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)

Those who aim to give an account of modal knowledge face two challenges: the integration challenge of reconciling an account of what is involved in knowing modal truths with a plausible story about how we can come to know them, and the reliability challenge of giving a plausible account of how we could have evolved a reliable capacity to acquire modal knowledge. I argue that recent counterfactual and dispositional accounts of modal knowledge cannot solve these problems regarding specifically metaphysical modal (...) truths—leaving us with the threat of skepticism about large portions of metaphysics, and certain other areas of philosophy. I argue, however, that both of these problems look insuperable only if we assume that metaphysical modal discourse serves a describing or tracking function. If we adopt instead a normativist approach to metaphysical modal discourse, which sees the basic function of modal discourse as giving us perspicuous ways of conveying, reasoning with, and renegotiating semantic rules, the problems show up very differently. The modal normativist can give a plausible response to both of the classic problems of how we can come to know metaphysical modal truths. (shrink)

Why Only Us? Language and Evolution By BerwickRobert C. and ChomskyNoamMassachusetts Institute of Technology, 2015. 224 pp. £17.95 paper.

Explanation in Ethics and Mathematics: Debunking and Dispensability By LeibowitzUri D. and SinclairNeilOxford University Press, 2016. x + 258 pp. £45.00.

Hartry Field’s epistemological challenge to the mathematical platonist is often cast as an improvement on Paul Benacerraf’s original epistemological challenge. I disagree. While Field’s challenge is more difficult for the platonist to address than Benacerraf’s, I argue that this is because Field’s version is a special case of what I call the ‘sociological challenge’. The sociological challenge applies equally to platonists and fictionalists, and addressing it requires a serious examination of mathematical practice. I argue that the non-sociological part of Field’s (...) challenge amounts to a minor reformulation of Benacerraf’s original challenge. So, I contend, Field’s challenge is not an improvement on Benacerraf’s. What is new to Field’s challenge is as much a problem for the fictionalist as it is for the platonist. (shrink)

ABSTRACTSome proponents of the evolutionary debunking argument against moral realism believe that replies that assume substantive moral claims beg the question. In this paper, I give a new account of what's wrong with such replies. On this account, many realists beg the question when they rely on substantive moral claims in their replies to the argument, but naturalists do not. While this account generalizes to some other domains, it allows perceptual and inductive realism to remain undebunked.

How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize (...) in this way the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. This paper suggests that, in order to naturalize mathematics through Darwinism, it is better to take the method of mathematics not to be the axiomatic method. (shrink)

I argue that recent attempts to deflect Access Problems for realism about a priori domains such as mathematics, logic, morality, and modality using arguments from evolution result in two kinds of explanatory overkill: the Access Problem is eliminated for contentious domains, and realist belief becomes viciously immune to arguments from dispensability, and to non-rebutting counter-arguments more generally.

Many philosophers believe that when a theory is committed to an apparently unexplainable massive correlation, that fact counts significantly against the theory. Philosophical theories that imply that we have knowledge of non-causal mind-independent facts are especially prone to this objection. Prominent examples of such theories are mathematical Platonism, robust normative realism and modal realism. It is sometimes thought that theists can easily respond to this sort of challenge and that theism therefore has an epistemic advantage over atheism. In this paper, (...) I will argue that, contrary to widespread thought, some versions of theism only push the challenge one step further and thus are in no better position than atheism. (shrink)

Scanlon’s Being Realistic about Reasons (BRR) is a beautiful book – sleek, sophisticated, and programmatic. One of its key aims is to demystify knowledge of normative and mathematical truths. In this article, I develop an epistemological problem that Scanlon fails to explicitly address. I argue that his “metaphysical pluralism” can be understood as a response to that problem. However, it resolves the problem only if it undercuts the objectivity of normative and mathematical inquiry.

I critically examine an evolutionary debunking argument against moral realism. The key premise of the argument is that there is no adequate explanation of our moral reliability. I search for the strongest version of the argument; this involves exploring how ‘adequate explanation’ could be understood such that the key premise comes out true. Finally, I give a reductio: in the sense in which there is no adequate explanation of our moral reliability, there is equally no adequate explanation of our inductive (...) reliability. Thus, the argument that would debunk our moral views would also, absurdly, debunk all inductive reasoning. (shrink)

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)

I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...) to doubt that our F-beliefs are modally secure. (shrink)

_ Source: _Page Count 24 Accounts of non-naturalist moral perception have been advertised as an empiricist-friendly epistemological alternative to moral rationalism. I argue that these accounts of moral perception conceal a core commitment of rationalism—to substantive a priori justification—and embody its most objectionable feature—namely, “mysteriousness.” Thus, accounts of non-naturalist moral perception do not amount to an interesting alternative to moral rationalism.

