Debunking arguments—also known as etiological arguments, genealogical arguments, access problems, isolation objec- tions, and reliability challenges—arise in philosophical debates about a diverse range of topics, including causation, chance, color, consciousness, epistemic reasons, free will, grounding, laws of nature, logic, mathematics, modality, morality, natural kinds, ordinary objects, religion, and time. What unifies the arguments is the transition from a premise about what does or doesn't explain why we have certain mental states to a negative assessment of their epistemic status. I examine (...) the common, underlying structure of the arguments and the different strategies for motivating and resisting the premises of debunking arguments. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...) that satisfies all of the constraints which have been placed on the Benacerraf Problem. The point generalizes to all arguments with the structure of the Benacerraf Problem aimed at realism about a domain meeting certain conditions. Such arguments include so-called "Evolutionary Debunking Arguments" aimed at moral realism. I conclude with some suggestions about the relationship between the Benacerraf Problem and the Gettier Problem. (shrink)

Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that (...) the minimalist gambit rests on a controversial thesis about epistemic priority: that explanatory concessions derive their epistemic import from what they reveal about counterfactual connections. We then challenge this epistemic priority thesis, which undermines the minimalist response to debunking arguments (in ethics and elsewhere). (shrink)

Orthodoxy has it that knowledge is absolute—that is, it cannot come in degrees. On the other hand, there seems to be strong evidence for the gradability of know-how. Ascriptions of know-how are gradable, as when we say that one knows in part how to do something, or that one knows how to do something better than somebody else. When coupled with absolutism, the gradability of ascriptions of know-how can be used to mount a powerful argument against intellectualism about know-how—the view (...) that know-how is a species of propositional knowledge. This essay defends intellectualism from the argument of gradability. It is argued that the gradability of ascriptions of know-how should be discounted as a rather superficial linguistic phenomenon, one that can be explained in a way compatible with the absoluteness of the state reported. (shrink)

That laws of nature play a vital role in explanation, prediction, and inductive inference is far clearer than the nature of the laws themselves. My hope here is to shed some light on the nature of natural laws by developing and defending the view that they involve genuine relations between properties. Such a position is suggested by Plato, and more recent versions have been sketched by several writers.~ But I am not happy with any of these accounts, not so much (...) because they lack detail or engender minor difficulties, though they do, but because they share a quite fundamental defect. My goal here is to make this defect clear and, more importantly, to present a rather different version of this general conception of laws that avoids it. I begin by considering several features of natural laws and argue that these are best explained by the view that laws involve properties, that this involvement takes the form of a genuine relation between properties, and, finally, that the relation is a metaphysically necessary one. In the second section I start at the other end, and by reflecting on the nature of properties arrive at a similar account of natural laws. In the final section I develop this account in more detail, with emphasis on the nature of the relation between properties it invokes. Along the way several natural objections to the account are answered. (shrink)

What are intuitions? According to doxastic views, they are doxastic attitudes or dispositions, such as judgments or inclinations to make judgments. According to perceptualist views, they are—like perceptual experiences—pre-doxastic experiences that—unlike perceptual experiences—represent abstract matters as being a certain way. In this paper I argue against doxasticism and in favor of perceptualism. I describe two features that militate against doxasticist views of perception itself: perception is belief-independent and perception is presentational. Then I argue that intuitions also have both features. The (...) upshot is that intuitions are importantly similar to perceptual experiences, and so should not be identified with doxastic attitudes or dispositions. I consider a popular argument from the introspective absence of sui generis intuition experiences in favor of doxasticism. I develop a conception of intuition experiences that helps to defuse this argument. (shrink)

According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then (...) propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices. (shrink)

This entry addresses the nature and epistemological role of intuition by considering the following questions: (1) What are intuitions?, (2) What roles do they serve in philosophical (and other “armchair”) inquiry?, (3) Ought they serve such roles?, (4) What are the implications of the empirical investigation of intuitions for their proper roles?, and (5) What is the content of intuitions prompted by the consideration of hypothetical cases?

