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)

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)

Manifest Activity presents and critically examines the model of human power, the will, our capacities for purposeful conduct, and the place of our agency in the natural world of one of the most important and traditionally under-appreciated philosophers of the 18th century: Thomas Reid. For Reid, contrary to the view of many of his predecessors, it is simply manifest that we are active with respect to our behaviours; it is manifest, he thinks, that our actions are not merely remote products (...) of forces that lie outside of our control. Reid holds, instead, that actions are all and only those events that spring from active power and he produces insightful and imaginative arguments for the claim that only a creature with a mind is capable of having active power. He believes that only human beings, and creatures 'above us', are capable of directing events towards ends, of endowing them with purpose or direction, the distinctive feature of action. However, he also holds that all events, and not merely human actions, are products of active power, power possessed either by human beings or by God. This collection of theses leads Reid to the view that human behaviour and the progress of nature are both essentially teleological. Patterns in nature are the products of laws of which God is the author; patterns in human conduct are the products of character and the laws that individuals set for themselves. Manifest Activity examines Reid's arguments for this view and the view's implications for the nature of character, motivation and the special kind of causation involved in the production of human behavior. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Iambic Poetics in the Roman Empire by Tom HawkinsGideon NisbetTom Hawkins. Iambic Poetics in the Roman Empire. Cambridge: Cambridge University Press, 2014. xi + 334 pp. Cloth, $99.This stimulating and highly readable book explores the ancient afterlife of three famous literary bully-boys: Archilochus, Semonides, and Hipponax, the unholy Trinity of archaic Greek iambus. Tom Hawkins sets out to examine their reception, not among the classical and Hellenistic Greek (...) poets to whom they were living forebears (although the Callimachean intertext is a lively presence, e.g., 40–51, 146–49), or in the literary flourishing that they in turn inspired in late Republican and “golden” Augustan Rome, but amid authors of the Empire and Late Antiquity, extending into a recognizably Christian age. Only one of the six authors chosen (Babrius) adopts an iambic meter, and three—Dio, Lucian, and Julian—do not even compose verse (or not here). Hawkins’ choices are piquant. He has sought out the kinds of text that classicists generally skip: odd, minor works by the less reputable pagans, and by the type of early churchman we tend [End Page 180] gratefully to surrender to our colleagues in theology. Indeed, some are scarcely read at all (qua texts) but merely dipped into as a source of corroborating factoids, at least until now (142, on Gregory Nazianzen). Hawkins contends that an “iambic tradition” of sorts remains culturally alive and vital throughout these early centuries c.e.: a tradition not so much of metrical continuation or even necessarily of working closely with the archaic texts, but nevertheless retaining a definite sense of the constituent elements (e.g., animal-fable, a scruffy narrator) that, variously combined, let the reader or audience know they are in dialogue with an “iambic mode” (terms are defined in the introduction’s first footnote, 2).Authors and readerships of these centuries had at their command much more of the text of the archaic iambicists than is available to us moderns, provided they cared to read it and could understand what they read (28–29 suggests it was often otherwise). Today, Archilochus et al. are mere tattered ghosts, pieced together by editorial ingenuity out of citations and mentions, and latterly read in papyrus fragments gleaned from ancient rubbish heaps (the heroes of this scholarly epic of reconstruction include the late Professor Martin West, news of whose death came shortly before this review went to press). Some of the Imperial poets and prose authors studied by Hawkins envisage an ideal reader to whom archaic iambus is an open book, but the true constant is the ancient biographical tradition about Archilochus in particular (the stories told about the others are often recognizable knock-offs, but all three are names to conjure with; there are grounds for thinking that Archilochus had become literally proverbial for invective abuse even among non-readers, 27). Hawkins is very good at showing how these interwoven life-stories took on a life of their own and continued to grow in the telling (9), all the more so perhaps as actual familiarity with the texts waned. Over several centuries and numerous genres, the malleable myth of iambus—the slighted outsider, embracing abjection to shock a complacent Establishment and shame his nemeses—proved endlessly useful as a temporary vantage point when authors felt like taking a walk on the wild side.The iambic tradition tracked by Hawkins thus has “more to do with the sediment of cultural memory about iambic poets and their poetry than with historical realities, but once we get beyond a fascination with origins, such sediment becomes the only reality worth talking about” (8). In Hawkins’ readings of his chosen texts, this textual-biographical muck is fertile stuff. Iteration and generic migration turn the iambic life-story into a potent and versatile literary trope which usefully combines ironic distance (to be, or even make like Archilochus is an obvious non-starter in such a belated and grown-up age), and thus self-evident deniability, with the implicit threat that traces of iambus’ murderous power may yet remain. For Hawkins, the hint is if anything strengthened by repeated, name-checking recusationes that keep the iambic biopic in the... (shrink)

