One of the most influential arguments for realism about mathematical objects is the indispensability argument. Simply put, this is the argument that insofar as we are committed to the existence of the physical objects existentially quantified over in our best scientific theories, we are also committed to the mathematical objects existentially quantified over in these theories. Following the Quine–Putnam formulation of the indispensability argument, some proponents of the indispensability argument have made the mistake of taking confirmational holism to be an (...) essential premise of the argument. In this paper, I consider the reasons philosophers have taken confirmational holism to be essential to the argument and argue that, contrary to the traditional view, confirmational holism is dispensable. (shrink)

In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. (...) It is also more general; the challenge applies equally to platonistic and non-platonistic accounts of mathematical truth. And it can be generalized beyond the case of mathematical knowledge to pose a challenge for, e.g., moral knowledge. (shrink)

The purpose of this dialogue between an ‘empirical realist’ and a ‘traditional ontologist’ is to clarify and evaluate the presuppositions of the kind of anti-ontological position exemplified by empirical realism. After ontology is defined and the empirical realist's position explained, the traditional ontologist pursues a series of dialectical developments and criticisms of the empirical realist's claim to have a coherently non-ontological position. The eventual conclusion is that the empirical realist's opposition to ontology just arbitrarily assumes ontology to be associated with (...) infallibilism and incompatible with fallibilism instead of conveying the illegitimacy of ontology itself or convincingly explaining the non-ontological standing of their position. The significance of this dialogue for critical realism is that it extends the case against anti-ontological epistemologies in general and empirical realism in particular by demonstrating the problems that result f.. (shrink)

Sex determines much about one's life, but what determines one's sex? The answer is complicated and incomplete: on close examination, ordinary notions of female and male are vague. In 2012, the International Olympic Committee further specified what they mean by woman in response to questions about who, exactly, is eligible to compete in women's Olympic events. I argue, first, that their stipulation is evidence that the use of vague terms is better described by semantic approaches to vagueness than by epistemic (...) approaches. In addition, the IOC's 2012 stipulation was made with sensitivity to its practical consequences. Linguistic actions often have morally relevant consequences, and I contend that, other things equal, we should adopt theories about language that acknowledge the responsibility we bear for what we say. Taking vagueness to be an epistemic phenomenon precludes the sense of agency needed for moral responsibility; taking it to be semantic does not. Thus I advance two arguments for semantic approaches to vagueness, as against epistemic approaches: one descriptive and one normative. (shrink)

Presentism is usually understood as the thesis that only the present exists whereas the rival theory of eternalism is usually understood as the thesis that past, present, and future things are all equally real. The significance of this debate has been threatened by the so-called triviality objection, which allegedly shows that the presentist thesis is either trivially true or obviously false: Presentism is trivially true if it is read as saying that everything that exists now is present, and it is (...) obviously false if read as saying that everything that has existed, exits or will exist is present. If eternalism is taken as the negation of presentism, it is also either trivially false or obviously true. In this paper, I try to respond to the triviality objection on behalf of presentism. In second section, I will examine how the argument proceeds. In third section, I will reflect on three possible ways to respond but will argue that none of them succeeds in giving a satisfactory solution. I will then try to clarify the core idea of presentism and to suggest that if we characterise presentism accurately, the problem will disappear. In fourth section, I will offer a plausible definition of presentism and will show how it can avoid the triviality objection and demonstrate why it is advantageous to accept the version of presentism I offer. (shrink)

In this essay I focus on the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Deleuze. Although I am interested in how this idea can be established, my primary concern is with something more basic: how the idea can even be properly thought. In the course of exploring this issue, which I do partly by borrowing some ideas about logical syntax from Wittgenstein's Tractatus, I try to show how there can be dialogue (...) between analytic philosophers and those of other traditions. (shrink)