Do the facts of evolution generate an epistemic challenge to moral realism? Some think so, and many “evolutionary debunking arguments” have been discussed in the recent literature. But they are all murky right where it counts most: exactly which epistemic principle is meant to take us from evolutionary considerations to the skeptical conclusion? Here, I will identify several distinct species of evolutionary debunking argument in the literature, each one of which relies on a distinct epistemic principle. Drawing on recent work (...) in epistemology, I will show that most of these initially plausible principles are false, spoiling the arguments that rely on them. And we will see that each argument threatens only one popular view of moral psychology: a “Representationalist” view on which our moral judgments rely crucially on a mental intermediary—e.g. a sentiment, gut reaction, or affect-laden intuition—delivered by our evolved moral faculty. In the end, only one evolutionary debunking argument remains a menace: an “ Argument from Symmetry ” that I will introduce to the literature. But we will see that it should worry only all naturalists, pressuring them into a trilemma: give up moral realism, accept a rationalism that is incongruous with naturalism, or give up naturalism. Non-naturalists are free and clear. (shrink)

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.

In an influential book, Gilbert Harman writes, "In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles [1977, 9 – 10]." What is the epistemological relevance of this contrast, if genuine? In this article, I argue that ethicists and philosophers of mathematics have misunderstood it. They have confused what I will call the justificatory challenge for realism about an (...) area, D – the challenge to justify our D-beliefs – with the reliability challenge for D-realism – the challenge to explain the reliability of our D-beliefs. Harman’s contrast is relevant to the first, but not, evidently, to the second. One upshot of the discussion is that genealogical debunking arguments are fallacious. Another is that indispensability considerations cannot answer the Benacerraf-Field epistemological challenge for mathematical realism. (shrink)

Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. It also provides advice (...) on which lines of discussion promise to be the most fruitful. (shrink)

Many hope that our values, purged of messy human contingency, could aspire to correspond with mind-independent, rationally obligatory, and eternal ethical facts. But if the arguments of this thesis are on the right track, we should reject the search for non-natural and mind-independent moral truths.

This chapter discusses epistemic objections to non-naturalist moral realism. The goal of the chapter is to determine which objections are pressing and which objections can safely be dismissed. The chapter examines five families of objections: (i) one involving necessary conditions on knowledge, (ii) one involving the idea that the causal history of our moral beliefs reflects the significant impact of irrelevant influences, (iii) one relying on the idea that moral truths do not play a role in explaining our moral beliefs, (...) (iv) one involving the claim that if moral realism is true then our moral beliefs are unlikely to be reliable, and (v) one involving the claim that moral realism is incompatible with there being a plausible explanation of our reliability about morality. The overall conclusion of the chapter is that the final objection is by far the most pressing. (shrink)

According to principles of modal security, evidence undermines a belief only when it calls into question certain purportedly important modal connections between one’s beliefs and the truth (e.g., safety or sensitivity). Justin Clarke-Doane and Dan Baras have advanced such principles with the aim of blocking evolutionary moral debunking arguments. We examine a variety of different principles of modal security, showing that some of these are too strong, failing to accommodate clear cases of undermining, while others are too weak, failing to (...) do their advertised work of blocking evolutionary moral debunking arguments. If there is a security principle that slips between the horns of this dilemma—one that is both viable and debunker-blocking—it remains to be formulated. (shrink)

In the recent literature on the nature of knowledge, a rivalry has emerged between modalism and explanationism. According to modalism, knowledge requires that our beliefs track the truth across some appropriate set of possible worlds. Modalists tend to focus on two modal conditions: sensitivity and safety. According to explanationism, knowledge requires only that beliefs bear the right sort of explanatory relation to the truth. In slogan form: knowledge is believing something because it’s true. In this paper, we aim to vindicate (...) explanationism from some recent objections offered by Gualtiero Piccinini, Dario Mortini, and Kenneth Boyce and Andrew Moon. Together, these authors present five purported counterexamples to the sufficiency of the explanationist analysis for knowledge. In addition, Mortini devises a clever argument that explanationism entails the violation of a plausible closure principle on knowledge. We will argue that explanationism is innocent of all these charges against it, and we hope that the strength of the defense we offer of explanationism is evidence in its favor, and a reason to investigate explanationism further as the long-elusive truth about the nature of knowledge. (shrink)