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)

The idea that there are some facts that call for explanation serves as an unexamined premise in influential arguments for the inexistence of moral or mathematical facts and for the existence of a god and of other universes. This book is the first to offer a comprehensive and critical treatment of this idea. It argues that calling for explanation is a sometimes-misleading figure of speech rather than a fundamental property of facts.

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

Evolutionary debunking arguments abound, but it is widely assumed that they do not arise for our perceptual beliefs about midsized objects, insofar as the adaptive value of our object beliefs cannot be explained without reference to the objects themselves. I argue that this is a mistake. Just as with moral beliefs, the adaptive value of our object beliefs can be explained without assuming that the beliefs are accurate. I then explore the prospects for other sorts of vindications of our object (...) beliefs—which involve “bootstrapping” from our experiences as of midsized objects—and I defend bootstrapping maneuvers against a variety of objections. Finally, I argue for an explanatory constraint on legitimate bootstrapping and show how some attempts to respond to debunking arguments run afoul of the constraint. (shrink)

I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is what causes (...) all the many properties and behaviors that are typically shared by all the instances of the kind. Accordingly, we know what is necessarily true of kinds by knowing what is essential to them in the sense of actually playing such causal-explanatory roles. Modal reasoning aimed at discovering metaphysical necessity thus proceeds via essentialist deduction: we move from essentialist truths to reach necessary truths. (shrink)

The paper outlines a view of normativity that combines elements of relativism and expressivism, and applies it to normative concepts in epistemology. The result is a kind of epistemological anti-realism, which denies that epistemic norms can be (in any straightforward sense) correct or incorrect; it does allow some to be better than others, but takes this to be goal-relative and is skeptical of the existence of best norms. It discusses the circularity that arises from the fact that we need to (...) use epistemic norms to gather the facts with which to evaluate epistemic norms; relatedly, it discusses how epistemic norms can rationally evolve. It concludes with some discussion of the impact of this view on "ground level" epistemology. (shrink)

In his précis of a recent book, Richard Joyce writes, “My contention…is that…any epistemological benefit-of-the-doubt that might have been extended to moral beliefs…will be neutralized by the availability of an empirically confirmed moral genealogy that nowhere…presupposes their truth.” Such reasoning – falling under the heading “Genealogical Debunking Arguments” – is now commonplace. But how might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs “neutralize” whatever “epistemological benefit-of-the-doubt that might have been extended (...) to” them? In this article, I argue that there appears to be no satisfactory answer to this question. The problem is quite general, applying to all arguments with the structure of Genealogical Debunking Arguments aimed at realism about a domain meeting two conditions. The Benacerraf-Field Challenge for mathematical realism affords an important special case. (shrink)

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.

Non-skeptical robust realists about normativity, mathematics, or any other domain of non- causal truths are committed to a correlation between their beliefs and non- causal, mind-independent facts. Hartry Field and others have argued that if realists cannot explain this striking correlation, that is a strong reason to reject their theory. Some consider this argument, known as the Benacerraf–Field argument, as the strongest challenge to robust realism about mathematics, normativity, and even logic. In this article I offer two closely related accounts (...) for the type of explanation needed in order to address Field's challenge. I then argue that both accounts imply that the striking correlation to which robust realists are committed is explainable, thereby discharging Field's challenge. Finally, I respond to some objections and end with a few unresolved worries. (shrink)

There are several important arguments in metaethics that rely on explanatory considerations. Gilbert Harman has presented a challenge to the existence of moral facts that depends on the claim that the best explanation of our moral beliefs does not involve moral facts. The Reliability Challenge against moral realism depends on the claim that moral realism is incompatible with there being a satisfying explanation of our reliability about moral truths. The purpose of this chapter is to examine these and related arguments. (...) In particular, this chapter will discuss four kinds of arguments – Harman’s Challenge, evolutionary debunking arguments, irrelevant influence arguments, and the Reliability Challenge – understood as arguments against moral realism. The main goals of this chapter are (i) to articulate the strongest version of these arguments; (ii) to present and assess the central epistemological principles underlying these arguments; and (iii) to determine what a realist would have to do to adequately respond to these arguments. (shrink)

The aim of this essay is to argue that, if a robust form of moral realism is true, then moral vagueness is ontic vagueness. The argument is by elimination: I show that neither semantic nor epistemic approaches to moral vagueness are satisfactory.