Geach and Thomson have argued that nothing is just plain good, because ‘good’ is, logically, an attributive adjective. The upshot, according to Geach and Thomson, is that consequentialism is unacceptable, since its very formulation requires a predicative use of ‘good’. Reactions to the argument have, for the most part, been uniform. Authors have converged on two challenging objections . First, although the logical tests that Geach and Thomson invoke clearly illustrate that ‘good’, as commonly used, is an attributive, they don’t (...) show that ‘good’ lacks an intelligible predicative interpretation. Second, even if the English word ‘good’ fails to express the property of goodness, we can just stipulate that ‘good*’ expresses goodness and thus formulate consequentialism accordingly. The second objection is one way of voicing skepticism about the method of drawing substantive philosophical conclusions from considerations about ordinary language. In this essay, we present an argument, inspired by Geach and Thomson, which isn’t susceptible to the same objections but which supports the same conclusion. The significance of our argument for ethics is obvious; it challenges the intelligibility of standard consequentialism, and even certain forms of non-consequentialism. One might be inclined to think that a more sophisticated consequentialism, which relies on ‘good {possible world/state of affairs/outcome}’ instead of just ‘good’, evades the criticism. But we explain why the criticism can’t be so easily evaded. (shrink)

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or some other premise which facilitates the (...) transfer of evidence to mathematical portions of scientific theories, the argument is implausible. (shrink)

The aim of this article is to provide an account of introspective knowledge concerning visual experiences that is in accordance with the idea of transparent introspection. According to transparent introspection, a person gains knowledge of her own current mental state M solely by paying attention to those aspects of the external world which M is about. In my view, transparent introspection is a promising alternative to inner sense theories. However, it raises the fundamental question why a person who pays attention (...) to something extra-mental should be epistemically justified in holding a belief about something intra-mental. In his Naturalizing the Mind, Fred Dretske solves this problem by conceiving of introspection concerning visual experiences as an inference based on a connecting belief. Although Dretske's account proves defective upon closer inspection, its essence can be salvaged by looking upon introspection as being a game of make-believe. (shrink)

This paper argues that the “Canberra Plan” picture of physicalistic reduction of mind--a picture shared by both its proponents and opponents, philosophers as diverse as David Armstrong, David Chalmers Frank Jackson, Jaegwon Kim, Joe Levine and David Lewis--neglects ground (Fine, 2001, 2012). To the extent that the point of view endorsed by the Canberra Plan has an account of the physical/functional ground of mind at all, it is in one version trivial and in another version implausible. In its most general (...) form, the point of view of the Canberra Plan is committed to unacceptably treating indexical or name-related facts as part of the ultimate physical/functional ground of the mental. (shrink)

Neuropragmatism is a research program taking sciences about cognitive development and learning methods most seriously, in order to reevaluate and reformulate philosophical issues. Knowledge, consciousness, and reason are among the crucial philosophical issues directly affected. Pragmatism in general has allied with the science-affirming philosophy of naturalism. Naturalism is perennially tested by challenges questioning its ability to accommodate and account for knowledge, consciousness, and reason. Neuropragmatism is in a good position to evaluate those challenges. Some ways to defuse them are suggested (...) here, along with recommendations about the specific kind of naturalism, a pluralistic and perspectival naturalism, that neuropragmatism should endorse. (shrink)

Quine's argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine's argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher's quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...) is a mistake, there is no science-independent perspective from which to validate science. I will argue that a great deal of the confusion surrounding Quine's argument is prompted by certain phrases in his seminal ‘Epistemology Naturalized’. Scrutinizing Quine's work both before and after the latter paper provides a better key to understanding his remarkable views about the epistemological relation between theory and evidence. (shrink)

The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards objects, whereas nominalists such as Field (...) have asserted that these apparent ontological commitments should not be taken at face value. In this article I argue for an intermediate position which upholds the legitimacy of ascribing a reference to abstract singular terms in an attenuated sense relative to the more robust ascription of reference applicable to names denoting concrete entities. In so doing I seek to clear up some confusions regarding the ramifications of such a thin notion of reference for ontological claims about mathematical objects. (shrink)

Boolos has suggested a plural interpretation of second-order logic for two purposes: to escape Quine’s allegation that second-order logic is set theory in disguise, and to avoid the paradoxes arising if the second-order variables are given a set-theoretic interpretation in second-order set theory. Since the plural interpretation accounts only for monadic second-order logic, Rayo and Yablo suggest an new interpretation for polyadic second-order logic in a Boolosian spirit. The present paper argues that Rayo and Yablo’s interpretation does not achieve the (...) goal. (shrink)

Intentionality, or the power of minds to be about, to represent, or to stand for things, remains central in the philosophy of mind. But the study of intentionality in the analytic tradition has been dominated by discussions of propositional attitudes such as belief, desire, and visual perception. There are, however, intentional states that aren't obviously propositional attitudes. For example, Indiana Jones fears snakes, Antony loves Cleopatra, and Jane hates the monster under her bed. The present paper explores such mental states (...) in an introductory but opinionated way. (shrink)

