are akin to mere logical existents, and are best characterised as non-essentially non-located entities. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us to (...) rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

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. (shrink)

Istnieje spór w obrębie filozofii sięgający już starożytności i polemiki Platona z Sofistami, dotyczący ugruntowania metafizyki jako dziedziny autonomicznej, która byłaby zdolna do badania swoistych elementów rzeczywistości, przysługujących tylko i wyłącznie metafizyce. We wstępnych rozważaniach przedstawiamy sposób, w jaki ten spór można rozumieć oraz jak można go rozwiązać. Tezą metafilozoficzną naszych analiz będzie stwierdzenie, że w celu ugruntowania metafizyki musimy wskazać na swoiste doświadczenie, które mogłoby zapewnić bezpośredni dostęp poznawczy do abstrakcyjnego przedmiotu metafizyki. W niniejszych badaniach, rolę tego doświadczenia będzie (...) pełnić intuicja, którą utożsamiamy z poznaniem apriorycznym – ujmowanym jednak nie jako poznanie pojęciowe bądź dedukcyjne – lecz jako poznanie naoczne, które (używając języka fenomenologii) źródłowo (materialnie) prezentuje nam swoistą sferę przedmiotową. By lepiej zrozumieć zjawisko intuitywnego poznania do którego bardzo często filozofowie implicite się odnosili (rzadziej zaś wprost) zrekonstruujemy stanowisko E. Chudnoffa. W trakcie rekonstrukcji skupimy się na najistotniejszych cechach poznania intuitywnego, które będą kluczem zarówno do zrozumienia wielości tradycyjnych już odniesień i niejawnych odwoływań do intuicji, jak i sposobem poprzez który możliwe stanie się ustalenie warunków możliwości ugruntowania metafizyki jako dziedziny autonomicznego badania rzeczywistości. (shrink)

The objective of this thesis is to present a naturalised metaphysics of information, or to naturalise information, by way of deploying a scientific metaphysics according to which contingency is privileged and a-priori conceptual analysis is excluded (or at least greatly diminished) in favour of contingent and defeasible metaphysics. The ontology of information is established according to the premises and mandate of the scientific metaphysics by inference to the best explanation, and in accordance with the idea that the primacy of physics (...) constraint accommodates defeasibility of theorising in physics. This metametaphysical approach is used to establish a field ontology as a basis for an informational structural realism. This is in turn, in combination with information theory and specifically mathematical and algorithmic theories of information, becomes the foundation of what will be called a source ontology, according to which the world is the totality of information sources. Information sources are to be understood as causally induced configurations of structure that are, or else reduce to and/or supervene upon, bounded (including distributed and non-contiguous) regions of the heterogeneous quantum field (all quantum fields combined) and fluctuating vacuum, all in accordance with the above-mentioned quantum field-ontic informational structural realism (FOSIR.) Arguments are presented for realism, physicalism, and reductionism about information on the basis of the stated contingent scientific metaphysics. In terms of philosophical argumentation, realism about information is argued for primarily by way of an indispensability argument that defers to the practice of scientists and regards concepts of information as just as indispensable in their theories as contingent representations of structure. Physicalism and reductionism about information are adduced by way of the identity thesis that identifies the substance of the structure of ontic structural realism as identical to selections of structure existing in re to combined heterogeneous quantum fields, and to the total heterogeneous quantum field comprised of all such fields. Adjunctly, an informational statement of physicalism is arrived at, and a theory of semantic information is proposed, according to which information is intrinsically semantic and alethically neutral. (shrink)

The paper presents and discusses phenomenological facts about perceptual spaces and percepts, but ends with a few thoughts about possible causal explanations of such spaces. The overarching double-sided hypothesis claims that - from a phenomenological point of view - each individual animal has at each consciously perceived moment of time a sense-modality-neutral perceptual space, and that these perceptual spaces are so-called container spaces. This means, to be concrete, that blind persons, deaf persons, and all perceptually non-handicapped persons have the same (...) kind of phenomenological perceptual space, a sense-modality-neutral container space. The causal reflections bring in James J. Gibson’s work on such matters. (shrink)

Explanation is asymmetric: if A explains B, then B does not explain A. Tradition- ally, the asymmetry of explanation was thought to favor causal accounts of explanation over their rivals, such as those that take explanations to be inferences. In this paper, we develop a new inferential approach to explanation that outperforms causal approaches in accounting for the asymmetry of explanation.

