I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.

Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response (e.g. Field’s program) accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to (...) standard mathematics. A second style of response (suggested, e.g., by Balaguer and Maddy) denies that indispensability entails realism: when we mathematize a physical problem we treat its physical content as if it were the mathematical representation; provided the two are sufficiently similar, we can use the mathematics to draw conclusions about the physics; even if we cannot represent physical facts without mathematical tools, as-if-fictionalism is reasonable. In this paper I argue that uses of mathematics in science reach deeper than is appreciated by this second response and, indeed, in the more general literature. More specifically, our confidence that we can use the mathematics to draw conclusions about the physics itself depends on mathematics. If the mathematical premises we employ in concluding that a certain application is trustworthy are false, we may lack a justification for supposing that the application will reliably lead us from correct input to correct output. For example, solutions to many physical problems require the determination of a function satisfying a differential equation. Sometimes (e.g., if the differential equation is linear) the existence of a solution for initial value problems can be established directly; where direct methods fail, the existence of a solution must be established indirectly, generally by constructing a sequence of functions that converges to a limit function that satisfies the initial value problem. Moreover, the solution often cannot be evaluated by analytic methods, and scientists must rely on finite element numerical methods to approximate the solution. Mathematical analysis of errors provides further useful information governing the choice of approximation method and of the step size and number of elements needed for the approximation to reach a desired precision. Mathematical physicists rely on the background mathematical theories (e.g., theory of differential equations) presupposed in proving the existence of the solutions and approximating them. It is difficult to see how they could do this while adding the fictionalist disclaimer, “But, you know, I don’t believe any of the mathematics I’m using”. It is difficult to see how a fictionalist pursuing the second strategy can account for the soundness of mathematical reasoning in mathematical physics and elsewhere in the sciences. The paper will fill out this argument by appeal to examples and attempt to make clear (a) how mathematics is indispensable to understanding – and thus underwriting our confidence in – applications that would otherwise be shaky approximations and idealizations and (b) how this role is difficult to square with fictionalism. (shrink)

In this paper I discuss lessons that metaphysicians might learn from Duhem. Given Duhem’s well known antipathy to metaphysics, you will likely think that this is a fairly inauspicious beginning with a predictable ending: i.e., physics is one thing, metaphysics another, and never the twain shall meet. If you will bear with me, however, I hope to persuade you differently. On the contrary, I will argue, Duhem was both a common sense and metaphysical realist, his nuanced views about the relationship (...) between physics and metaphysics are poorly understood, and properly understood contain important lessons for contemporary metaphysics. I’ll spend most of the paper rehabilitating Duhem and finish with some lessons for metaphysicians. (shrink)

SummaryBenacerraf challenges us to account for the reliability of our mathematical beliefs given that there appear to be no natural connections between mathematical believers and mathematical ontology. In this paper I try to do two things. I argue that the interactionist view underlying this challenge renders inexplicable not only the reliability of our mathematical beliefs, construed either platonistically or naturalistically , but also the reliability of most of our beliefs in physics. I attempt to counter Benacerraf's challenge by sketching an (...) alternative conception of reliability explanations which renders explicable the reliability of our beliefs in physics and in mathematics but in which mathematical and formal considerations themselves play a central role. My main thesis is that abstract objects do not strike us, but that this is irrelevant to the reliability of our mathematical and physical beliefs. (shrink)

In this paper I argue three things: (1) that the interactionist view underlying Benacerraf's (1973) challenge to mathematical beliefs renders inexplicable the reliability of most of our beliefs in physics; (2) that examples from mathematical physics suggest that we should view reliability differently; and (3) that abstract mathematical considerations are indispensable to explanations of the reliability of our beliefs.

