Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

Mental fictionalism is not the benign view that we may better understand the mind if we think of mental states as something like useful fictions, but the more radical view that mental states just are useful fictions. This paper argues that, if one were to treat mental states as a kind of fiction, the genre of fiction best suited to this purpose would be fantasy make-believe, in which magic is a central feature. After defending a promising fictionalist account of mental (...) discourse as a kind of prop-oriented make believe against recent criticism, the paper ultimately concludes that mental fictionalism faces further, potentially insurmountable, challenges. Most significantly, there is a problematic disanalogy between folk psychology and fiction: our mental state attributions aim to track truth, and this crucial aspect of our mental discourse cannot be captured if we interpret it as a kind of fictional discourse. For this and other reasons, the cost of adopting mental fictionalism likely outweighs its benefits. Whether or not these problems can be resolved, there is still much to be gained from taking mental fictionalism seriously: in doing so we may illuminate several important features of our own folk psychology that often go unnoticed. (shrink)

According to naturalized metaphysics, metaphysics should be informed by our current best science and not rely on a priori reasoning. Consequently, naturalized metaphysics tends to dismiss metaphysicians’ attempts to quarrel with science. This paper argues that naturalized metaphysics should instead welcome such conflicts between metaphysics and science. Naturalized metaphysics is not eliminative of metaphysics. So, if such conflicts are driven by the immediate absence in science of an answer to a metaphysical question, then the conflict should not be dismissed, but (...) instead be received as an occasion to do naturalized metaphysics. That conflicts between metaphysics and science might be beneficial for naturalized metaphysics is exemplified by the case of non-spatial theories of quantum gravity. These theories are criticized by metaphysicians who, often following David Lewis, argue that spatial distance is an indispensable fundamental element in any coherent metaphysics due to its role as the world-making relation. The resulting conflict, however, is found to be well-motivated since the non-spatial theories of quantum gravity offer no alternative world-making relation to spatial distance. Rather than dismissing this conflict, naturalized metaphysics should therefore receive the Lewisians’ resistance as a call to search for one. How this plays out as a negotiation between the scientific theory and the metaphysical question is exemplified in the last part of the paper where entanglement is proposed as an alternative world-making relation in loop quantum gravity. (shrink)

Ontological expressivism is the view that ontological existence claims express non-cognitive mental states. I develop a version of ontological expressivism that is modeled after Gibbard’s (2003) norm-expressivism. I argue that, when speakers assess whether, say, composite objects exist, they rely on assumptions with regard to what is required for composition to occur. These assumptions guide their assessment, similar to how norms may guide the assessment of normative propositions. Against this backdrop, I argue that “some objects have parts”, uttered in the (...) context of an ontological disagreement, expresses a noncognitive disposition to assess the truth of propositions by using only rules of assessment according to which the proposition that some objects have parts is to be evaluated as true. (shrink)

In recent metaphysics, the questions of whether fictional entities exist, what their nature is, and how to explain truths of statements such as “Sherlock Holmes lives at 221B Baker Street” and “Holmes was created by Arthur Conan Doyle” have been subject to much debate. The main aim of my thesis is to wrestle with key proponents of the abstractionist view that fictional entities are abstract objects that exist (van Inwagen 1977, 2018, Thomasson 1999 and Salmon 1998) as well as Walton’s (...) (1990) pretense view, which denies the existence of such entities. In the process, I propose modifications to these views to deal with problems they face and show how the modifications better account for the philosophical data. -/- Key abstractionists (van Inwagen 1977, Thomasson 1999) make a strict distinction between discourse within fiction, in which statements about literary characters cannot be literally true, and discourse about fiction, as it occurs in literary criticism, where statements about fictional characters can be literally true. Fictional objects are postulated to account for the truth of the latter. This runs into trouble because statements thought to be literally true are not literal. (Yagisawa 2001, Friend 2002) I provide a uniform analysis to account for the truth of statements involving fictional characters by appealing to a presupposition involving a metaphor in both contexts. The presupposition is that there is an x such that x is fictional; x is likened to a real person; and x is and ought to be treated/counted as a real person for all relevant intents and purposes. -/- More generally, I adopt Everett and Schroeder’s (2015) realist view that fictional characters are ideas constituted by mental representations. This, to me, better accounts for how fictional characters are created within the world’s causal nexus (unlike non-spatiotemporal entities in abstractionism), among other things. One key challenge they face is to explain how ideas can possess properties such as being a detective. I present a fine-grained version of their view, according to which the mental representations constituting fictional entities encode mind-dependent properties. Moreover, I explain how reference to such representations is possible, using Bencivenga’s (1983) Neo-Kantian view of reference and Karttunen’s (1976) view on discourse referents. Finally, I suggest that the identity of fictional characters is interest-relative. The constant, and sometimes radical, change of properties that, fictional characters can undergo is taken to be a consequence of the fact that unified mental representations are bundles of simpler mental representations. As change occurs, simpler representations are replaced by others. -/- A key theme that runs through the thesis is that neither fictionality nor pretense is relevant to the semantics of fictional sentences—a claim bolstered by Matravers’ (2014) arguments. Whether or not my account works, this claim, as well as the new philosophical data I bring up, are some of the challenges I pose to the heart of established views. (shrink)