There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...) is hard to see how one might argue, on epistemological grounds, for moral antirealism while maintaining commitment to mathematical realism. But it may be possible to do the opposite. (shrink)

Moral disagreement is widely held to pose a threat for metaethical realism and objectivity. In this paper I attempt to understand how it is that moral disagreement is supposed to present a problem for metaethical realism. I do this by going through several distinct (though often related) arguments from disagreement, carefully distinguishing between them, and critically evaluating their merits. My conclusions are rather skeptical: Some of the arguments I discuss fail rather clearly. Others supply with a challenge to realism, but (...) not one we have any reason to believe realism cannot address successfully. Others beg the question against the moral realist, and yet others raise serious objections to realism, but ones that—when carefully stated—can be seen not to be essentially related to moral disagreement. Arguments based on moral disagreement itself have almost no weight, I conclude, against moral realism. (shrink)

Little is known about the aetiology of philosophical intuitions, in spite of their central role in analytic philosophy. This paper provides a psychological account of the intuitions that underlie philosophical practice, with a focus on intuitions that underlie the method of cases. I argue that many philosophical intuitions originate from spontaneous, early-developing, cognitive processes that also play a role in other cognitive domains. Additionally, they have a skilled, practiced, component. Philosophers are expert elicitors of intuitions in the dialectical context of (...) professional philosophy. If this analysis is correct, this should lead to a reassessment of experimental philosophical studies of expertise. (shrink)

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

A number of examples of studies from the field ‘The Philosophy of Mathematical Practice’ (PMP) are given. To characterise this new field, three different strands are identified: an agent-based, a historical, and an epistemological PMP. These differ in how they understand ‘practice’ and which assumptions lie at the core of their investigations. In the last part a general framework, capturing some overall structure of the field, is proposed.

MEANING POSTULATES REINSTATED If I am right in agreeing with Cresswell that the "logicarrlexicaT distinction is one of degree rather than one of kind, that in turn impugns the distinction between the official truth-rules that define logical ...

Non-naturalist realists are committed to the belief, famously voiced by Parfit, that if there are no non-natural facts then nothing matters. But it is morally objectionable to conditionalise all our moral commitments on the question of whether there are non-natural facts. Non-natural facts are causally inefficacious, and so make no difference to the world of our experience. And to be a realist about such facts is to hold that they are mind-independent. It is compatible with our experiences that there are (...) no non-natural facts, or that they are very different from what we think. As Nagel says, realism makes scepticism intelligible. So the non-naturalist must hold that you might be wrong that your partner matters, even if you are correct about every natural, causal fact about your history and relationship. But to hold that conditional attitude to your partner would be a moral betrayal. So believing non-naturalist realism involves doing something immoral. (shrink)

We are fallible creatures, prone to making all sorts of mistakes. So, we should be open to evidence of error. But what constitutes such evidence? And what is it to rationally accommodate it? I approach these questions by considering an evolutionary debunking argument according to which (a) we have good, scientific, reason to think our moral beliefs are mistaken, and (b) rationally accommodating this requires revising our confidence in, or altogether abandoning the suspect beliefs. I present a dilemma for such (...) debunkers, which shows that either we have no reason to worry about our moral beliefs, or we do but we can self-correct. Either way, moral skepticism doesn’t follow. That the evolutionary debunking argument fails is important; also important, however, is what its failure reveals about rational belief revision. Specifically, it suggests that getting evidence of error is a non-trivial endeavor and that we cannot learn that we are likely to be mistaken about some matter from a neutral stance on that matter. (shrink)

In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin Clarke-Doane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms of (something like) general epistemic norms of (...) coincidence avoidance. (shrink)

Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...) turns out to be logical space for a response to the improved challenge where no such space appeared to exist. (shrink)

