This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.

When I was first studying Hegel I encountered quite divergent readings of his views on religion. The teacher who first presented Hegel to me was a Jesuit, Quentin Lauer at Fordham University, who read Hegel as a Christian theologian providing a better metaphysical system for understanding the doctrines of the Trinity and Incarnation. When I studied at Yale, Kenley Dove read Hegel as the first thoroughly atheistic philosopher, who presented the conditions of thought without reference to any foundational absolute being. (...) Meanwhile, also at Yale, John Findlay read us a deeply Neo-Platonic Hegel who taught about absolute forms held in a cosmic mind. In giving my own reading I want to talk about the ways Hegel redefines both metaphysics and religion. I would like to approach these issues by way of the medieval controversy over double truth, which was a previous conflict between religion and science. (shrink)

I argue that fictionalism about grounding is unmotivated, focusing on Naomi Thompson’s (2022) recent proposal on which the utility of the grounding fiction lies in its facilitating communication about what metaphysically explains what. I show that, despite its apparent dialectical kinship with other metaphysical debates in which fictionalism has a healthy tradition, the grounding debate is different in two key respects. Firstly, grounding talk is not indispensable, nor even particularly convenient as a means of communicating about metaphysical explanation. This undermines (...) the revolutionary proposal. Secondly, talk of grounding primarily occurs within metaphysics, which means the usual options for motivating a non-literal interpretation are ineffective. This undermines the hermeneutic proposal. (shrink)

I defend pretence hermeneutic fictionalism against the Autism Objection. The objection is this: since people with autism have no difficulty in engaging with mathematics even if they cannot pretend, it is not the case that engagement with mathematics involves pretence. I show that a previous response to the objection is inadequate as a defence of the kind of pretence hermeneutic fictionalism put forward as a semantic thesis about the discourse in question. I claim that a more general response to the (...) Autism Objection is to deny the premise that people with autism cannot pretend. To motivate this response, I appeal to psychological studies suggesting that people with autism can understand pretence and they can pretend under certain conditions. Finally, I provide explanations for why it is the case that people with autism do not have a problem with engaging in mathematics whereas they have so much difficulty with other kinds of figurative language and pretence. (shrink)

The debate concerning the ontological status of musical works is perhaps the most animated debate in contemporary analytic philosophy of music. In my view, progress requires a piecemeal approach. So in this article I hone in on one particular musical work concept – that of the classical Western art musical work; that is, the work concept that regulates classical art-musical practice. I defend a fictionalist analysis – a strategy recently suggested by Andrew Kania as potentially fruitful – and I develop (...) a version of such an analysis in line with a broad commitment to philosophical naturalism. (shrink)

Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.

Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to (...) refer to an entity whose existence or non-existence is a factual matter, e.g. ‘the king of France’: the failure of the presupposition that there is a unique French king makes some sentences with the term ‘the king of France’, in particular “The king of France is bald”, gappy. In this paper I will show that the sentence “The king of France is bald” must be false, and not gappy, according to Yablo’s own criteria and that, furthermore, the presupposition that the term ‘the king of France’ refers presents a fail-safe mechanism in the same way Yablo thinks abstract presuppositions do—this undermines his argument for metaontological antirealism. (shrink)

In his latest book Aboutness, Stephen Yablo has proposed a new ‘easy road’ nominalist strategy: instead of engaging in the hard work of paraphrasing a scientific theory which presupposes numbers in a nominalistically acceptable way, nominalists are, according to Yablo, entitled to accept the theory as true, while rejecting the existence of numbers, if from the theory’s content the presupposition that there are numbers can be subtracted away, yielding thus a number-free content remainder. Perfect extricability, i.e. extricability in every possible (...) world, of the presupposition that there are numbers from any content apparently involving them is, in Yablo’s view, sufficient to make the existence of numbers moot. In this paper I will argue that perfect extricability fails as a criterion of ontological mootness. (shrink)

In his latest book Aboutness, Stephen Yablo has proposed a new ‘easy road’ nominalist strategy: instead of engaging in the hard work of paraphrasing a scientific theory which presupposes numbers in a nominalistically acceptable way, nominalists are, according to Yablo, entitled to accept the theory as true, while rejecting the existence of numbers, if from the theory’s content the presupposition that there are numbers can be subtracted away, yielding thus a number-free content remainder. Perfect extricability, i.e. extricability in every possible (...) world, of the presupposition that there are numbers from any content apparently involving them is, in Yablo’s view, sufficient to make the existence of numbers moot. In this paper I will argue that perfect extricability fails as a criterion of ontological mootness. (shrink)

