Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)
Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are (...) extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is.. (shrink)
When a person acts from ignorance, he is culpable for his action only if he is culpable for the ignorance from which he acts. The paper defends the view that this principle holds, not just for actions done from ordinary factual ignorance, but also for actions done from moral ignorance. The question is raised whether the principle extends to action done from ignorance about what one has most reason to do. It is tentatively proposed that the principle holds in full (...) generality. (shrink)
It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.
This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)
Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...) empiricism so understood is self-undermining. (shrink)
1. Professor Brandom’s paper is addressed to a methodological question: When we set out to account for the intentionality of thought and language, what resources may we exploit? Which notions may we use? Brandom is a famously ambitious theorist. Unlike his colleague, John McDowell, Brandom has long maintained that we should at least aspire to explain intentionality in non-intentional terms. This leaves it open, however, which non-intentional resources are legitimate.
This chapter explores bridge-law non-naturalism: the view that when a particular thing possesses a moral property or stands in a moral relation, this fact is metaphysically grounded in non-normative features of the thing in question together with a general moral law. Any view of this sort faces two challenges, analogous to familiar challenges in the philosophy of science: to specify the form of the explanatory laws, and to say when a fact of that form qualifies as a law. The chapter (...) explores three strategies for answering these questions, all of which maintain that a moral law is a true generalization of the form [It is normatively necessary that whatever ϕs is F]. (shrink)
This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague objects (...) ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)
Fictionalism about possible worlds is the view that talk about worlds in the analysis of modality is to be construed as ontologically innocent discourse about the content of a fiction. Versions of the view have been defended by D M Armstrong (in "A Combinatorial Theory of Possibility") and by myself (in "Modal Fictionalism', "Mind" 99, July 1990). The present note argues that fictionalist accounts of modality (both Armstrong's version and my own) fail to serve the fictionalists ontological purposes because they (...) imply that as a matter of necessity there exist many worlds. (shrink)
According to one sort of epistemic relativist, normative epistemic claims (e.g., evidence E justifies hypothesis H) are never true or false simpliciter, but only relative to one or another epistemic system. In chapter 6 of Fear of Knowledge, Paul Boghossian objects to this view on the ground that its central notions cannot be explained, and that it cannot account for the normativity of epistemic discourse. This paper explores how the dogged relativist might respond.
Wallace does not provide an explicit account of moral fairness. Rather he gives substance the notion by articulating two concrete principles governing blame which are meant to be—and in some sense clearly are—demands of fairness.
The paper examines the conditions under which we are responsible for actions performed under duress, focusing on a real case in which a soldier was compelled at gunpoint to participate in the massacre of civilian prisoners. The case stands for a class of cases in which the compelled act is neither clearly justified nor clearly excused on grounds of temporary incapacity, but in which it is nonetheless plausible that the agent is not morally blameworthy. The theoretical challenge is to identify (...) the excuse in such cases and to explain its basis. The paper argues that when mortal duress excuses in cases of this sort, it does so because the compelled act, though impermissible and freely chosen, nonetheless fails to manifest ‘an insufficiently good will’. The argument depends on a potentially controversial thesis in the ethics of concern, namely, that a thoroughly decent moral agent—someone who cares enough about morality and the values that underlie it—will not always be moved to do what he knows he ought to do. (shrink)
According to Parfit, the best version of Kantian ethics takes as its central principle Kantian Contractualism: the thesis that everyone ought to follow the principles whose universal acceptance everyone could rationally will. This paper examines that thesis, identifies a class of annoying counterexamples, and suggests that when Kantian Contractualism is modified in response to these examples, the resulting principle is too complex and ad hoc to serve as the 'supreme principle of morality'.
In Being Realistic About Reasons T. M. Scanlon argues that particular fact about reasons are explained by contingent non-normative facts together with pure normative principles. A question then arises about the modal status of these pure principles. Scanlon maintains that they are necessary in a sense, and suggests that they are ‘metaphysically’ necessary. I argue that the best view for Scanlon to take, given his other commitments, is that these pure normative principles are metaphysically contingent in some cases and necessary (...) only in a weaker sense. (shrink)
ABSTRACTThe paper explores Stephen Yablo's suggestion that ‘If-Thenism’ in the philosophy of mathematics is best formulated as the thesis that the real content of a mathematical claim C is the result of subtracting the potentially problematic metaphysical commitments of mathematics from C [Yablo 2017]. Yablo's proposal assumes that some propositions make others true. The present discussion assumes that propositions are coarse-grained sets of possible worlds and asks what Yablo's proposal looks like on that assumption. The conclusion is that the adequacy (...) of the proposal turns on hard-to-settle questions about the truthmakers for propositions expressed by material conditionals. (shrink)
We know a great deal about what is possible, so modal knowledge must be possible, not just in principle but by ordinary methods. Christopher Peacocke’s leading thought in Chapter 4 of Being Known is that this fact places significant constraints on philosophical treatments of modality. Modal realism is ruled out on the ground that it renders modal truth “radically inaccessible”, and actualism is forced upon us. It goes without saying that any account of the modal facts must eventually dovetail with (...) some account of how we know them. But Peacocke’s approach is animated by the thought that there is a mystery about modal knowledge—a transposed version of Benacerraf’s puzzle about mathematical knowledge under Platonism. Peacocke clearly believes that modal realism renders the problem intractable. But what exactly is the mystery in the modal case? And why exactly does modal realism preclude a solution? Peacocke himself does not say. The ‘access problem’ for modal realism is clearly decisive for him; but it is very much in the background. Nonetheless, for several reasons, it will help to start here. (shrink)