This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...) to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic. (shrink)

Theodore Sider’s recent book, “Writing the Book of the World”, employs a primitive notion of metaphysical structure in order to make sense of substantive metaphysics. But Sider and others who employ metaphysical primitives face serious epistemological challenges. In the first section I develop a specific form of this challenge for Sider’s own proposed epistemology for structure; the second section develops a general reliability challenge for Sider’s theory; and the third and final section argues for the rejection of Siderean structure in (...) the course of answering a transcendental argument against such rejection. (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)

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)

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

Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...) remarks about the big three schools. This seems a reasonable approach to the issues both because most observers are familiar, at least in a general way, with the tenets of Intuitionism, Formalism, and Logicism, and because it is in reaction to these that contemporary Platonism has taken shape. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I (...) believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) as it is exercised by ordinary people. I do so by looking at the different theories that have been put forward in the recent debate, and showing for each of these that they are unable to account for the mathematical practices of ordinary people. In order to show that these practices do need to be accounted for, I also argue that ordinary people are doing mathematics, i.e. that they engage in properly mathematical practices. Because these practices are properly mathematical, they should be accounted for by any philosophy of mathematics. The conclusion of my thesis, then, is that current theories fail to do something that they should do, while remaining neutral on how well they perform when it comes to accounting for the practices of professional mathematicians. (shrink)

The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.

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)

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone, that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, (...) and offer another - considerably simpler - solution. (shrink)

Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...) account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (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)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

The fact that debunkers can turn to the argument from disagreement for help is ofcourse not a surprise. After all, both types of challenge basically pursue the same,skeptical conclusion. What I have tried to show, however, is that they are related in amore intimate way.

This chapter examines the status of inference to the best explanation in naturalistic metaphysics. The methodology of inference to the best explanation in metaphysics is studied from the perspective of contemporary views on scientific explanation and explanatory inferences in the history and philosophy of science. This reveals serious shortcomings in prevalent attempts to vindicate metaphysical "explanationism" by reference to similarities between science and naturalistic metaphysics. This critique is brought out by considering a common gambit of methodological unity: (1) Both metaphysics (...) and science employ inference to the best explanation. (2) One has no reason to think that if explanationism is truth-conducive in science, it is not so in metaphysics. (3) One has a positive reason to think that if explanationism is truth-conducive in science, it is also so in metaphysics. (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)

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)

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

Evolutionary debunking arguments move from a premise about the influence of evolutionary forces on our moral beliefs to a skeptical conclusion about those beliefs. My primary aim is to clarify this empirically grounded epistemological challenge. I begin by distinguishing among importantly different sorts of epistemological attacks. I then demonstrate that instances of each appear in the literature under the ‘evolutionary debunking’ title. Distinguishing them clears up some confusions and helps us better understand the structure and potential of evolutionary debunking arguments.

Can Quine’s criterion for ontological commitment be comparatively applied across different logics? If so, how? Cross-logical evaluations of discourses are central to contemporary philosophy of mathematics and metaphysics. The focus here is on the influential and important arguments of George Boolos and David Lewis that second-order logic and plural quantification don’t incur additional ontological commitments over and above those incurred by first-order quantifiers. These arguments are challenged by the exhibition of a technical tool—the truncation-model construction of notational equivalents—that compares the (...) ontological role and increased expressive strength of non-first-order ideology to first-order ideology. (shrink)

In this essay, the tension that Benacerraf identifies for theories of mathematical truth is used as the vehicle for arguing against a particular desideratum for semantic theories. More specifically, I place in question the desideratum that a semantic theory, provided for some area of discourse, should run in parallel with the semantic theory holding for the rest of the language. The importance of this desideratum is also made clear by means of tracing out the subtle implications of its rejection.

Hartry Field has argued that mathematical realism is epistemologically problematic, because the realist is unable to explain the supposed reliability of our mathematical beliefs. In some of his discussions of this point, Field backs up his argument by saying that our purely mathematical beliefs do not ‘counterfactually depend on the facts’. I argue that counterfactual dependence is irrelevant in this context; it does nothing to bolster Field's argument.