These days it is widely agreed that there is no such thing as absolute motion and rest; the motion of an object can only be characterized with respect to some chosen frame of reference.1 This is a fact of which many of us are well-aware, and yet a cursory consideration of the ways we ascribe motion to objects gives the impression that it is a fact we persistently ignore. We insist to the police officer that we came to a full (...) and complete stop at the stop sign, we fret that traffic is moving too slowly, we observe that the sun has dropped below the hills on the horizon, all without ever saying which frames of reference we have in mind. (shrink)

A central question for ontology is the question of whether numbers really exist. But it seems easy to answer this question in the affirmative. The truth of a sentence like ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of is ‘The number of students who came to the party is seven’. But appears to entail the existence of a number, and so it seems that we must (...) conclude that numbers exist. This is sometimes called the puzzle of how we can get something from nothing. Most extant attempts to solve the puzzle take it for granted that is ontologically innocent, and focus their attention either on or on the transition from to. We argue that both attempts go wrong at the first step: the assumption that is ontologically innocent is undermined by a highly attractive and independently well-motivated degree-based account of number word constructions. Thus the degree-based account provides a straightforward linguistic resolution of the puzzle of how we can get something from nothing. But the paper also has a second aim. The semantics we present treats ‘seven’ as a referring expression that refers to a degree of a certain sort. But what are degrees? We consider various anti-platonist proposals that seek to account for degrees in terms of relations between concrete entities, and argue that they are incompatible with the Universal Density of Measurement hypothesis of Fox and Hackl. While the UDM cannot yet claim to be the consensus view among degree-based semanticists, our aim is to use it to illustrate how views about the nature of degrees can be evaluated by considering the properties degrees must have if they are to play the explanatory roles they are called upon to play in linguistics. In the present state of development of degree-based semantics there are difficult open questions about what these properties are. These questions need to be addressed if we are to develop a clear picture of what natural language semantics has to contribute to ontology and metaphysics. (shrink)

Pairs of sentences like the following pose a problem for ontology: (1) Jupiter has four moons. (2) The number of moons of Jupiter is four. (2) is intuitively a trivial paraphrase of (1). And yet while (1) seems ontologically innocent, (2) appears to imply the existence of numbers. Thomas Hofweber proposes that we can resolve the puzzle by recognizing that sentence (2) is syntactically derived from, and has the same meaning as, sentence (1). Despite appearances, the expressions ‘the number of (...) moons of Jupiter’ and ‘four’ do not function semantically as singular terms in (2). Hofweber’s primary evidence for this proposal concerns differences in the focus-related communicative functions of (1) and (2). In this paper I raise several serious problems for Hofweber’s proposal, and for his attempt to support it by appeal to focus-related phenomena. I conclude by offering independent evidence for an alternative, purely pragmatic resolution of the ontological puzzle. (shrink)

Fictionalism has recently returned as a standard response to ontologically problematic domains. This article assesses moral fictionalism. It argues (i) that a correct understanding of the dialectical situation in contemporary metaethics shows that fictionalism is only an interesting new alternative if it can provide a new account of normative content: what is it that I am thinking or saying when I think or say that I ought to do something; and (ii) that fictionalism, qua fictionalism, does not provide us with (...) any new resources for providing such an account. (shrink)

Recent debates about mathematical ontology are guided by the view that Platonism's prospects depend on mathematics' explanatory role in science. If mathematics plays an explanatory role, and in the right kind of way, this carries ontological commitment to mathematical objects. Conversely, the assumption goes, if mathematics merely plays a representational role then our world-oriented uses of mathematics fail to commit us to mathematical objects. I argue that it is a mistake to think that mathematical representation is necessarily ontologically innocent and (...) that there is an argument from mathematics' representational capacity to Platonism. Given that it is common ground between the Platonist and nominalist that mathematics plays a representational role in science, this representationalist argument is to be preferred over the explanatory, or enhanced, indispensability argument. (shrink)

In this paper, I argue that various disputes in ontology have important ramifications and so are worth taking seriously. I employ a criterion according to which whether a dispute matters depends on how integrated it is with the rest of our theoretical projects. Disputes that arise from previous tensions in our theorizing and have additional implications for other issues matter, while insular disputes do not. I apply this criterion in arguing that certain ontological disputes matter; specifically, the disputes over concrete (...) possible worlds and coincident material objects. Finally, I consider how one could show that some ontological disputes do not matter, using a Platonism/nominalism dispute as an example. (shrink)