One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals to Boghossian’s notion of (...) epistemic analyticity are particularly common here, as are appeals to some broadly pragmatic account of the good standing of basic beliefs. I argue, though, that these appeals are hopeless: an argument adapted from the Benacerraf–Field challenge shows that, even if some such theory can deliver the verdict that our beliefs about abstract objects have some prima facie good standing, this good standing will inevitably be defeated. (shrink)

At the core of the recent debate over moral debunking arguments is a disagreement between explanationist and modalist approaches. Explanationists think that the lack of an explanatory connection between our moral beliefs and the moral truths, given a non-naturalist realist conception of morality, is a reason to reject non-naturalism. Modalists disagree. They say that, given non-naturalism, our beliefs have the appropriate modal features with respect to truth -- in particular they are safe and sensitive -- so there is no problem. (...) -/- There is something of a stand-off here. I argue, though, that by looking at the role explanatory and modal factors have to play in theory choice more generally, and, in particular, by considering the practice of theory choice in science, we can see that the explanationist is right. The lack of an explanatory connection between our moral beliefs and the moral truths is a reason to reject non-naturalist realism about morality. (shrink)

The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are postulated (...) to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles stereotypical philosophy. We conclude by distinguishing two ideas that have long been associated -- realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective in roughly the sense that the question, ‘Is the Parallel Postulate is true?’, understood as one of pure mathematics, fails to be. Another is a kind of pragmatism. Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones. -/- . (shrink)

The Reliability Challenge to moral non-naturalism has received substantial attention recently in the literature on moral epistemology. While the popularity of this particular challenge is a recent development, the challenge has a long history, as the form of this challenge can be traced back to a skeptical challenge in the philosophy of mathematics raised by Paul Benacerraf. The current Reliability Challenge is widely regarded as the most sophisticated way to develop this skeptical line of thinking, making the Reliability Challenge the (...) strongest epistemic challenge to normative nonnaturalism. In this paper, I argue that the innovations that have occurred since Benacerraf’s statement of the challenge are misconceived and confused in a number of ways. The Reliability Challenge is not the most potent epistemic challenge to moral non-naturalism. The most potent challenge comes from the fact that there is a causal condition on knowledge – or, more precisely, a becaual condition – that non-natural moral facts cannot satisfy. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...) will then advocate the theory on the grounds that it accomplishes all of Lewis’s “new work” while providing a gain in parsimony and a new account of fine-grained content. I will close with a discussion of how the theory also affords a new reply to two objections to uninstantiated universals: Armstrong’s charge that they are inconsistent with naturalism, and a Benacerraf-Field-style objection about epistemic access. (shrink)

In this thesis, I will explore the epistemological evolutionary debunking arguments in meta-ethics. I will defend these arguments by accomplishing two tasks: I will offer the best way to understand the EDA and I will also respond to two strongest objections to the EDA. Firstly, in Part I of this thesis, I will offer my account of how the EDA should be best formulated. I will start from how evolution has significantly influenced our moral beliefs. I will then explain why, (...) due to their evolutionary origin, our moral beliefs are not tracking the moral truth reliably. Furthermore, I will argue that the fact that our moral beliefs are not tracking the moral truth also provides an undercutting and a higher-order defeater for those beliefs. As a result, I will conclude that the epistemic status of our moral beliefs is undermined because of these two kinds of defeaters. Secondly, in Part II of this thesis, I will turn my attention to the two strongest objections to the EDA – the Conceptual Truth Objection and the Third Factor Objection. I will first offer two responses to the Conceptual Truth Objection and, based on these two responses, I will argue that the Conceptual Truth Objection fails as a challenge to the EDA. I will then also argue that there currently doesn’t exist an acceptable version of the Third Factor Objection and it is also unlikely that such a version could be constructed in the future. I will finally conclude that both objections are problematic and they are thus unable to give us reason to doubt the EDA. (shrink)

Many moral debunking arguments are driven by the idea that the correlation between our moral beliefs and the moral truths is a big coincidence, given a robustly realist conception of morality.One influential response is that the correlation is not a coincidence because there is a common explainer of our moral beliefs and the moral truths. For example, the reason that I believe that I should feed my child is because feeding my child helps them to survive, and natural selection instills (...) in me beliefs and dispositions that help my children survive since that is conductive to my genes continuing through the generations. Similarly, the reason that it's morally good to feed my child is because it helps them to survive, and survival is morally valuable.But if we look at some cases from scientific practice, and from everyday life, we can see, I argue, why this response fails. A correlation can be coincidental even if there is a common explainer. I give an account of the nature of coincidence that draws upon recent literature on scientific explanation and argue that the correlation between moral belief and moral truth is a coincidence, even given such common explainers. And I use this to defend a certain form of debunking argument. (shrink)