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)

The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, others ‘thin’ (...) and ontologically peripheral—and examine this distinction in relation to some notable ‘ontic’ accounts of explanation. I also discuss the issue in the broader context of other ‘explanationist’ realist arguments. (shrink)

I develop a non-representationalist account of mathematical thought, on which the point of mathematical theorizing is to provide us with the conceptual capacity to structure and articulate information about the physical world in an epistemically useful way. On my view, accepting a mathematical theory is not a matter of having a belief about some subject matter; it is rather a matter of structuring logical space, in a sense to be made precise. This provides an elegant account of the cognitive utility (...) of mathematics. Further, it makes explicit how the brand of non-representationalism I develop is compatible with there being substantive rationality constraints on our mathematical theorizing. (shrink)

This paper argues for a certain kind of anti-metaphysicalism about the temporal ontology debate, i.e., the debate between presentists and eternalists over the existence of past and future objects. Three different kinds of anti-metaphysicalism are defined—namely, non-factualism, physical-empiricism, and trivialism. The paper argues for the disjunction of these three views. It is then argued that trivialism is false, so that either non-factualism or physical-empiricism is true. Finally, the paper ends with a discussion of whether we should endorse non-factualism or physical-empiricism. (...) An initial reason is provided for thinking that non-factualism might be true, but in the end, the paper leaves this question open. The paper also argues against a certain kind of necessitarianism about the temporal ontology debate; but this isn't an extra job—the falsity of this necessitarian view falls out of the other arguments as a sort of corollary. (shrink)

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)

There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a (...) liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses. (shrink)

The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist (...) response. Either way, the explanatory indispensability argument is no improvement on the standard one. (shrink)

Jonas Olson presents a critical survey of moral error theory, the view that there are no moral facts and so all moral claims are false. Part I explores the historical context of the debate; Part II assesses J. L. Mackie's famous arguments; Part III defends error theory against challenges and considers its implications for our moral thinking.

Which concepts should we use to think and talk about the world, and to do all of the other things that mental and linguistic representation facilitates? This is the guiding question of the field that we call ‘conceptual ethics’. Conceptual ethics is not often discussed as its own systematic branch of normative theory. A case can nevertheless be made that the field is already quite active, with contributions coming in from areas as diverse as fundamental metaphysics and social/political philosophy. In (...) this pair of papers, we try to unify the field, reflecting on its basic nature, structure, and methodology. (shrink)

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)

The indispensability argument seeks to establish the existence of mathematical objects. The success of the indispensability argument turns on finding cases of genuine extra- mathematical explanation. In this paper, I identify a new case of extra- mathematical explanation, involving the search patterns of fully-aquatic marine predators. I go on to use this case to predict the prevalence of extra- mathematical explanation in science.

The paper discusses the ontology of Zdzisław Augustynek, especially the part of this ontology that relates to space and time. This position is analyzed as an attempt to implement two methodological postulates, namely the postulates of reductionism and scientific realism.

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

The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the (...) realist position, I propose a new type of example, drawing on probabilistic considerations. 1 Introduction2 Mathematical Explanations2.1 ‘Simplicity’3 An Average Story: The Banana Game3.1 Some clarifications3.2 Hopes and troubles for the nominalist3.3 New hopes?3.4 New troubles4 Conclusion. (shrink)

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)

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)

An argument is epistemically self-defeating when either the truth of an argument’s conclusion or belief in an argument’s conclusion defeats one’s justification to believe at least one of that argument’s premises. Some extant defenses of the evidentiary value of intuition have invoked considerations of epistemic self-defeat in their defense. I argue that there is one kind of argument against intuition, an unreliability argument, which, even if epistemically self-defeating, can still imply that we are not justified in thinking intuition has evidentiary (...) value. (shrink)

Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? Second, the Grounding (...) Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstract objects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)

Develops an empirical argument against naive realism-disjunctivism: if naive realists accept "internal dependence", then they cannot explain the evolution of perceptual success. Also presents a puzzle about our knowledge of universals.