This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which of (...) these entities we have compelling reasons to accept. A look at [Quine 1953] shows that the criterion concerned the postulation of entities by theories, but it is often misread as an attempt to say something about either or. The core of the paper is an exposition of two formulations of the criterion. I first state a schema improving on that of [Scheffler and Chomsky 1959]. The second formulation is a single principle and construes commitment as a relation between theories and predicates: ontological commitment to the entities that satisfy a given predicate. Both criteria are extensional and are formulated for constructional systems, in the sense of [Carnap 1928] and [Goodman 1951], rather than for theories construed as interpreted sets of sentences. This solves a problem raised by [Halvorson 2019]. Their analyticity is substantiated by showing that their most controversial consequences are instances of Tarski’s Convention. (shrink)

In this paper, I argue that Amie Thomasson’s Easy Ontology rests on a vicious circularity that is highly damaging. Easy Ontology invokes the idea of application conditions that give rise to analytic entailments. Such entailments can be used to answer ontological questions easily. I argue that the application conditions for basic terms are only circularly specifiable showing that Thomasson misses her self-set goal of preventing such a circularity. Using this circularity, I go on to show that Easy Ontology as a (...) whole collapses. (shrink)

What is the relationship between mental states and items of material culture, like notebooks, maps or lists? The extended mind thesis offers an influential and controversial answer to this question. According to ExM, items of material culture can form part of the material basis for our mental states. Although ExM offers a radical view of the location of mental states, it fits comfortably with a traditional, representationalist account of the nature of those states. I argue that proponents of ExM would (...) do better to adopt a fictionalist approach to mental states. In so doing, I suggest, they could retain the important insights underlying the extended mind thesis, while avoiding its more problematic consequences. (shrink)

Conflicts between our best philosophical theories (BPTs) and our common beliefs are widespread. For example, if eliminativism is our BPT, then our BPT conflicts with common beliefs about the existence of middle-sized composite artifacts. “Compatibilism” is the name usually given to a theoretical attitude, according to which, in the case of a conflict between BPT and a common belief P, we should try to find a reconciliation. The two major variants of compatibilism are “semantic compatibilism” (SC) and “cognitive compatibilism” (CC). (...) According to SC, to be reconciled with BPT is the “real” version of the content of our ordinary assertions; according to CC, to be reconciled with BPT is the mental state we are “really” in while thinking P. In this paper, we present a new kind of compatibilism, epistemic compatibilism (EC). According to EC, to be reconciled with BPT is the explanation of why we believe that P. After presenting EC, we will argue that it fares better than SC and CC for at least two related reasons: EC does not rely on any form of what we call semantic or cognitive “recarving”; thus, EC avoids some sceptical problems that aect the other two versions of compatibilism. (shrink)

There is growing debate about what is the correct methodology for research in the ontology of artworks. In the first part of this essay, I introduce my view: I argue that semantic descriptivism is a semantic approach that has an impact on meta-ontological views and can be linked with a hermeneutic fictionalist proposal on the meta-ontology of artworks such as works of music. In the second part, I offer a synthetic presentation of the four main positive meta-ontological views that have (...) been defended in philosophical literature about artworks and of some criticisms that can be lodged against them: Amie Thomasson’s global descriptivism, Andrew Kania’s local descriptivism, Julian Dodd’s folk-theoretic modesty, and David Davies’ rational accountability view. In the conclusion, I show the advantages of my view. (shrink)