There’s the question of what there is, and then there’s the question of what ultimately exists. Many contend that, once we have this distinction clearly in mind, we can see that there is no sensible debate to be had about whether there are such things as properties or tables or numbers, and that the only ontological question worth debating is whether such things are ultimate (in one or another sense). I argue that this is a mistake. Taking debates about ordinary (...) objects as a case study, I show that the arguments that animate these debates bear directly on the question of which objects there are and cannot plausibly be recast as arguments about what’s ultimate. I then address the objection that, because they are easy answerable, questions about what there is cannot be a proper subject of ontological debate. (shrink)

Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ (...) claims about mathematical objects, and discuss this view in a broader setting. (shrink)

Many contemporary philosophers rate error theories poorly. We identify the arguments these philosophers invoke, and expose their deficiencies. We thereby show that the prospects for error theory have been systematically underestimated. By undermining general arguments against all error theories, we leave it open whether any more particular arguments against particular error theories are more successful. The merits of error theories need to be settled on a case-by-case basis: there is no good general argument against error theories.

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

ABSTRACTEcumenical Alethic Pluralism is a novel kind of alethic pluralism. It is ecumenical in that it widens the scope of alethic pluralism by allowing for a normatively deflated truth property alongside a variety of normatively robust truth properties. We establish EAP by showing how Wright’s Inflationary Arguments fail in the domain of taste, once a relativist treatment of the metaphysics and epistemology of that domain is endorsed. EAP is highly significant to current debates on the nature of truth insofar as (...) it involves a reconfiguration of the dialectic between deflationists and pluralists. (shrink)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...) express mathematical concepts—they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition. (shrink)

Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...) to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.

In this thesis I seek to advance our understanding of what intuitions are. I argue that intuitions are experiences of a certain kind. In particular, they are experiences with representational content, and with a certain phenomenal character. -/- In Chapter 1 I identify our target and provide some important reliminaries. Intuitions are mental states, but which ones? Giving examples helps: a person has an intuition when it seems to her that torturing the innocent is wrong, or that if something is (...) red it is coloured. We can also provide an initial characterisation of the state by saying that it has representational content, often causes belief, and appears to justify belief. In addition, there is something it is like to have an intuition: intuition has a certain phenomenal character. -/- Some argue that intuition does not explain anything which cannot be explained by other mental states. One version of this view takes intuition to reduce to belief. In Chapter 2 I argue that this entails that agents are rationally criticisable in situations where we know they are not, and that such views are therefore untenable. A parallel argument shows that the corresponding approach to perception fails. This suggests a similarity in nature: both intuition and perception are experiences. -/- Others take intuition to reduce to a disposition to have a belief. In Chapter 3 I consider a line of argument against such views, find it unsuccessful, and present two new arguments. One is likely to be dialectically ineffective. The other suffers no such weakness: it shows that the proposed reduction fails. As before, the argument also applies to perception, and suggests that intuition and perception are both experiences. -/- In the remainder of the thesis I develop an account of intuition as an experience. I distinguish between content-specific and attitude-specific phenomenology, and argue that intuition lacks the former (Chapter 4), but has the latter (Chapter 5). This allows us to say what intuition is: it is is an experience with representational content and with attitude-specific phenomenology of a certain kind. -/- In Chapter 6 I put this account of intuition to use. When a person has a perceptual or intuitional experience, I argue that simply having the experience is what makes the subject justified in believing what the experience represents. Moreover, what explains that intuition and perception can justify belief in this way is precisely their phenomenal character. (shrink)

ABSTRACT The idea that two words can be instances of the same word is a central intuition in our conception of language. This fact underlies many of the claims that we make about how we communicate, and how we understand each other. Given this, irrespective of what we think words are, it is common to think that any putative ontology of words, must be able to explain this feature of language. That is, we need to provide criteria of identity for (...) word-types which allow us to individuate words such that it can be the case that two particular word-instances are instances of the same word-type. One solution, recently further developed by Irmak, holds that words are individuated by their history. In this paper, I argue that this view either fails to account for our intuitions about word identity, or is too vague to be a plausible answer to the problem of word individuation. (shrink)