Thought experiments invite us to evaluate philosophical theses by making judgements about hypothetical cases. When the judgements and the theses conflict, it is often the latter that are rejected. But what is the nature of the judgements such that they are able to play this role? I answer this question by arguing that typical judgements about thought experiments are in fact judgements of normal counterfactual sufficiency. I begin by focusing on Anna-Sara Malmgren’s defence of the claim that typical judgements about (...) thought experiments are mere possibility judgements. This view is shown to fail for two closely related reasons: it cannot account for the incorrectness of certain misjudgements, and it cannot account for the inconsistency of certain pairs of conflicting judgements. This prompts a reconsideration of Timothy Williamson’s alternative proposal, according to which typical judgements about thought experiments are counterfactual in nature. I show that taking such judgements to concern what would normally hold in instances of the relevant hypothetical scenarios avoids the objections that have been pressed against this kind of view. I then consider some other potential objections, but argue that they provide no grounds for doubt. (shrink)

According to Originalism, word types are non-eternal continuants which are individuated by their causal-historical lineage and have a unique possible time of origination. This view collides with the intuition that individual words can be added to the lexicon of a language at different times, and generates other problematic consequences. The paper shows that such undesired results can be accommodated without abandoning Originalism.

As the subtitle “A Syncretistic Account of Fictional Entities” makes clear, Alberto Voltolini intends in this book to argue for a syncretic view of the ontology and the semantics of fiction. In the process, he offers sympathetic and clear presentations of the main contenders in the field, discussing first ontological matters (chapters 1–4) and then semantic questions (chapters 5–6), and concluding with an ‘ontological’ argument for the allegedly syncretic brand of realism about fictional entities he has by then endorsed. The (...) book will therefore be very useful for all those who want to have a guided overview of the state of the art in the field, and very helpful if used as a main text for an introductory graduate course. (shrink)

Singular terms used in fictions for fictional characters raise well-known philosophical issues, explored in depth in the literature. But philosophers typically assume that names already in use to refer to “moderatesized specimens of dry goods” cause no special problem when occurring in fictions, behaving there as they ordinarily do in straightforward assertions. In this paper I continue a debate with Stacie Friend, arguing against this for the exceptionalist view that names of real entities in fictional discourse don’t work there as (...) they do in simple-sentence assertions, but rather as fictional names do. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Many have pointed out that the utility of mathematical objects is somewhat disconnected from their ontological status. For example, one might argue that arithmetic is useful whether or not numbers exist. We explore this phenomenon in the context of Divine Conceptualism, which claims that mathematical objects exist as thoughts in the divine mind. While not arguing against DC claims, we argue that DC claims can lead to epistemological uncertainty regarding the ontological status of mathematical objects. This weakens DC attempts to (...) explain the utility of mathematical objects on the basis of their existence. To address this weakness, we propose an appeal to Liggins’ theory of Belief Expressionism. Indeed, we point out that BE is amenable to the ontological claims of DC while also explaining the utility of mathematical objects apart from reliance upon their existence. We illustrate these themes via a case study of Peano Arithmetic. (shrink)

Peter van Inwagen has in recent decades made significant and influential contributions to metaphysics. In his Material Beings he advanced a novel ontology according to which chairs and other medium-sized dry goods don’t really exist. He went on to make important contributions to metaontology. Parts of his Ontology, Identity, and Modality and Existence: Essays in Ontology defend a broadly Quinean conception of existence questions and how to address them. I argue that the metaontology articulated in those later works is in (...) fact inconsistent with his defense of his ontology advanced in his earlier work. (shrink)

In this paper I outline an alternative to hermeneutic fictionalism, an alternative I call indifferentism, with the same advantages as hermeneutic fictionalism with respect to ontological issues but avoiding some of the problems that face fictionalism. The difference between indifferentism and fictionalism is this. The fictionalist about ordinary utterances of a sentence S holds, with more orthodox views, that the speaker in some sense commits herself to the truth of S. It is only that for the fictionalist this is truth (...) in the relevant fiction. According to the indifferentist, by contrast, we are simply non-committal – or indifferent – with respect to some aspects of what is literally said in our assertive utterances. (shrink)