Does Carnap’s treatment of philosophical questions about existence, such as “Are there numbers?” and “Are there physical objects?”, depend on his analytic–synthetic distinction? If so, in what way? I answer these questions by clarifying, defending, and developing the reading of Carnap’s paper “Empiricism, Semantics, and Ontology” that W. V. Quine proposes, with little justification or explanation, in his paper “On Carnap’s Views on Ontology”. The primary methodological value of studying Quine’s reading of “Empiricism, Semantics, and Ontology” is that it prompts (...) us to look for, and helps us to see the significance of, passages by Carnap that reveal the logical foundations of his views on ontology. Guided in this way by Quine’s reading, I show that (1) in “Empiricism, Semantics, and Ontology” Carnap’s preferred treatment of philosophical questions relies on paraphrasing them so that their answers are immediately obvious elementary logical truths, and are therefore, by his standards, trivially analytic; and (2) in its most general form, Carnap’s treatment of philosophical questions about existence depends on his controversial view that the analytic truths of a language L may include sentences that are not elementary logical truths, but that are nevertheless, by Carnap’s standards, analytic-in-L simply because we have stipulated that they are to be among the “meaning postulates” of L. (shrink)

Anti-exceptionalism about logic takes logic to be, as the name suggests, unexceptional. Rather, in naturalist fashion, the anti-exceptionalist takes logic to be continuous with science, and considers logical theories to be adoptable and revisable accordingly. On the other hand, the Adoption Problem aims to show that there is something special about logic that sets it apart from scientific theories, such that it cannot be adopted in the way the anti-exceptionalist proposes. In this paper I assess the damage the Adoption Problem (...) causes for anti-exceptionalism, and show that it is also problematic for exceptionalist positions too. My diagnosis of why the Adoption Problem affects both positions is that the self-governance of basic logical rules of inference prevents them from being adoptable, regardless of whether logic is exceptional or not. (shrink)

ABSTRACTCarnap famously argued that there are two kinds of questions and claims concerning the existence or reality of entities: internal and external ones. We focus on Carnapian external ontological claims of the form: ‘Xs really exist’, where ‘X’ stands for some traditional metaphysical category, such as ‘substance’, ‘fact’ or ‘structure’. While Carnap considered them as meaningless, we consider them as faultlessly meaningful. However, in line with an expressivist guise, we do not claim that they have the meaning they have in (...) virtue of representing a certain range of entities in the world or describing pieces of reality. Quite the contrary, we maintain that they are meaningful because they perform a function that is fundamentally expressive, that is, a non-descriptive function. In particular, they may imply a distinctive type of metalinguistic expressive function. Moreover, we avoid accuses of mentalism insofar as we explain the meaning of external ontological claims in terms of the practical commitments to the adoption of certain linguistic forms they express, rather than as expressing some kind of mental state. (shrink)

Some Buddhists claim that all phenomena are empty of inherent existence and thereby endorse a kind of global anti‐realism. Buddhist global fictionalists argue that for these Buddhists, ordinary discourse is best understood in global fictionalist terms. I argue here that these attempts fail because the types of fictionalism that these accounts are modeled after structurally rely on a non‐fictionalist domain of discourse to establish normative constraints within the target fictionalist domain. If the goal of appealing to fictionalism is to help (...) explain how discourse involving reference to entities that are unreal can still be governed by non‐arbitrary norms of acceptance, such that some conventional claims can be meaningfully described as conventionally true in contrast to other such claims that are conventionally false, then Buddhist global fictionalism undermines its own goals. It does so by eliminating the very feature of a fictionalist account – the ability to appeal to a non‐fictionalist domain – that makes possible the norms that fictionalism is invoked to explain in the first place. (shrink)

This is a slightly opinionated review of three main factions in metaontology: Quineans, Carnapians, and Meinongians. Emphasis is given to the last camp, as the metaontological aspect of Meinongianism has been underappreciated. The final section then offers some general remarks about the legitimacy of ontology, touching on ideas I have developed in other publications.