In this entry I present one of the most hotly debated issues in contemporary analytic philosophy regarding the nature of fictional entities and the motivations that might be adduced for and against positing them into our ontology. The entry is divided in two parts. In the first part I offer an overview of the main accounts of the metaphysics of fictional entities according to three standard realist views, fictional Meinongianism, fictional possibilism and fictional creationism. In the second part I describe (...) two main kinds of arguments for or against positing fictional entities into our ontology. The first kind is traditionally inspired by the linguistic data coming from our talk about fictional characters. The second kind is more recent and it builds on genuine ontological considerations. (shrink)

According to Crane’s schematicity thesis (ST) about intentional objects, intentionalia have no particular metaphysical nature qua thought-of entities; moreover, the real metaphysical nature of intentionalia is various, insofar as it is settled independently of the fact that intentionalia are targets of one’s thought. As I will point out, ST has the ontological consequence that the intentionalia that really belong to the general inventory of what there is, the overall domain, are those that fall under a good metaphysical kind, i.e., a (...) kind such that its members figure (for independent reasons) in such an inventory. Negatively put, if there are no things of a certain metaphysical kind, thoughts about things of that kind are not really committed to such things. Pace Crane, however, this does not mean that the intentionalia that are really there are only those that exist. For existence, qua first-order property, is no metaphysical kind. Thus, there may really be intentionalia that do not exist, provided that they belong to good metaphysical kinds. (shrink)

In this paper, I will defend the claim that there are three existence properties: the second-order property of being instantiated, a substantive first-order property (or better a group of such properties) and a formal, hence universal, first-order property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinong-like option that positively endorses both the former and the latter first-order property is the (...) correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties). (shrink)

I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges from physical relations among all existents. I also argue that there are no physical singularities in space-time. Singular space-time models do not belong to the ontology of the world: they are not things but concepts, i.e. defective solutions of Einstein’s field equations. I briefly discuss the actual (...) implication of the so-called singularity theorems in General Relativity and some problems related to ontological assumptions of Quantum Gravity. (shrink)

Philosophers and cognitive scientists have worried that research on animal mind-reading faces a ‘logical problem’: the difficulty of experimentally determining whether animals represent mental states (e.g. seeing) or merely the observable evidence (e.g. line-of-gaze) for those mental states. The most impressive attempt to confront this problem has been mounted recently by Robert Lurz. However, Lurz' approach faces its own logical problem, revealing this challenge to be a special case of the more general problem of distal content. Moreover, participants in this (...) debate do not agree on criteria for representation. As such, future debate should either abandon the representational idiom or confront underlying semantic disagreements. (shrink)

Dieser Band versammelt Beiträge zu den drei klassischen Disziplinen der Philosophie – dem Wahren, dem Guten, dem Schönen. Ihre Autoren zeichnet aus, dass sie aus dem akademischen Umfeld Michael Sukales zu seiner Zeit am Institut für Philosophie an der Carl-von-Ossietzky-Universität Oldenburg stammen. Ihm ist dieses Buch zum Abschied von seiner aktiven Lehrtätigkeit in Oldenburg gewidmet. Die thematische Vielfalt der enthaltenen Texte spiegelt die Bandbreite seines philosophischen Schaffens wider.

This paper investigates the nature of scientific realism. I begin by considering the anomalous fact that Bas van Fraassen’s account of scientific realism is strikingly similar to Arthur Fine’s account of scientific non-realism. To resolve this puzzle, I demonstrate how the two theorists understand the nature of truth and its connection to ontology, and how that informs their conception of the realism debate. I then argue that the debate is much better captured by the theory of truthmaking, and not by (...) any particular theory of truth. To be a scientific realist is to adopt a realism-relevant account of what makes true the scientific theories one accepts. The truthmaking approach restores realism’s metaphysical core—distancing itself from linguistic conceptions of the debate—and thereby offers a better characterization of what is at stake in the question of scientific realism. (shrink)