It is commonly presupposed that all instances of the deflationary reference schema ‘F’ applies to x if and only if x is ‘are correct. This paper argues, mainly on the basis of concrete example, that we have little reason to be confident about this presupposition: our tendency to believe the instances is based on local successes that may not be globally extendible. There is a problem of semantic projection, Ii argue, and standard accounts that would resolve or dissolve the problem (...) are problematic. (shrink)

Russell’s views about the proper logical and epistemological treatment of names conspired to lead him to set aside considerations that support the claim that names are not definite descriptions. Though he appreciated those considerations, he famously argued that ordinary names are truncated definite descriptions. Nevertheless, his appreciation of the distinctive semantic behavior of ordinary names combined with his view that acquaintance comes in degrees led him to attempt to secure a semantically privileged status for ordinary names: only special kinds of (...) descriptions can go proxy for ordinary names “used as names”. The paper attempts to tell this story, filling in gaps where Russell doesn’t provide sufficient elaboration, and to draw some general conclusions about acquaintance-based approaches to names and singular thoughts. (shrink)

Scientific Realism and Antirealism Debates about scientific realism concern the extent to which we are entitled to hope or believe that science will tell us what the world is really like. Realists tend to be optimistic; antirealists do not. To a first approximation, scientific realism is the view that well-confirmed scientific theories are approximately true; … Continue reading Scientific Realism and Antirealism →.

According to externalism, reference is a relation between uses of an expression and features of the environment. Moreover, the reference relation is normative , and the referential relata of our expressions are explanatory of successful language use. This paper largely agrees with the broad conception underlying externalism: it is what people do with words that makes them have the references they have, and the world constrains what people can successfully do with words. However, the paper strongly disagrees with the details (...) . A centrally important feature of what people do with words is how they use them in inferential contexts. When due attention is given to the reference-determining role played by inferential properties of expressions, I argue, we arrive at a more satisfactory account of semantic norms and explanations. Much of the argument is based on a detailed look at the language of chemical classification used in the late 19th century. (shrink)

Book Information Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism. Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism Colin Cheyne , Dordrecht: Kluwer Academic Publishers , 2001 , xvi + 236 , £55 ( cloth ) By Colin Cheyne. Dordrecht: Kluwer Academic Publishers. Pp. xvi + 236. £55.

In this book physicist Roland Omnès addresses some big questions in philosophy of mathematics. Anyone who reflects on the history and practice of mathematics and the sciences, especially physics, will naturally be struck by some remarkable coincidences. First, often newly developed mathematics was not well understood. But its successful applications and its agreement with intuitive representations of reality promoted confidence in its correctness even absent clear foundations . Later, this confidence is vindicated when a proper setting for the concepts and (...) techniques is discovered . Second, often mathematical concepts designed for one purpose later turn out to have pervasive applications that could not have been imagined by the original practitioners. Third, many of the most important results obtained in physics since the late nineteenth century were driven by the search for precise, comprehensive, consistent theoretical frameworks: the sequence special relativity, general relativity, relativistic quantum mechanics, string theory can be seen as one that increases comprehensiveness by consistent unification. The fundamental theoretical work has little to do with empirical investigation and a lot to do with mathematical and conceptual investigation of invariances and symmetries. Fourth, mathematical principles guarantee existence principles needed by physics . Such coincidences naturally invite questions: Why is confidence in the consistency of a successful piece of mathematics so often vindicated? Why does mathematics turn out to be so comprehensive and fruitful in unexpected …. (shrink)

History and Philosophy of Logic, Volume 0, Issue 0, Page 1-2, Ahead of Print.

I discuss Earman's program to achieve an objective account of the Higgs mechanism within the C∗ algebraic approach to quantum field theory. Pointing to three results obtained within this approach, I argue that if one follows Earman and understands the Higgs mechanism as a constraint, it appears to be a genuine quantum phenomenon that does not simply arise through the correspondence principle. This casts further this casts doubts on the validity of the Dirac conjecture that identifies first-class constraints and gauge (...) transformations and that provides a major motivation for both Earman's program and Struyve's demonstration that a gauge-invariant account of the Higgs mechanism can be accomplished at the classical level. (shrink)