How hard is it to answer an ontological question? Ontological trivialism,, inspired by Carnap’s internal-external distinction among “questions of existence”, replies “very easy.” According to, almost every ontologically disputed entity trivially exists. has been defended by many, including Schiffer and Schaffer. In this paper, I will take issue with. After introducing the view in the context of Carnap-Quine dispute and presenting two arguments for it, I will discuss Hofweber’s argument against and explain why it fails. Next, I will introduce a (...) modified version of ontological trivialism, i.e. negative ontological trivialism,, defended by Hofweber, according to which some ontologically disputed entities, e.g. properties, trivially do not exist. I will show that fails too. Then I will outline a Meinongian answer to the original question, namely, ‘How hard is it to answer an ontological question?’ The Carnapian intuition of the triviality of internal questions can be saved by the Meinongian proposal that quantification and reference are not ontologically committing and the Quinean intuition of the legitimacy of interesting ontological questions can be respected by the Meinongian distinction between being and so-being. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options (...) available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. (shrink)

This paper reflects on metametaphysics and as such develops a metametameta-physical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his 'Empiricism, Semantics and Ontology' as an example, with regard to how it exhibits self-reference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from meta-theories with global scope, as the 'meta' (...) approach aims to transcend the scope of that which it is theorizing about, whilst the global nature will place itself back within the scope of that which it is theorizing about, which together result in the theory referring to itself whilst refuting itself. I argue that any global metametaphysical theory that draws a limit to thought will face self-reference problems leading to contradictory realms. My conclusion is conditional: If we want to meta-philosophize in such a way and treat quietist meta-theories as being true, then we need to be dialetheist and utilize a paraconsistent logic in order to accommodate the contradictions that result from such theorizing. (shrink)

In this paper a parallel is drawn between the problem of epistemic access to abstract objects in mathematics and the problem of epistemic access to idealized systems in the physical sciences. On this basis it is argued that some recent and more traditional approaches to solving these problems are problematic.

The main task in this paper is to detail and investigate Carnap’s conception of a “linguistic framework”. On this basis, we will see whether Carnap’s dichotomies, such as the analytic-synthetic distinction, are to be construed as absolute/fundamental dichotomies or merely as relative dichotomies. I argue for a novel interpretation of Carnap’s conception of a LF and, on that basis, will show that, according to Carnap, all the dichotomies to be discussed are relative dichotomies; they depend on conventional decisions concerning the (...) logical syntax of LF. Thus, all of the dichotomies directly hinge on the conception of the LF. The LF’s logical structure, in turn, is an immediate consequence of adopting the linguistic doctrine of logical truths. As we will see, no appeal to any of these distinctions is necessary in establishing a LF and all of its components. I will also draw attention to the differences between what Carnap labels a “way of speaking”, “language”, and “artificial language”. Consequently, I will briefly conclude that none of Quine’s major objections address the main points of Carnap’s theory. (shrink)

Mental fictionalism is the view that, even if mental states do not exist, it is useful to talk as if they do. Mental states are useful fictions. Recent philosophy of mind has seen a growing interest in mental fictionalism. To date, much of the discussion has concerned the general features of the approach. In this paper, I develop a specific form of mental fictionalism by drawing on Kendall Walton’s work on make-believe. According to the approach I propose, talk of mental (...) states is a useful pretence for describing people and their behaviour. I try to clarify and motivate this approach by comparing it to well-known alternatives, including behaviourism, instrumentalism and eliminativism. I also consider some of the challenges that it faces. (shrink)

Quine is routinely perceived as saving metaphysics from Carnapian positivism. Where Carnap rejects metaphysical existence claims as meaningless, Quine is taken to restore their intelligibility by dismantling the former’s internal–external distinction. The problem with this picture, however, is that it does not sit well with the fact that Quine, on many occasions, has argued that metaphysical existence claims ought to be dismissed. Setting aside the hypothesis that Quine’s metaphysical position is incoherent, one has to conclude that his views on metaphysics (...) are subtler than is often presupposed; both the received view that Quine saved metaphysics and the opposite view that Carnap and Quine are on the same anti-metaphysical team seem too one-sided if we take seriously Quine’s own pronouncements on the issue. In this paper, I offer a detailed reconstruction of Quine’s perspective on metaphysical existence claims. Scrutinizing his published work as well as unpublished papers, letters, and notebooks, I show how Quine is able to both blur the boundary between scientific sense and metaphysical nonsense and to argue that we cannot ask what reality is really like in a distinctively philosophical way. I argue that although Quine’s position is much closer to Carnap’s than the received view suggests, it still differs in two crucial respects. (shrink)