The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not (...) decisive against the eleatic and sketch a way to capture the important intuitions behind both views. (shrink)

The compact and, with \ M\, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius A* in the middle of the central stellar cluster. Simultaneous near-infrared and X-ray observations of SgrA* have revealed insights into (...) the emission mechanisms responsible for the powerful near-infrared and X-ray flares from within a few tens to one hundred Schwarzschild radii of such a putative SMBH. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target for very long baseline interferometry observations currently being prepared by the event horizon telescope. These observations in combination with the infrared interferometry experiment GRAVITY at the very large telescope interferometer and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. The large body of evidence continues to discriminate the identification of SgrA* as a SMBH from alternative possibilities. It is, however, unclear when the ever mounting evidence for SgrA* being associated with a SMBH will suffice as a convincing proof. Additional compelling evidence may come from future gravitational wave observatories. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about “realism and underdetermination”, as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts. (shrink)

I consider whether evolutionary explanations can debunk our moral beliefs. Most contemporary discussion in this area is centred on the question of whether debunking implications follow from our ability to explain elements of human morality in terms of natural selection, given that there has been no selection for true moral beliefs. By considering the most prominent arguments in the literature today, I offer reasons to think that debunking arguments of this kind fail. However, I argue that a successful evolutionary debunking (...) argument can be constructed by appeal to the suggestion that our moral outlook reflects arbitrary contingencies of our phylogeny, much as the horizontal orientation of the whale’s tail reflects its descent from terrestrial quadrupeds. An introductory chapter unpacks the question of whether evolutionary explanations can debunk our moral beliefs, offers a brief historical guide to the philosophical discussion surrounding it, and explains what I mean to contribute to this discussion. Thereafter follow six chapters and a conclusion. The six chapters are divided into three pairs. The first two chapters consider what contemporary scientific evidence can tell us about the evolutionary origins of morality and, in particular, to what extent the evidence speaks in favour of the claims on which debunking arguments rely. The next two chapters offer a critique of popular debunking arguments that are centred on the irrelevance of moral facts in natural selection explanations. The final chapters develop a novel argument for the claim that evolutionary explanations can undermine our moral beliefs insofar as they show that our moral outlook reflects arbitrary contingencies of our phylogeny. A conclusion summarizes my argument and sets out the key questions that arise in its wake. (shrink)

Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...) scientific theories range over. In this paper, I argue that all three arguments fail and they fail for much the same reason; would-be nominalists are thus left facing Field's hard road. (shrink)

Traditionally one main emphasis of the quantum mechanical measurement theory is on the question how the pure state of the compound system 'measured system + measuring apparatus' is transformed into the 'mixture' of all possible results of that measurement, weighted with their probability: the so-called “disappearance of the interference terms”. It is argued in this note that in reality there is no such transformation, so that there is no need to account for such a transformation theoretically. _German_ Gewöhnlich liegt ein (...) Hauptgewicht der quantenmechanischen Messtheorie auf der Frage des Übergangs vom,reinen Fall' des Gesamtsystems,gemessenes System + Messgerät' in das,Gemenge' aus allen möglichen Messergebnissen, gewichtet mit ihren Wahrscheinlichkeiten: Das sog.,,Verschwinden der Interferenzterme“. In dieser Notiz wird die Meinung vertreten, dass es einen solchen Übergang faktisch nicht gibt, so dass es nicht notwendig ist, eine theoretische Erklärung für den Übergang zu geben. (shrink)

The essay revisits the puzzle of the ‘passage’ of time in relation to EPR-type measurements and asks what philosophical consequences can be drawn from them. Some argue that the lack of invariance of temporal order in the measurement of a space-like related EPR pair, under relativistic motion, casts serious doubts on the ‘reality’ of the lapse of time. Others argue thatcertain features of quantum mechanics establisha tensed theory of time – understood here as Possibilism or the growing block universe. The (...) paper analyzes the employment of frame-invariant entropic clocks in a relativistic setting and argues that tenselessness does not imply timelessness. But this conclusion does not support a tensed theory of time, which requires a preferred foliation. It is argued that the only reliable inference from the EPR example and the use of entropic clocks is an inference not just to a Leibnizian order of the succession of events but a frame-invariant order according to some selected clocks. (shrink)

Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the (...) stronger mathematics, and this poses a challenge for the nominalist position. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

In this dissertation, I argue that we should be pluralists about truth and in turn, eliminativists about the property Truth. Traditional deflationists were right to suspect that there is no such property as Truth. Yet there is a plurality of pluralities of properties which enjoy defining features that Truth would have, were it to exist. So although, in this sense, truth is plural, Truth is non-existent. The resulting account of truth is indebted to deflationism as the provenance of the suspicion (...) that Truth doesn't exist. But it would be hasty to simply classify the account as deflationary. Each of the 'truth-like' properties that it recognizes is highly substantive--that is, complex and explanatorily potent. So we should deflate Truth by recognizing that it doesn't exist, but we should also recognize that one of the most vital tasks in truth theory is to discover the essences of the many truth-like properties. My aim here is to do precisely this. (shrink)

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

Mereological realism holds that the world has a mereological structure – i.e. a distribution of mereological properties and relations. In this article, I defend Eleaticism about properties, according to which there are no causally inert non-logical properties. I then present an Eleatic argument for mereological anti-realism, which denies the existence of both mereological composites and mereological simples. After defending Eleaticism and mereological anti-realism, I argue that mereological anti-realism is preferable to mereological nihilism. I then conclude by examining the thesis that (...) composition is identity and noting its consequences for the question of mereological structure. (shrink)

Sydney Shoemaker’s causal theory of properties is an important starting place for some contemporary metaphysical perspectives concerning the nature of properties. In this paper, I discuss the causal and intrinsic criteria that Shoemaker stipulates for the identity of genuine properties and relations, and address George Molnar’s criticism that holding both criteria presents an unbridgeable hypothesis in the causal theory of properties. The causal criterion requires that properties and relations contribute to the causal powers of objects if they are to be (...) deemed genuine rather than ‘mere-Cambridge’. The intrinsic criterion requires that all genuine properties and relations be intrinsic. Molnar’s S-property argument says that these criteria conflict if one considers extrinsic spatiotemporal properties and relations to contribute causally. In this paper, I argue that a solution to the contradiction that Molnar identifies involves a denial of discreteness between objects, leading to a power holist perspective and a resulting deflationary account of intrinsicality. (shrink)

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. (shrink)

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

This paper responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims—claims of the form such-tmd-so exist—requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails.

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.

A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can (...) do to make an explanation mathematical ; realists think something can be done, but they are not clear about what that something is. I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism. I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist. (shrink)

Recently Colin Cheyne and Charles Pigden have challenged supporters of mathematical indispensability arguments to give an account of how causally inert mathematical entities could be indispensable to science. Failing to meet this challenge, claim Cheyne and Pigden, would place Platonism in a no win situation: either there is no good reason to believe in mathematical entities or mathematical entities are not causally inert. The present paper argues that Platonism is well equipped to meet this challenge.

Thomas Scanlon and Derek Parfit have recently defended a meta-ethical view that is supposed to satisfy realistic intuitions about morality, without the metaphysical implications that many find hard to accept in other realist views. Both philosophers argue that truths in the normative domain do not have ontological implications, while truths in the scientific domain presuppose a metaphysical reality. What distinguishes Scanlon and Parfit’s approach from other realistic meta-ethical theories is that they maintain that normative entities exist in a way that (...) is different from (some) non-normative entities. Moreover, they think that this view about the way normative entities exist helps to answer the metaphysical worries that are often thought to plague non-naturalism. To make sense of this idea, I develop their view as a version of alethic pluralism: the position that there is more than one truth property. I argue, however, that when their view is developed in this way it fails to satisfy realistic intuitions about morality. This shows that on a plausible and initially promising reading of what it takes for a normative entity to exist in a way that is different from non-normative entities, Parfit’s and Scanlon’s non-metaphysical moral realism fails to be more realistic than contemporary versions of anti-realism. (shrink)