RECENT STUDIES IN NORMATIVE ETHICS have concentrated on act evaluations, neglecting, almost ignoring, agent evaluations. A partial explanation of this defect is found in two related ones: the neglect of act evaluations other than the obligation notions, and the failure to do justice even to them. In each case, neglecting the "other" concepts is implicated in serious misunderstandings of what is considered—or more accurately, what is over-considered. Take, for example, the view that it is obligatory to obtain for oneself the (...) greatest good one can, e.g., pleasure. Even a cursory study of prudence and other primarily self-regarding notions could have saved Moore, Ross, Ewing, and many others from holding or committing themselves to this silly view. (shrink)

Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent calculus from a ground sequent, that is, a logical axiom. We discuss the similarities and differences of these derived rules as well as their interaction with the implication right rule under cut and the structural axiom. We further consider the question of analyticity of cuts (...) in calculi using one of the new rules instead of the standard left implication rule. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 30, Number 2, November 2004, pp. 265-296 A Symposium on Louis E. Loeb, Stability and Justification in Hume's Treatise The Unity of Hume's Philosophical Project MICHAEL WILLIAMS 1. Introduction In both his Treatise of Human Nature and Enquiry concerning Human Understanding, Hume presents a protean figure.1 By turns, he appears as a naturalistic theorist of the mind, a proto-Positivist critic of speculative metaphysics, and an (...) utter skeptic. Can these various characters be seen to work together? On the whole, Hume's interpreters seem to think not. The typical approach is to pick a dominant personality, leaving Hume's other philosophicalpersonae to be squeezed in as an afterthought, deprecated, or simply ignored. Louis Loeb is a shining exception.2 His new book, subtle and densely argued, offers an account of Hume's epistemology that makes a sustained effort to come to terms with its multi-faceted character. However, while Loeb's interpretation marks a real advance in our understanding of Hume, it is not one that I find ultimately persuasive. As I shall try to show, for all his insights, Loeb too fails to provide a satisfyingly unified account of Hume's philosophical pro j ect. In the course of explaining why I think this, I shall indicate how I think a better account ought to go. 2. Varieties of Skepticism The key to understanding Hume is to come to terms with the ways in which Hume is and is not a skeptic. So before going farther it will be useful to distinguish the Michael Williams is Krieger-Eisenhower Professor of Philosophy at The Johns Hopkins University, 347 Gilman Hall, Baltimore, MD 21218, USA. e-mail: [email protected] 266 Michael Williams various forms that skepticism takes, or might be thought to take, in Hume's epistemological writings. The distinctions I shall introduce will also make it easier to characterize different ways of reading Hume, Loeb's included. First, we must distinguish between epistemological skepticism, which has to do with knowledge and belief, and conceptual skepticism which has to do with meaning. So for example, where an epistemological skeptic may wonder whether beliefs of a certain broad kind can be justified, a conceptual skeptic will wonder whether the words we use to express such purported beliefs are so much as meaningful. It seems clear that both kinds of skepticism figure in Hume's theory of the understanding. However, commentators differ sharply over their relative importance. Second, we must distinguish two forms of epistemological skepticism: theoretical (or Academic) skepticism and suspensive skepticism (or Pyrrhonism). As its name suggests, theoretical skepticism is a thesis (or family of theses) about the epistemic status of human beliefs: for example, the thesis that such and such beliefs do not amount to knowledge or are not justifiable. It is important to note that one can entertain such a thesis in a purely speculative or theoretical way, without becoming inclined to relinquish any fundamental beliefs. By contrast, Pyrrhonism involves an actual breakdown in belief. Again, though we seem to be able to find both Academic and Pyrrhonian elements in Hume's epistemological outlook, commentators are seriously at odds over how to put them together. Third, both theoretical and suspensive skepticism can be either qualified (Hume says "mitigated") or unqualified (we can say "radical"). The most important form of qualified theoretical skepticism is anti-Rationalism. Anti-Rationalism embraces such theses as that our beliefs never amount to knowledge, or are not supportable by (what we can show to be) truth-conducive reasons. By contrast, theoretical skepticism in its most radical form is the claim that no beliefs are in any sense more reasonable than others: i.e., that normative-epistemological distinctions between beliefs are completely indefensible. We can make an analogous distinction with respect to suspensive skepticism. A qualifiedly skeptical outlook might take the form of anti-Dogmatism: we hold beliefs, but in an open-minded, fallibilist spirit, taking nothing to be altogether certain, suspending final judgment. Alternatively, we might suffer a complete breakdown of belief. Once more, we find serious differences of opinion among commentators. In what way is Hume's skepticism mitigated, or qualified, if indeed it is qualified... (shrink)