Much contemporary ontological inquiry takes place within the so-called ‘Quinean tradition’ but, given that some aspects of Quine’s project have been widely abandoned even by those who consider themselves Quineans, it is unclear what this amounts to. Fortunately recent work in metaontology has produced two relevant results here: a clearer characterisation of the metaontology uniting the aforementioned Quineans, most notably undertaken by Peter van Inwagen, and a raft of criticisms of that metaontology. In this paper I critique van Inwagen’s Quinean (...) metaontology, finding that certain challenges, supplemented by pressure to reflect more closely Quine’s work, should drive Quineans to adopt a stronger metaontology incorporating more of Quine’s radical views. I conclude that while van Inwagen’s Quineanism is problematic there are prospects for a viable, more wholeheartedly Quinean, metaontology. (shrink)

In this entry I will offer a survey of the contemporary debate on fic- tionalism, which is a distinctive anti-realist view about certain regions of discourse that are valued for their usefulness rather than their truth.

This project investigates naturalized metaphysics as a recent trend in analytic metaphysics originating in the naturalist attitude of James Ladyman and Don Ross in their seminal work Everything must Go: Metaphysics Naturalized (2007). The primary focus, however, will be the more recent article “Neo-Positivist Metaphysics” (2012) by Alyssa Ney that originates in this tradition. The project will conclude that naturalized metaphysics is an unsuccessful attempt at an answer to the question ’how is metaphysics possible’. More precisely, the project will establish (...) that any answer to this question must instruct how to succeed at attempts at assertions about the Kantian thing in itself. This requirement is the result of an argument that no other conception of ’reality’ is robust enough to accommodate an ambitious metaphysics. Subsequently, it will be argued that naturalized metaphysics is conceived by its proponents as an attempt at such an answer, but that naturalized metaphysics does not provide the required instruction. This problem occurs because of Carnap’s challenge to metaphysics. Carnap observes that no assertion can be made outside a linguistic framework which has the consequence that metaphysical assertions must be about the conceptual conventions of the linguistic framework rather than the thing in itself. It is the view of Ney and the other proponents of naturalized metaphysics that metaphysics is possible as a naturalized metaphysics; a metaphysics that appropriately defers or yields to the findings of science. The project argues that this requirement does nothing to ensure that Carnap’s challenge is avoided. The challenge is equally significant to naturalized and non-naturalized metaphysics, so long as both require that successful attempts at metaphysics must be assertions about the thing in itself. -/- The project concludes that until or unless Carnap’s challenge is refuted, naturalized metaphysics remain impossible, just like the metaphysics it is supposed to replace. (shrink)

Idioms – expressions like kick the bucket and let the cat out of the bag – are strange. They behave in ways that ordinary multi-word expressions do not. One distinctive and troublesome feature of idioms is their unpredictability: The meanings of sentences in which idiomatic phrases occur are not the ones that we would get by applying the usual compositional rules to the usual meanings of their (apparent) constituents. This sort of behavior requires an explanation. I will argue that the (...) right explanation is that the sentences are being interpreted through a pretense. (What this means, exactly, will be explained in what follows.) This is a surprising claim, for two reasons. On the one hand, it seems that adopting a pretense account is overkill—it’s a far more radical move than is required to account for the phenomena. On the other hand, it seems that a pretense account is hopeless—that there is a fatal overgeneration problem for pretense accounts of idiom that causes them to fail, as Jason Stanley charges, “as badly as it is possible for an account of idiom to fail.” So I will have some work to do. (shrink)

I argue that metaphysical views of material objects should be understood as 'packages', rather than individual claims, where the other parts of the package include how the theory addresses 'recalcitant data', and that when the packages meet certain general desiderata - which all of the currently competing views *can* meet - there is nothing in the world that could make one of the theories true as opposed to any of the others.