Plausibly, agents act freely iff their actions are responses to reasons. But what sort of relationship between reason and action is required for the action to count as a response? The overwhelmingly dominant answer to this question is modalist. It holds that responses are actions that share a modally robust or secure relationship with the relevant reasons. This thesis offers a new alternative answer. It argues that responses are actions that can be explained by reasons in the right way. This (...) explanationist answer comes apart from the modalist answer. For it holds that actions are responses to reasons if they are explained by those reasons even if they don’t share a modally robust relationship. Explanationism thus offers a novel way of vindicating the intuition that alternative possibilities don’t matter to responding to reasons and (consequently) free agency. The key dialectical position the thesis develops is that both modalism and explanationism constitute attempts to capture he core type of relationship encoded by the notion of a response. Responses to reasons, at core, involve a non-accidental relationship between reason and action. We can either understand non-accidentality as a modal phenomenon – as a modally robust tracking between two facts. Or we can understand non-accidentality as an explanatory phenomenon – as a special explanatory relationship between two facts. According to my rival explanationist proposal, two facts share a non-accidental relationship iff we can give a unified explanation of why both obtain. Unified explanations are explanations of why [p&q] that cannot be decomposed into two (or more) separate independent explanations of p and of q. Consequently, according to explanationism about responding to reasons, actions are responses to reasons iff those reasons offer a rational explanation of the action that cannot be decomposed into separate independent components. (shrink)

Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...) version of Field’s epistemological objection which has both Neutrality and Force can be construed. (shrink)

This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...) and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is intelligible. The book concludes with a complementary ‘pluralism’ about modality, logic and normative theory, highlighting its revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism. (shrink)

Non-naturalism is the view that normative properties are response-independent, irreducible to natural properties, and causally inefficacious. An underexplored question for non-naturalism concerns the metasemantics of normative terms. Ideally, the non-naturalist could remain ecumenical, but it appears they cannot. Call this challenge the metasemantic challenge. This chapter suggests that non-naturalists endorse an epistemic account of reference determination of the sort recently defended by Imogen Dickie, with some modifications. An important implication of this account is that, if correct, a fully fleshed out (...) moral epistemology will simultaneously rebut metasemantic objections to non-naturalism. Thus, both the metasemantic and the more widely discussed epistemological challenges in effect amount to one. Before setting out the positive view, the chapter considers why all of the traditional metasemantic theories cause trouble for the non-naturalist. This includes discussions of teleosemantics, conceptual role semantics, as well as Schroeter and Schroeter’s “connectedness” model. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument strongly motivates nominalism, it also undermines (...) certain nominalist theories. (shrink)

Shamik Dasgupta (2016) proposes to tame the Principle of Sufficient Reason (PSR) to apply to only non-autonomous facts, which are facts that are apt for explanation. Call this strategy to tame the PSR the taming strategy. In a recent paper, Della Rocca (2020a) argues that proponents of the taming strategy, in attempting to formulate a restricted version of the PSR, nevertheless find themselves committed to endorsing a form of radical monism, which, in turn, leads right back to an untamed-PSR. Suppose, (...) for the sake of argument, that Della Rocca is right. My question is this: Is there reason to believe the principle of sufficient reason (in its untamed version)? In this paper, I argue that it is impossible for there to be a reason to believe the untamed-PSR. (shrink)

Sensitivity has sometimes been thought to be a highly epistemologically significant property, serving as a proxy for a kind of responsiveness to the facts that ensure that the truth of our beliefs isn’t just a lucky coincidence. But it's an imperfect proxy: there are various well-known cases in which sensitivity-based anti-luck conditions return the wrong verdicts. And as a result of these failures, contemporary theorists often dismiss such conditions out of hand. I show here, though, that a sensitivity-based understanding of (...) epistemic luck can be developed that respects what was attractive about sensitivity-based approaches in the first place but that's immune to these failures. (shrink)

The dominant theory of the evolution of moral cognition across a variety of fields is that moral cognition is a biological adaptation to foster social cooperation. This chapter argues, to the contrary, that moral cognition is likely an evolutionary exaptation: a form of cognition where neurobiological capacities selected for in our evolutionary history for a variety of different reasons—many unrelated to social cooperation—were put to a new, prosocial use after the fact through individual rationality, learning, and the development and transmission (...) of social norms. This chapter begins with a brief overview of the emerging behavioral neuroscience of moral cognition. It then outlines a novel theory of moral cognition that I have previously argued explains these findings better than alternatives. Finally, it shows how the evidence for this theory of moral cognition and human evolutionary history together suggest that moral cognition is likely not a biological adaptation. Instead, like reading sheet music or riding a bicycle, moral cognition is something that individuals learn to do—in this case, in response to sociocultural norms created in our ancestral history and passed down through the ages to enable cooperative living. (shrink)