Quinean Ontological Naturalism addresses the question “What is there?” Advocates of the view maintain that we can answer this question by applying Quine’s criterion of ontological commitment to our best scientific theories. In this paper, I discuss two major objections that are commonly offered to this view, what I call the “Paraphrase Objection” and “First Philosophy Objection”. I argue that these objections arise from a common uncharitable characterization of the Quinean Ontological Naturalist’s project that fails to distinguish two distinct roles (...) for Quine’s Criterion, a descriptive role and a normative role. The objections target the descriptive role, but only the normative role is important to Quinean Ontological Naturalism. (shrink)

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...) the indispensability argument. (shrink)

Whatever the attractions of Tolkein's world, irrealists about fictions do not believe literally that Bilbo Baggins is a hobbit. Instead, irrealists believe that, according to The Lord of the Rings {Bilbo is a hobbit}. But when irrealists want to say something like “I am taller than Bilbo”, there is nowhere good for them to insert the operator “according to The Lord of the Rings”. This is an instance of the operator problem. In this paper, I outline and criticise Sainsbury's (2006) (...) spotty scope approach to the operator problem. Sainsbury treats the problem as syntactic, but the problem is ultimately metaphysical. (shrink)

In the past few years, deflationary positions in the debate on the nature of composite material objects have become prominent. According to Ted Sider these include the thesis of quantifier variance, against which he has defended ontological realism. Recently, Sider has considered the possibility of rejecting his arguments against the vagueness of the unrestricted quantifiers in terms of translation functions. Against this strategy, he has presented an intuitive complaint and has argued that it can only be resisted if quantifier variance (...) is accepted. But this is false. In this paper I argue, against Sider, that there is a coherent way to combine the rejection of quantifier variance with the vagueness of the unrestricted quantifiers. I sketch a model to show this, and then I consider, on the basis of it, several versions of the indeterminacy argument against the vagueness of the unrestricted quantifiers that Sider has formulated over the years. (shrink)

Surprisingly, over the decade or so since its publication, Bhaskar's Dialectic: The Pulse of Freedom has received relatively little in the way of systematic analysis either by critical realists or their critics. There have been, however, a number of critiques that have dealt with some of its themes and developments in a variety of contexts. In the following study, I assess the argument of Alex Callinicos. Callinicos' critique, though in many ways sympathetic, is fundamental to critical realism. Engaging with it (...) provides a means to develop and clarify a number of arguments about aspects of critical realism in general and also provides a useful staging point to set forth a basic and consistent ordering of inquiry for a critique of DPF. The initial purpose of the analysis is not so much a defence of DPF but an assessment of the construction of an argument brought to bear on it. I argue that the form of the argument deployed is problematic in a way that detracts from the substance of the critique of the content of DPF. This is not to suggest that DPF is immune to criticism but rather to suggest that a fuller analysis of the DPF argument and its potential remains to be made. The ultimate purpose of the analysis is to use this assessment of a strategy of critique—an argumentation schema or discursive form—to create an alternative approach to critically appraising DPF. Fundamental to Callinicos' argument is the nature of transcendental argument. (shrink)

Metaontology – the study of the nature of ontological issues – has flourished in recent years. The focus of this summary will be on some views and arguments that are central to today’s debate. One theme will be that of how seriously to take ontology: whether there is reason to take a skeptical or deflationary attitude toward ontological claims, as theorists like Rudolf Carnap, Hilary Putnam, and Eli Hirsch in different ways have urged. The other theme will be that of (...) the viability of the Fregean and Quinean approaches to ontology that have been and still are central to analytic philosophy. (shrink)

Sellars was committed to the irreducibility of the semantic, the intentional, and the normative. Nevertheless, he was also committed to naturalism, which is prima facie at odds with his other theses. This paper argues that Sellars maintained his naturalism by being linguistically pluralistic but ontologically monistic . There are irreducibly distinct forms of discourse, because there is an array of distinguishable functions that language and thought perform, but we are not ontologically committed to the array of apparently non-natural entities or (...) relations mentioned in the metalanguage. However, there is an underlying relation between language and world presupposed by all empirically meaningful language. In his early work Sellars sought to describe this relation in linguistic terms as a form of 'pure description', but inadequacies in that notion drove him towards the naturalistic relation between language and world that he came to call 'picturing'. (shrink)