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)

This paper seeks to uncover and rationally reconstruct four theoretical prescriptions that H. L. A. Hart urged philosophers to observe and follow when investigating and theorizing about the nature of law. The four prescriptions may appear meager and insignificant when each is seen in isolation, but together as an inter-connected set they have substantial implications. In effect, they constitute a central part of Hart’s campaign to put philosophical investigations about the nature of law onto a path to a genuine research (...) program. The paper takes note of certain prevalent and robust trends in contemporary legal philosophy that detract its practitioners from the four prescriptions, and that have them revert to the some older modes of thinking from which Hart sought a decisive break. A number of contemporary legal philosophers’ views and commitments are taken up and assessed, and in particular those of John Gardner and Leslie Green. (shrink)

This thesis explores attempts to characterise the structure of reality. Three notions stand out: Lewisian naturalness, Sider’s ‘structure’, and grounding, where the latter has become the most popular way to characterise the structure of reality in the contemporary literature. I argue that none of these notions, as they are currently understood, are suited for limning the metaphysical structure of reality. In the first part of the thesis I argue that, by the lights of the relevant theories, both naturalness and structure (...) fall short of the theoretical role carved out for those posits. In the second part of the thesis I present two challenges to the ‘orthodox’ conception of grounding. The first contests the standard assumption that grounding is asymmetric, both by citing what I take to be best described as symmetric instances of grounding, and by developing and arguing for a new theory of metaphysical structure – ‘metaphysical interdependence’ – which takes grounding to be nonsymmetric. The second challenge concerns the relationship between grounding and explanation, and leads to a dilemma for the grounding theorist. My proposed resolution to the dilemma is to adopt an antirealist approach to grounding, which I further motivate and develop in the final chapter. (shrink)

An "overview article" that (a) clarifies the nature of theological anti-realism and how that thesis should be formulated, and (b) negatively assesses some of the most common arguments for being a theological anti-realist.

The mere fact that ontological debates are possible requires us to address the question, what is it to claim that a certain entity or kind of entity exists—in other words, what do we do when we make an existence-claim? I develop and defend one candidate answer to this question, namely that to make an existence-claim with regard to Fs is to claim that we can refer to Fs. I show how this theory can fulfil the most important explanatory desiderata for (...) a theory of existence; I also defend it against the charges of illegitimate ‘semantic ascent’ and of making existence counterfactually dependent on human linguistic ability. (shrink)

Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to standard mathematics. A (...) second style of response denies that indispensability entails realism: when we mathematize a physical problem we treat its physical content as if it were the mathematical representation; provided the two are sufficiently similar, we can use the mathematics to draw conclusions about the physics; even if we cannot represent physical facts without mathematical tools, as-if-fictionalism is reasonable. In this paper I argue that uses of mathematics in science reach deeper than is appreciated by this second response and, indeed, in the more general literature. More specifically, our confidence that we can use the mathematics to draw conclusions about the physics itself depends on mathematics. If the mathematical premises we employ in concluding that a certain application is trustworthy are false, we may lack a justification for supposing that the application will reliably lead us from correct input to correct output. For example, solutions to many physical problems require the determination of a function satisfying a differential equation. Sometimes the existence of a solution for initial value problems can be established directly; where direct methods fail, the existence of a solution must be established indirectly, generally by constructing a sequence of functions that converges to a limit function that satisfies the initial value problem. Moreover, the solution often cannot be evaluated by analytic methods, and scientists must rely on finite element numerical methods to approximate the solution. Mathematical analysis of errors provides further useful information governing the choice of approximation method and of the step size and number of elements needed for the approximation to reach a desired precision. Mathematical physicists rely on the background mathematical theories presupposed in proving the existence of the solutions and approximating them. It is difficult to see how they could do this while adding the fictionalist disclaimer, “But, you know, I don’t believe any of the mathematics I’m using”. It is difficult to see how a fictionalist pursuing the second strategy can account for the soundness of mathematical reasoning in mathematical physics and elsewhere in the sciences. The paper will fill out this argument by appeal to examples and attempt to make clear how mathematics is indispensable to understanding – and thus underwriting our confidence in – applications that would otherwise be shaky approximations and idealizations and how this role is difficult to square with fictionalism. (shrink)