Utterances within the context of telling fictional tales that appear to be assertions are nevertheless not to be taken at face value. The present paper attempts to explain exactly what such 'pseudo-assertions' are, and how they behave. Many pseudo-assertions can take on multiple roles, both within fictions and in what I call 'participatory criticism' of a fiction, especially when they occur discourse-initially. This fact, taken together with problems for replacement accounts of pseudo-assertion based on the implicit prefixing of an 'in (...) the fiction' operator, suggest that pseudo-assertion is best understood as a kind of make-believe. This proposal is elaborated and defended, and some applications to fictionalism are tentatively explored. (shrink)

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number of (...) themes in recent philosophy of mathematics (concerning a priority and fictionalism, for example) in revealing new light. (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)

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

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)

In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...) mathematics in our scientific explanations is a purely expressive one, merely allowing us to say more about the physical world than we would otherwise be able to. Mathematical objects do not need to exist for mathematics to play this role. This proposal puts a normative constraint on our use of mathematical language: we ought to use mathematically presented theories to express belief only in the consequences they have for non-mathematical things. In Part II, I will argue that what the normative proposal recommends is in fact what people generally do in both pure and applied mathematical contexts. I motivate this claim by showing that it is predicted by our best general means of analysing natural language. I provide a semantic theory of applied arithmetical sentences that reveals they do not purport to refer to numbers, as well as a pragmatic theory for pure mathematical language use which reveals that pure mathematical utterances do not typically communicate content that implies the existence of mathematical objects. In conclusion, I show that the emerging hermeneutic fictionalist position is preferable to any alternative interpretation of mathematical discourse as aimed at describing a domain of independently existing abstract mathematical objects. (shrink)

Questions about necessity (or what has to be, or what cannot be otherwise) and possibility (or what can be, or what could be otherwise) are questions about modality. Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function. However, despite its name, “Modal Fictionalism” in its (...) usual manifestations is not primarily fictionalism about claims of necessity and possibility, but rather a fictionalist approach to claims about possible worlds. (For instance, modal fictionalism is not normally fictionalist about the claim that “it is possible that there be a species of tail-less kangaroo”, but rather about the claim that “there is a possible world in which there is a species of tail-less kangaroo”.) The practice of taking possible worlds to be merely convenient fictions, or of treating talk about possible worlds as being useful without being literally correct, is quite common in philosophical circles. It is only recently, however, that philosophers have seriously examined the implications of taking possible worlds to be merely fictional objects, like Sherlock Holmes or a frictionless surface. (shrink)

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the (...) term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893-1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951). (shrink)

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...) description of Mars. But whereas Mars is a physical object, the number 3 is (according to platonism) an abstract object. And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. This view has been endorsed by Plato, Frege (1884, 1893-1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001). (shrink)

The paper provides an opinionated survey of recent contributions – roughly, in the last decade – to our understanding of how names and other referring expressions work in fictional discourse and addresses well-known philosophical worries that they raise. Views about the semantics of referring expressions in fictional discourse are usually accompanied by metaphysical views on the ontology of fictional characters, so this will also come under our focus.

There are advantages to thrift over honest toil. If we can make do without numbers we avoid challenging questions over the metaphysics and epistemology of such entities; and we have a good idea, I think, of what a nominalistic metaphysics should look like. But minimizing ontology brings its own problems; for it seems to lead to error theory— saying that large swathes of common-sense and best science are false. Should recherche philosophical arguments really convince us to give all this up? (...) Such Moorean considerations are explicitly part of the motivation for the recent resurgence of structured metaphysics, which allow a minimal (perhaps nominalistic) fundamental ontology, while avoiding error-theory by adopting a permissive stance towards ontology that can be argued to be grounded in the fundamental. This paper evaluates the Moorean arguments, identifying key epistemological assumptions. On the assumption that Moorean arguments can be used to rule out error-theory, I examine deflationary ‘representationalist’ rivals to the structured metaphysics reaction. Quinean paraphrase, fictionalist claims about syntax and semantics are considered and criticized. In the final section, a ‘direct’ deflationary strategy is outlined and the theoretical obligations that it faces are articulated. The position advocated may have us talking a lot like a friend of structured metaphysics—but with a very different conception of what we’re up to. (shrink)

Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches inevitably (...) lead to the dilemma in question. In contrast, the present proposal sticks with classical semantic values, but allows the compositional rules associated with these to admit of exceptions. I show how such an approach can be developed systematically. (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)

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)

I offer an explicit account of the underdetermination thesis as well as of the many challenges it poses to scientific realism; a way to answer to these challenges is explored and outlined, by shifting attention to the content of theories. I argue that, even if we have solid grounds (as I contend we do) to support that some varieties of the underdetermination thesis are true, scientific realism can still offer an adequate picture of the aims and achievements of science.

One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)