This article further explains and develops a recent, comprehensive semantic naturalization theory, namely the interactive indexing (II) theory as described in my 2008 Minds and Machines article Semantic Naturalization via Interactive Perceptual Causality (Vol. 18, pp. 527–546). Folk views postulate a concrete intentional relation between cognitive states and the worldly states they are about. The II theory eliminates any such concrete intentionality, replacing it with purely causal relations based on the interactive theory of perception. But intentionality is preserved via purely (...) abstract propositions about the world that index, or correlate with, appropriate cognitive states. Further reasons as to why intentionality must be abstract are provided, along with more details of an II-style account of representation, language use and propositional attitudes. All cognitive representation is explained in terms of classification or sorting dispositions indexed by appropriate propositions. The theory is also related to Fodor’s representational theory of mind, with some surprisingly close parallels being found in spite of the purely dispositional basis of the II theory. In particular, Fodor’s insistence that thinking about an item cannot be reduced to sorting dispositions is supported via a novel two-level account of cognition—upper level propositional attitudes involve significant intermediate processing of a broadly normative epistemic kind prior to the formation of sorting dispositions. To conclude, the weak intentional realism of the II theory—which makes intentional descriptions of the world dispensable—is related to Dennett’s ‘intentional stance’ view, and distinguished from strong (indispensable) intentional realist views. II-style dispositions are also defended. (shrink)

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories—such as object , property , and relation —are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical (...) form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach—including Frege’s notorious paradox of the concept horse—are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments. (shrink)

According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...) is just as it in fact is, then T’ bear on this claim. It concludes that, while analogies with theories that attempt to eliminate unobservable concrete entities provide good reason to regard theories of the former sort as explanatorily bad, this reason does not apply to theories of the latter sort. (shrink)

Consider the kinds of macroscopic concrete objects that common sense and the sciences allege to exist: tables, raindrops, tectonic plates, galaxies, and the rest. Are there any such things? Opinions differ. Ontological liberals say they do; ontological radicals say they don't. Liberalism seems favored by its plausible acquiescence to the dictates of common sense abetted by science; radicalism by its ontological parsimony. Priority theorists claim we can have the virtues of both views. They hold that tables, raindrops, etc., exist, but (...) they aren't fundamental. The ontological liberal's ontology provides the correct inventory of existent individuals. The ontological radical's more restricted ontology provides the correct inventory of fundamental individuals. The priority theorist claims that the derivative individuals are "no addition in being" to the fundamental ones, so we can have our cake and eat it too. It would be nice if priority theorists were right. In this paper I argue, with regret, that they are not. One upshot is that the sort of explanations which underwrite the priority theorist's distinction between fundamental and derivative individuals do not mitigate our ontological commitments. Another is that we still have to choose between the charms of liberalism and radicalism. (shrink)

Terms such as ‘exist’, ‘actual’, etc., (hereafter, “ontic terms”) are recognized as having uses that are not ontologically committing, in addition to the usual commissive uses. (Consider, e.g., the Platonic and the neutral readings of ‘There is an even prime’.) In this paper, I identify five different noncommissive uses for ontic terms, and (by a kind of via negativa) attempt to define the commissive use, focusing on ‘actual’ as my example. The problem, however, is that the resulting definiens for the (...) commissive ‘actual’ is itself equivocal between a commissive and a noncommissive reading. I thus consider other proposals for defining the commissive use, including two proposals from David Lewis. However, each proposal is found to be equivocal in the same way—and eventually I argue that it is impossible to define an ontic term unequivocally. Even so, this is not meant to overshadow that we can understand an ontic term as univocally commissive, in certain conversational contexts. I close by illustrating the import of these observations for the Hirsch–Sider debate in metaontology. (shrink)

In this paper, it is argued that metaphysics, conceived as an inquiry into the ultimate nature of mind-independent reality, is a rationally indispensable intellectual discipline, with the a priori science of formal ontology at its heart. It is maintained that formal ontology, properly understood, is not a mere exercise in conceptual analysis, because its primary objective is a normative one, being nothing less than the attempt to grasp adequately the essences of things, both actual and possible, with a view to (...) understanding as far as we can the fundamental structure of reality as a whole. Accordingly, it is urged, the deliverances of formal ontology have a modal and epistemic status akin to those of other a priori sciences, such as mathematics and logic, rather than constituting rivals to the claims of the empirical sciences, such as physics. (shrink)