While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate this (...) phenomenon. One of the important upshots is that, contrary to the current consensus, low prior probability is not a necessary condition for calling for explanation. In the final section I explain how the results of this inquiry help us make progress in assessing Hartry Field’s style of reliability argument against mathematical Platonism and against robust realism in other domains of necessary facts, such as ethics. (shrink)

Objects appear to fall into different sorts, each with their own criteria for identity. This raises the question of whether sorts overlap. Abstractionists about numbers—those who think natural numbers are objects characterized by abstraction principles—face an acute version of this problem. Many abstraction principles appear to characterize the natural numbers. If each abstraction principle determines its own sort, then there is no single subject-matter of arithmetic—there are too many numbers. That is, unless objects can belong to more than one sort. (...) But if there are multi-sorted objects, there should be cross-sortal identity principles for identifying objects across sorts. The going cross-sortal identity principle, ECIA2 of Cook and Ebert (2005), solves the problem of too many numbers. But, I argue, it does so at a high cost. I therefore propose a novel cross-sortal identity principle, based on embeddings of the induced models of abstracts developed by Walsh (2012). The new criterion matches ECIA2’s success, but offers interestingly different answers to the more controversial identifications made by ECIA2. (shrink)

Modalists think that knowledge requires forming your belief in a “modally stable” way: using a method that wouldn't easily go wrong, or using a method that wouldn't have given you this belief had it been false. Recent Modalist projects from Justin Clarke-Doane and Dan Baras defend a principle they call “Modal Security,” roughly: if evidence undermines your belief, then it must give you a reason to doubt the safety or sensitivity of your belief. Another recent Modalist project from Carlotta Pavese (...) and Bob Beddor defends “Modal Virtue Epistemology”: knowledge is a belief that is maximally modally robust across “normal” worlds. We'll offer new objections to these recent Modalist projects. We will then argue for a rival view, Explanationism: knowing something is believing it because it's true. We will show how Explanationism offers a better account of undermining defeaters than Modalism, and a better account of knowledge. (shrink)

Evolutionary debunkers claim that evolutionary explanations of moral phenomena lead to sceptical conclusions. The aim of this paper is to show that even if we grant debunkers the speculative claims that evolution provides the best explanation of moral phenomena and that there are no other moral phenomena for which moral facts/properties are indispensable, the sceptical conclusions debunkers seek to establish still do not follow. The problem for debunkers is to link the empirical explanatory claim to the normative conclusion that moral (...) beliefs are unjustified. The paper argues that debunkers face a dilemma, and that neither of the two options available to them supports the sceptical conclusions for which they aim. Consequently, it is claimed, the dialectical force of evolutionary debunking arguments is, at best, exceedingly weak. (shrink)

The idea that justified modal belief can be accounted for in terms of empirically justified, non-modal belief is enjoying increasing popularity in the epistemology of modality. One alleged reason to prefer modal empiricism over more traditional, rationalist modal epistemologies is that empiricism avoids the problem with the integration challenge that arise for rationalism, assuming that we want to be realists about modal metaphysics. In this paper, I argue that given two very reasonable constraints on what it means to meet the (...) integration challenge for modality, empiricism is currently at best on a par with, but potentially worse off than, rationalist alternatives, with respect to the integration challenge. (shrink)

This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...) of the argument. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

Modal Security is an increasingly discussed proposed necessary condition on undermining defeat. Modal Security says, roughly, that if evidence undermines (rather than rebuts) one’s belief, then one gets reason to doubt the belief's safety or sensitivity. The primary interest of the principle is that it seems to entail that influential epistemological arguments, including Evolutionary Debunking Arguments against moral realism and the Benacerraf-Field Challenge for mathematical realism, are unsound. The purpose of this paper is to critically examine Modal Security in detail. (...) We develop and discuss what we take to be the strongest objections to the principle. One of the aims of the paper is to expose the weakness of these objections. Another is to reveal how the debate over Modal Security interacts with core problems in epistemology — including the generality problem, and the distinction between direct and indirect evidence. (shrink)

Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. (...) I argue that some are are merely apparent, while others are of little consequence. There is a difference between the cases. But it is not an epistemological difference per se. The difference, surprisingly, is that ethical knowledge, if it is practical, cannot fail to be objective in a way that mathematical knowledge can. One upshot of the discussion is radicalization of Moore’s Open Question Argument. Another is that the concepts of realism and objectivity, which are widely identified, are actually in tension. (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)