It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for moral realism is equally a challenge for (...) mathematical realism. It is widely thought not to be. In this paper, I argue that the Evolutionary Challenge for moral realism is equally a challenge for mathematical realism. Along the way, I substantially clarify the Evolutionary Challenge, discuss its relation to more familiar epistemological challenges, and broach the problem of moral disagreement. The paper should be of interest to ethicists because it places pressure on anyone who rejects moral realism on the basis of the Evolutionary Challenge to reject mathematical realism as well. And the paper should be of interest to philosophers of mathematics because it presents a new epistemological challenge for mathematical realism that bears, I argue, no simple relation to Paul Benacerraf's familiar challenge. (shrink)

In this paper I assume that we have some intuitive knowledge—i.e. beliefs that amount to knowledge because they are based on intuitions. The question I take up is this: given that some intuition makes a belief based on it amount to knowledge, in virtue of what does it do so? We can ask a similar question about perception. That is: given that some perception makes a belief based on it amount to knowledge, in virtue of what does it do so? (...) A natural idea about perception is that a perception makes a belief amount to knowledge in part by making you sensorily aware of the concrete objects it is about. The analogous idea about intuition is that an intuition makes a belief amount to knowledge in part by making you intellectually aware of the abstract objects it is about. I expand both ideas into fuller accounts of perceptual and intuitive knowledge, explain the main challenge to this sort of account of intuitive knowledge (i.e. the challenge of making sense of intellectual awareness), and develop a response to it. (shrink)

It is our contention that an ontological commitment to propositions faces a number of problems; so many, in fact, that an attitude of realism towards propositions—understood the usual “platonistic” way, as a kind of mind- and language-independent abstract entity—is ultimately untenable. The particular worries about propositions that marshal parallel problems that Paul Benacerraf has raised for mathematical platonists. At the same time, the utility of “proposition-talk”—indeed, the apparent linguistic commitment evident in our use of 'that'-clauses (in offering explanations and making (...) predictions)—is also in need of explanation. We account for this with a fictionalist analysis of our use of 'that'-clauses. Our account avoids certain problems that arise for the usual error-theoretic versions of fictionalism because we apply the notion of semantic pretense to develop an alternative, pretense-involving, non-error-theoretic, fictionalist account of proposition-talk. (shrink)

Ontologically minimal truth law semantics are provided for various branches of formal logic (classical propositional logic, S5 modal propositional logic, intuitionistic propositional logic, classical elementary predicate logic, free logic, and elementary arithmetic). For all of them logical validity/truth is defined in an ontologically minimal way, that is, not via truth value assignments or interpretations. Semantical soundness and completeness are proved (in an ontologically minimal way) for a calculus of classical elementary predicate logic.

In a recent paper Weinberg (2007) claims that there is an essential mark of trustworthiness which typical sources of evidence as perception or memory have, but philosophical intuitions lack, namely that we are able to detect and correct errors produced by these “hopeful” sources. In my paper I will argue that being a hopeful source isn't necessary for providing us with evidence. I then will show that, given some plausible background assumptions, intuitions at least come close to being hopeful, if (...) they are reliable. If this is true, Weinberg's new challenge comes down to the claim that philosophical intuitions are not reliable since they are significantly unstable. In the second part of my paper I will argue that and why the experimentally established instability of folk intuitions about philosophical cases does not show that philosopher's expert intuitions about these cases are instable. (shrink)

This article discusses the argument we cannot have knowledge of abstract entities because they are not part of the causal order. The claim of this article is that the argument fails because of equivocation. Assume that the “causal order” is concerned with contingent facts involving time and space. Even if the existence of abstract entities is not contingent and does not involve time or space it does not follow that no truths about abstract entities are contingent or involve time or (...) space. I argue that it is the latter which is required to obtain the desired conclusion. (shrink)