In this paper, 1 examine the role of the delta function in Dirac’s formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The inrlispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its rlispensability. I first discuss the (...) significance of the delta function in Dirac’s work, and explore the strategy that he devised to overcome its use. l then argue that even if mathematical theories turned out to be indispensable, this wouidn’t justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac’s discovery of antimatter, there’s no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac’s work. (shrink)

The Eleatic Visitor speaks forcefully when he insists, ‘Necessarily, whenever there is speech, it is speech of something; it is impossible for it not to be of something’. For ‘if it were not of anything, it would not be speech at all; for we showed that it is impossible for there to be speech that is speech of nothing’. Presumably, at 263c10, when he claims to have ‘shown’ that it is impossible for speech to be of nothing, the Visitor is (...) referring back to the Parmenidean puzzles at Sophist 237ff. (shrink)

Metaphysics is concerned with the foundations of reality. It asks questions about the nature of the world, such as: Aside from concrete objects, are there also abstract objects like numbers and properties? Does every event have a cause? What is the nature of possibility and necessity? When do several things make up a single bigger thing? Do the past and future exist? And so on. -/- Metametaphysics is concerned with the foundations of metaphysics. It asks: Do the questions of metaphysics (...) really have answers? If so, are these answers substantive or just a matter of how we use words? And what is the best procedure for arriving at them—common sense and conceptual analysis? Or assessing competing hypotheses with quasi-scientific criteria? -/- This volume gathers together sixteen new essays that are concerned with the semantics, epistemology, and methodology of metaphysics. My aim is to introduce these essays within a more general (and mildly opinionated) survey of contemporary challenges to metaphysics . (shrink)

This paper is an examination of evidential holism, a prominent position in epistemology and the philosophy of science which claims that experiments only ever confirm or refute entire theories. The position is historically associated with W.V. Quine, and it is at once both popular and notorious, as well as being largely under-described. But even though there’s no univocal statement of what holism is or what it does, philosophers have nevertheless made substantial assumptions about its content and its truth. Moreover they (...) have drawn controversial and important conclusions from these assumptions. In this paper I distinguish three types of evidential holism and argue that the most oft-cited and controversial thesis is entirely unmotivated. The other two theses are much overlooked, but are well-motivated and free from controversial implications. (shrink)

Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals (...) why these proofs—written in the vernacular to this very day—succeed in conforming to those norms. (shrink)

There are two doctrines for which Quine is particularly well known: the doctrine of ontological commitment and the inscrutability thesis—the thesis that reference and quantification are inscrutable. At first glance, the two doctrines are squarely at odds. If there is no fact of the matter as to what our expressions refer to, then it would appear that no determinate commitments can be read off of our best theories. We argue here that the appearance of a clash between the two doctrines (...) is illusory. The reason that there is no real conflict is not simply that in determining our theories’ ontological commitments we naturally rely on our home language but also (and more importantly) that ontological commitment is not intimately tied to objectual quantification and a reference-first approach to language. Or so we will argue. We conclude with a new inscrutability argument which rests on the observation that the notion of objectual quantification, when properly cashed out, deflates. (shrink)

Grice and Strawson's 'In Defense of a Dogma is admired even by revisionist Quineans such as Putnam (1962) who should know better. The analytic/synthetic distinction they defend is distinct from that which Putnam successfully rehabilitates. Theirs is the post-positivist distinction bounding a grossly enlarged analytic. It is not, as they claim, the sanctified product of a long philosophic tradition, but the cast-off of a defunct philosophy - logical positivism. The fact that the distinction can be communally drawn does not show (...) that it is based on a real difference. Subcategories that can be grouped together by enumeration will do the trick. Quine's polemical tactic (against which Grice and Strawson protest) of questioning the intelligibility of the distinction is indeed objectionable, but his argument can be revived once it is realized that 'analytic' et al. are theoretic terms, and there is no extant theory to make sense of them. Grice and Strawson's paradigm of logical impossibility is, in fact, possible. Their attempt to define synonymy in Quinean terms is a failure, nor can they retain analyticity along with the Quinean thesis of universal revisability. The dogma, in short, is indefensible. (shrink)

Philosophy of mathematics for the last half-century has been dominated in one way or another by Quine’s indispensability argument. The argument alleges that our best scientific theory quantifies over, and thus commits us to, mathematical objects. In this paper, I present new considerations which undermine the most serious challenge to Quine’s argument, Hartry Field’s reformulation of Newtonian Gravitational Theory.