Prop oriented make-believe is make-believe utilized for the purpose of understanding what I call “props,” actual objects or states of affairs that make propositions “fictional,” true in the make-believe world. I, David Hills, and others have claimed that prop oriented make-believe lies at the heart of the functioning of many metaphors, and one variety of fictionalism in metaphysics invokes prop oriented make-believe to explain away apparent references to entities some find questionable or problematic (fictional characters, propositions, moral properties, numbers). Elisabeth (...) Camp has argued against my and David Hills’ views of metaphor. Her arguments, many of them echoed by Catharine Wearing, demolish a very implausible account of metaphor, but leave entirely untouched the views that Hills and I actually proposed. Clarifying what we say about metaphor serves also as a defense of fictionalist theories that invoke prop oriented make-believe. (shrink)

Yablo argued that some metaphors are representationally essential: they enable us to express contents that we would not be able to express without them. He defended a fictionalist view of mathematical language by making the case that it similarly serves as a representational aid. Against this, Colyvan argued that metaphorical/figurative language can never play an essential role in explanation and that mathematical language often does, hence concluding that Yablo’s fictionalism is untenable. I show that Colyvan’s thesis about explanation is highly (...) implausible in the absence of a challenge to Yablo’s position on representationally essential metaphors, which Colyvan does not attempt. I also briefly discuss other attempts to produce a simple knock-out argument against fictionalism and show them wanting. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

The syntactic priority thesis (henceforth SP) asserts that the truth of appropriate sentential contexts containing what are, by syntactic criteria, singular terms, is sufficient to justify the attribution of objectual reference to such terms (Wright, 1983, 24). One consequence that the neo-Fregean draws from SP is that it is through an analysis of the syntactic structure of true statements that 'ontological questions are to be understood and settled' (Wright, 1983, 25). Despite the significant literature on SP, little consideration has been (...) given to this bold meta-ontological claim.1 My concern here is accordingly not with specific applications of SP to debates in the philosophy of mathematics, but rather with the .. (shrink)

Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (shrink)

One way to challenge the substantiveness of a particular philosophical issue is to argue that those who debate the issue are engaged in a merely verbal dispute. For example, it has been maintained that the apparent disagreement over the mind/brain identity thesis is a merely verbal dispute, and thus that there is no substantive question of whether or not mental properties are identical to neurological properties. The goal of this paper is to help clarify the relationship between mere verbalness and (...) substantiveness. I first argue that we should see mere verbalness as a certain kind of discourse defect that arises when the parties differ as to what each takes to be the immediate question under discussion. I then argue that mere verbalness, so understood, does not imply that the question either party is attempting to address is a non-substantive one. Even if it turns out that the parties to the mind/brain dispute are addressing subtly different questions, these might both be substantive questions to which their respective metaphysical views provide substantive answers. One reason it is tempting to reach deflationary conclusions from the charge of mere verbalness is that we fail to distinguish it from the claim that a sentence under dispute is, in a certain sense, indisputable. Another reason is that we fail to distinguish mere verbalness from a certain sort of indeterminacy. While indisputability and indeterminacy plausibly capture forms of nonsubstantiveness, I argue that mere verbalness is insufficient to establish either indisputability or indeterminacy. (shrink)

This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...) (called modal Meinongianism), applies it to specific fields, and discusses its open problems. Part I of the book provides a historical introduction to, and critical discussion of, the dominant philosophical view of existence: the “Kantian-Fregean-Quinean” perspective. Part II is the full-fledged introduction to the Meinongian theories of existence as a real property of individuals: after starting with the so-called naïve Meinongian conception and its problems, it provides a self-contained presentation of the main neo-Meinongian proposals, and a detailed discussion of their strengths and weaknesses. Part III develops a specific neo-Meinongian theory of existence employing a model-theoretic semantic framework. It discusses its application to the ontology and semantics of fictional objects, and its open problems. The methodology of the book follows the most recent trends in analytic ontology. In particular, the meta-ontological point of view is largely privileged. (shrink)

This article is an evaluation of Le Poidevin’s use of Carnap ’s stance on ontology within the philosophy of religion. Le Poidevin claims that 1) theists need to take God to be a putative entity within space-time in order for their claim that God exists to be meaningful, and that 2) instrumentalism about theology is viable. I argue that although Le Poidevin’s response to Carnap ’s argument is no less problematic than that argument itself, his position is in fact thoroughly (...) un-Carnapian. The upshot is that his discussion provides some support to atheism, but none to either of his two official conclusions. (shrink)