Grounded in the canonical gospels and other New Testament passages, especially Philippians 2:1-11, this study offers an account of humility from a Christian perspective.

Frontmatter -- Vorwort -- Inhalt -- 1 Antike Melancholie -- 2 Die Acedia des Mittelalters -- 3 Moderne Metamorphosen -- Anmerkungen.

_ "LaBossiere brilliantly tackles many of the toughest ethical dilemmas of our times, from gender selection, cloning and sexual inequality to violence in the media and the conduct of warfare. In an age of snap judgments and stereotypes, he approaches his topics in a refreshingly open-minded fashion. His quick wit and firm knowledge of contemporary culture bring philosophy full-force into the 21st century." —Paul Halpern, Professor Of Physics, University Of The Sciences in Philadelphia and author of What's Science Ever Done (...) for Us? From the author's introduction: Philosophy, as I see it, is not about believing certain tenets or accepting certain dogmas. Philosophy is about asking questions, seeking answers and entertaining doubt. Critical to that endeavor is a willingness to be rationally provoked by different ideas and to see where they might lead—assuming they turn out to be worth following. If you find that you disagree with me, so much the better. The search for truth and wisdom benefits most from dissent. It is uncritical agreement that derails this search and leaves people stuck in the dark. Of course, if you do agree with me on some points, that is cool, too. _ I n this stimulating book, Michael C. LaBossiere takes a provocative look at issues in contemporary politics, culture and society through the lens of philosophy. Collected from LaBossiere's regular column in The Philosopher's Magazine, this fascinating set of philosophical provocations assumes no background in philosophy and focuses on matters that are of popular interest to the general public, yet are also philosophically significant. Topics range across a whole host of controversial issues that are of genuine interest to the reader, including same sex marriage, video games, gene therapy, true love, chance, torture, gender, god, the media, and freedom. >. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 122.4 (2001) 533-565 [Access article in PDF] Rome Personified, Rome Epitomized: Representations of Rome in the Poetry of the Early Fifth Century Michael Roberts The last years of the fourth and the beginning of the fifth century (the reigns of Theodosius and his sons) mark a crucial stage in the Christianization of Rome. 1 The hold of the city and all it stood for (...) on the imagination of the ruling classes was as strong as ever. But Theodosian legislation had definitively established the dominance of Christianity in the empire, and even in Rome the aristocracy was becoming progressively more Christian. 2 These changing circumstances find expression in the way Rome was represented in contemporary literature. While still indebted to the traditional language of the laudes Romae and to well-established literary traditions, the authors of the period find new ways to inflect the image of Rome that mirror their differing religious and cultural allegiances.Three poets make the largest contributions to that evolution in the representation of Rome. Claudius Claudianus was born in Alexandria (c. 370) but came to Rome in 394. His first Latin poem celebrated the consuls of 395, Probinus and Olybrius, but thereafter most of his poems served the interests of his patron and the emperor Honorius' chief minister, the Vandal general Stilicho. Of particular importance for the representation of Rome are his consular panegyrics, for the consulships of Honorius (396, 398, and 404) and Stilicho (400), and his two historical epics on the campaigns against the African warlord Gildo (De bello Gildonico 398) and against Alaric in 401-402 (De bello Getico 402). Claudian wrote his last dated poem in 404. Nothing is heard of him after that date and it is likely he died soon thereafter.Claudian's Christian contemporary, Aurelius Prudentius Clemens, was born, according to the verse preface he wrote to his collected works, in 348. After a successful career in the imperial administration, he [End Page 533] withdrew from public life to devote his poetic talents to the service of God. Two works are especially relevant to the representation of Rome, the Contra Symmachum, in two books, completed in 402 or early 403, though book 1 may have been written earlier, and the Peristephanon, a collection of poems on the martyrs, including the Roman martyrs Lawrence (Perist. 2), Hippolytus (Perist. 11), Peter and Paul (Perist. 12), and Agnes (Perist. 14). Peristephanon 9 and 11 refer to a journey the poet took to Rome, generally dated to 401/402, but it is quite possible that this was not his first trip to the capital. 3The third poet, Rutilius Namatianus, a traditionally minded pagan, was praefectus urbi in 414. His poem, the De reditu suo, which does not survive in its entirety, describes his return from Rome to his native Gaul in 417. 4 It is haunted by the destruction caused in northern Italy and Gaul by the recent barbarian invasions, but it begins with an extended paean of praise to Rome, the eternal city, which always grows stronger by its reverses. Rutilius' patriotic devotion to the city and the idea of Rome provides an optimistic counterpoint to the evidence of destruction and desolation that runs as a leitmotif through the poem.Rome figures in the three poets in two guises. It may appear personified as a woman, whose attributes index the power and status of the city and empire as well as the contemporary circumstances of the Roman state. 5 As an alternative to this metaphorical representation of Rome, the city may be encapsulated by certain, especially charged details of topography, in an epitome of its urban geography that stands in a metonymic (or synecdochic) relationship to the city as a whole. Thus, to take an example from a later period, when Paulinus of Pella came at an advanced age to write his life story in the Eucharisticos, he mentions a trip that he took to Rome in the company of his parents in a.d. 379. At the time he was not... (shrink)