One of a pair ofbooks selected from Stanley Rosen's career as a philosopher, scholar, and teacher over the last half of a century. They represent both the vast range of his learning in the most important philosophers of the tradition and the daring and penetration of his exploration of the fundamental philosophical questions. Yet the essays are written with an accessibility that is an expression of Rosen's thesis that our ordinary experience and speech provides the only stable ground (...) for understanding and evaluating extraordinary thought and experiences. Rosen proposes that only a qualified Platonism in which the preservation of the link between the good and the rational on the everyday level was preserved on the philosophical level, can do justice to our experience of ourselves. The notions of form and intuition play a central role in his proposal to preserve the spontaneity of the soul and the heterogeneity of its objects. The essays were originally written for a variety of purposes: there are panoramic reviews of his philosophical intentions, intricate analyses of fundamental problems, challenging interpretations of classical texts, reviews of other authors, and informal commentaries on the state of philosophy in our time. Taken together these essays provide a key to the some of the most decisive questions in philosophy and a valuable explication of some the central themes of Rosen's work. The essays were selected from articles, chapters, and unpublished lectures that were composed over the last five decades. They are distributed into two volumes by their focus upon ancient and modern themes, a convenient division that is not meant to imply a doctrinal chasm. On the contrary, it is one of Rosen's arguments that those who wish to preserve ancient wisdom are best served by the demonstration of the both parties address the same essential human nature, however much the practical and theoretical demands differ from epoch to epoch. (shrink)

This very interesting and extremely useful study raises the question, by virtue of its title and what it does not do, of what is, or ought to be, meant by the philosophy of mathematics. The author begins his study of Euclid with a brief discussion of Hilbert's axiomatization of geometry. The two main points in this discussion are: "Hilbertian geometry and many other parts of modern mathematics are the study of structure", i.e., of the interpretations of axiom-systems; and intuition of (...) geometrical form becomes irrelevant to the content of mathematics. Greek mathematics, and specifically Euclid, cannot be understood in these terms; hence, Euclid's use of the axiomatic method differs from ours. One may also say that logic, "the theory of structure-preserving inference", becomes central to modern mathematics, as it was not for Euclid. But, the author continues, it does not follow that one cannot exhibit the logical structure employed by Euclid. The bulk of Mueller's book is concerned to do just this, thanks to a formalization of Euclid which attempts to be faithful to his principal concepts, while at the same time employing contemporary logical techniques. (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)

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)

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.

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)

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)

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)

ABSTRACT Bennett argues that the various building relations are all directed, necessitating and generative. This note provides interpretations of these conditions different from Bennett’s. According to Bennett, the full builders for an entity must necessitate its existence alone or in conjunction with other items that are not builders. I suggest that the full builders must necessitate the built item outright. According to Bennett, building is generative only in the sense that when the xx build y we are thereby “licensed” to (...) say that y exists/obtains because the xx exist/obtain. I suggest that the building relations are unified by the fact that when the xx build y, the xx together metaphysically ground y. This entails, contra Bennett, that causation is not a building relation. (shrink)

Viewed from a suitable distance, David Lewis's ontological scheme is simplicity itself. Absolutely everything that exists, according to Lewis, is either a spatiotemporal particular, or a set theoretic construction from such particulars, or a mereological aggregate of such items. Set theoretic constructionalism is not an incidental feature of Lewis's system. The master argument of On the Plurality of Worlds is that a pluriverse composed of infinitely many concrete universes constitutes a “paradise for philosophers. Given his other views, his account of (...) classes has profound implications for general metaphysics, implying as it does an account of the nature of properties and instantiation, propositions and propositional truth, the nature of events, and so on. But Lewis does not consider those implications. The aim of this chapter is to close the circle by bringing Lewis's mature account of sets into contact with his larger ontological scheme. (shrink)

The thesis defends the legitimacy of a 'platonistic' metaphysic, according to which there exist non-spatiotemporal 'abstract' objects, against a series of recent nominalist challenges. After distinguishing the nominalism I intend to discuss from a range of distinct views with which it has been historically confused, I take up the core of the nominalist's challenge: the suggestion that abstract objects, if there were such things, would be incapable of causal interaction with us and our surroundings, and hence unknowable. I suggest that (...) every attempt to make this line of thought precise is either internally incoherent or depends upon an implausible conception of rational opinion. There is no a priori case for nominalism grounded in the theory of knowledge. I then take up Hartry Field's case for nominalism, which I take to be grounded in a broadly Quinean conception of philosophical and scientific methodology. And once again it is suggested that there is no way to develop the case in detail against the background of an independently plausible normative epistemology. Finally I take up one strand in the positive case for platonism: the 'Fregean' view that the existence of abstract objects is an analytic consequence of certain independently unproblematic states of affairs. I offer a reconstruction of certain arguments due to Crispin Wright, and tentatively endorse one development of this line of thought. If this is right, nominalism is not simply undermotivated: it is an essentially unstable account of what there is. (shrink)

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.

Nominalism is the view that mathematical objects do not exist. This chapter delimits several types of nominalistic projects: revolutionary programs that attempt to change mathematics and hermeneutic programs that attempt to interpret mathematics. Some programs accord with naturalism, and some oppose naturalism. Steven Yablo’s fictionalism is brought into the fold and discussed at some length.

Review of John Burgess' and Gideon Rosen's A Subject with no Object.

In response to parts I-III of G Rosen's "What is Constructive Empiricism?", "Philosophical Studies", 74, 1994, 143-178, this paper examines several construals of the position of constructive empiricism. At issue, in part, is the equation of intentional aspects of science with the intentions and opinions of scientists. In addition it is necessary to distinguish the constructive empiricist -- a philosopher holding that acceptance of theories in science need not involve belief that they are true -- from the scientific agnostic' (...) who accepts but does not believe current science. What is at stake for empiricism is a view of science that will admit it as a paradigm for rational inquiry. (shrink)