In _Church-going, Going, Gone!_ Michael Horan argues that although the Christian Church in Britain may be in terminal decline, that is not to be equated with a national decline in spiritual values. Most if not all people have some level of awareness of what he calls the 'Other-than-oneself', even though they have rejected, or never accepted, the Church’s now outdated teaching._ Church-going, Going, Gone!_ is concerned less with teaching than with learning. The book provides atheists, agnostics and believers-in-exile, as (...) well as those who have given little thought to belief, with a framework for collaborating as learners, working toward equality, peace and reconciliation, and dedicated to unselfish and imaginative social action. A new movement of the human spirit is beginning. (shrink)

Most people have a story to tell about a remarkable coincidence that in some instances changed the course of their lives. These uncanny occurrences have been variously interpreted as evidence of divine influence, fate, or the collective unconscious. Less common are explanations that explore the social situations and personal preoccupations of the individuals who place the most weight on coincidences. Drawing on a variety of coincidence stories, renowned anthropologist Michael Jackson builds a case for seeing them as allegories of (...) separation and loss—revealing the hope of repairing sundered lives, reconnecting estranged friends, reuniting distant kin, closing the gap between people and their gods, and achieving a sense of emotional and social connectedness with others in a fragmented world. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Ethical Theory and Responsibility Ethics: A Metaethical Study of Niebuhr and Levinas by Kevin JungMichael SohnEthical Theory and Responsibility Ethics: A Metaethical Study of Niebuhr and Levinas KEVIN JUNG Frankfurt am Main: Peter Lang, 2011. 237 pp. $69.95In Ethical Theory and Responsibility Ethics, Kevin Jung presents a historical and constructive analysis of two of the most prominent defenders of responsibility ethics: H. Richard Niebuhr and Emmanuel Levinas. The (...) Niebuhr and Levinas specialist will find detailed, historical discussions and clear, rigorous analyses of these thinkers’ philosophical and theological thought. But where Jung’s project really makes a distinct contribution to the field of ethics—and where his work may be of interest to the nonspecialist—is when he brings their insights and oversights into critical conversation with analytic philosophy. Rendering a mutually productive dialogue, he persuasively argues that categories within analytic philosophy cohere with and clarify their respective positions; conversely, their concrete responsibility ethics may contribute to analytic philosophy. [End Page 223]Chapter 1 introduces key concepts and issues within contemporary analytic philosophy relevant to responsibility ethics; these concepts and issues resurface toward the end of the book when Jung puts them in dialogue with the ethical theories of Niebuhr and Levinas. Chapter 2 reconstructs the philosophical and theological background of Niebuhr’s moral theory, engaging a number of influential thinkers—Friedrich Schleiermacher, Albrecht Ritschl, Ernst Troeltsch, Karl Barth, Josiah Royce, and Martin Buber—who shaped his thought. Chapter 3 examines more closely Niebuhr’s responsibility ethics itself. In the next two chapters, Jung applies the same structure of analysis to Levinas’s ethical theory: he considers Levinas’s philosophical and theological context; engages the works of Edmund Husserl, Martin Heidegger, Franz Rosenzweig, and Buber; and then exposits Levinas’s own distinct position. Jung traverses and navigates complex and divergent concepts and ideas proposed by Niebuhr and Levinas with clarity and finesse. His purpose is to interpret their arguments in light of their respective positions in ethical theory. In the final two chapters, Jung’s work turns more explicitly constructive when he puts their theories into conversation with analytic philosophy.The specialist in Niebuhr or Levinas studies may find that Jung’s attempts to clarify their thought with foreign, extrinsic categories do violence to their works. Indeed, on occasion Jung seems to shoehorn their ideas into analytical concepts that may not do full justice to the full breadth of their thought. For instance, Jung rightly indicates that Levinas rejects a certain kind of abstract ethical universalism on the basis of his emphasis on the concrete relation to the particular other. But to conclude from this that he is an ethical particularist does not adequately account for the categorically imperative nature of the ethical demands and responsibility to the other that Levinas proposes. In other words, it seems to me that Levinas offers a form of ethical universalism that begins precisely in the concrete situation without collapsing into an ethical particularism.Despite these minor reservations, Jung’s work is to be commended not only for its excellent exposition and rigorous studies of Niebuhr and Levinas but also for its successful attempt overall to clarify and give greater coherence to their ideas with the tools of analytic philosophy. In so doing, Jung provides robust theoretical reflection on responsibility ethics in a time of augmented human power and capacities. [End Page 224]Michael SohnCleveland State UniversityCopyright © 2014 Society of Christian Ethics... (shrink)

Most anyone interested in such topics as creation mythology, Jungian theory, or the idea of "secret teachings" in ancient Judaism and Christianity has found "gnosticism" compelling. Yet the term "gnosticism," which often connotes a single rebellious movement against the prevailing religions of late antiquity, gives the false impression of a monolithic religious phenomenon. Here Michael Williams challenges the validity of the widely invoked category of ancient "gnosticism" and the ways it has been described. Presenting such famous writings and movements (...) as the Apocryphon of John and Valentinian Christianity, Williams uncovers the similarities and differences among some major traditions widely categorized as gnostic. He provides an eloquent, systematic argument for a more accurate way to discuss these interpretive approaches.The modern construct "gnosticism" is not justified by any ancient self-definition, and many of the most commonly cited religious features that supposedly define gnosticism phenomenologically turn out to be questionable. Exploring the sample sets of "gnostic" teachings, Williams refutes generalizations concerning asceticism and libertinism, attitudes toward the body and the created world, and alleged features of protest, parasitism, and elitism. He sketches a fresh model for understanding ancient innovations on more "mainstream" Judaism and Christianity, a model that is informed by modern research on dynamics in new religious movements and is freed from the false stereotypes from which the category "gnosticism" has been constructed. (shrink)

The doctrine of double effect has a firm, respected position within Roman Catholic medical ethics. Neil M. Gorsuch, a judge on the U.S. Court of Appeals for the Tenth Circuit, believes that this doctrine also enjoys a central place within U.S. law. This essay examines and assesses Gorsuch’s thesis. National Catholic Bioethics Quarterly 11.1 (Spring 2011): 31–40.