In “How an Unsurpassable Being can Create a Surpassable World,” Daniel and Frances Howard-Snyder employ a fascinating thought experiment in anattempt to show that a morally unsurpassable being can create a surpassable world. Imagine that for each positive integer there is a world that a good,omnipotent, omniscient being can create. Jove randomly selects a number and creates the corresponding world; Thor simply creates world 888. The Howard-Snyders argue that it is logically possible that Jove is morally unsurpassable. William Rowe counters (...) that Thor morally surpasses Jove, thus contradictingthe claim that Jove is morally unsurpassable. Does either Jove or Thor morally surpass the other? How do their strategies compare? Could a morally unsurpassable being employ Jove’s strategy? The purpose of this paper is to answer these questions. (shrink)

Snyder’s book ‘Exploiting hope’ is as relevant as ever. His book is about the hope of desperate individuals seeking treatments that cannot be found in conventional medicine. The book engages with hope in the setting of phase I cancer trials, stem cell interventions, right-to-try laws and crowd funding, offering a new language to explain our discomfort with some of these quests. At the same time the book seems particularly relevant given current events. While despair and quests for novel interventions touched (...) only a few patients with specific conditions up to a year ago, they are now familiar to us all. Early on in the COVID-19 pandemic all of us probably experienced hope for interventions that could save us... (shrink)

This article discussed Jeremy Snyder’s book “Exploiting Hope. How the Promise of New Medical Interventions Sustains Us—and Makes Us Vulnerable”, 2021, Oxford University Press.

Commentary on Jeremy Snyder, Is Health Worker Migration a Case of Poaching?

ABSTRACT:This commentary develops my position on the ethics of price gouging in response to Jeremy Snyder's article, “What's the Matter with Price Gouging.” First, it explains how the “nonworseness claim” supports the moral permissibility of price gouging, even if it does not show that price gougers are morally virtuous agents. Second, it argues that questions about price gouging and distributive justice must be answered in light of the relevant possible institutional alternatives, and that Snyder's proposed alternatives to price gouging (...) fare worse on the dimension of justice than a system in which goods are allocated by a system of market prices. (shrink)

This paper develops my position on the ethics of price gouging in response to Jeremy Snyder's article, "What's the Matter with Price Gouging." First, it explains how the "nonworseness claim" supports the moral permissibility of price gouging, even if it does not show that price gougers are morally virtuous agents. Second, it argues that questions about price gouging and distributive justice must be answered in light of the relevant possible institutional alternatives, and that Snyder's proposed alternatives to price gouging (...) fare worse on the dimension of justice than a system in which goods are allocated by a system of market prices. (shrink)

In this short essay, we sketch a theory of faith that features resilience in the face of challenges to relying on those in whom you have faith. We argue that it handles a variety of both religious and secular faith-data, e.g., the value of faith in relationships of mutual faith and faithfulness, how the Christian and Hebrew scriptures portray pístis and ʾĕmûnāh, and the character of faith as it is often expressed in popular secular venues.

Does faith that p entail belief that p? If faith that p is identical with belief that p, it does. But it isn’t. Even so, faith that p might be necessarily partly constituted by belief that p, or at least entail it. Of course, even if faith that p entails belief that p, it does not follow that faith that p is necessarily partly constituted by belief that p. Still, showing that faith that p entails belief that p would be (...) a significant step in that direction. Can we take that step? In this essay, I assess, and reject, seven reasons to think we can. Along the way, I discuss having faith in a person, being a person of faith, believing something by faith, and believing a person. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...) concludes. (shrink)

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...) gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (shrink)

This essay is a detailed study of William P. Alston’s view on the nature of Christian faith, which I assess in the context of three problems: the problem of the skeptical Christian, the problem of faith and reason, and the problem of the trajectory. Although Alston intended a view that would solve these problems, it does so only superficially. Fortunately, we can distinguish Alston’s view, on the one hand, from Alston’s illustrations of it, on the other hand. I argue that, (...) although Alston’s view only superficially solves these problems, Alston’s illustrations of it suggest a substantive way to solve them, a way that I sketch briefly. (shrink)

The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, worth (...) stressing---since often neglected. My argument for this is based on the account of duality developed by De Haro: which is illustrated here with several examples, from both elementary physics and string theory. Thus I argue that in some examples, including in string theory, two dual theories disagree in their claims about the world. I also spell out how this remark implies a limitation of proposals to understand theoretical equivalence as either logical equivalence or a weakening of it. (shrink)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction. One theme will be a contrast between (...) two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories. And this framework is powerful enough to deduce that what seemed “manna from heaven” is to be expected: the good fortune is generic. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind. (shrink)

I have two main aims. The first is general, and more philosophical. The second is specific, and more closely related to physics. The first aim is to state my general views about laws and causation at different ”levels’. The main task is to understand how the higher levels sustain notions of law and causation that ”ride free’ of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to (...) give a framework for describing dynamics at different levels, emphasizing how the various levels’ dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed ”micro’ and ”macro’, which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis’ five types of top-down causation. (shrink)

Reprinted in Philosophy of Religion: An Anthology, Wadsworth, 2013, 6th edition, eds. Michael Rea and Louis Pojman. In this essay, I argue that the moral skepticism objection to what is badly named "skeptical theism" fails.

In some circles, faith is said to be one of three theological virtues, along with hope and agape. But not everyone thinks faith is a virtue, theological or otherwise. Indeed, depending on how we understand it, faith may well conflict with the virtues. In this chapter we will focus on the virtue of humility. Does faith conflict with humility, or are they in concord? In what follows, we will do five things. First, we will sketch a theory of the virtue (...) of humility. Second, we will summarize a common view of faith, arguably held by Thomas Aquinas among others, and we will argue that Thomistic faith is not an intellectual virtue and that it conflicts with humility in the domain of inquiry. Third, we will plump for an older view of faith, one that predates Aquinas by at least 1500 years, Markan faith. Fourth, we will argue that Markan faith is an intellectual virtue and it is in concord with humility in the domain of inquiry. Fifth, we will argue that Markan faith, unlike Thomistic faith, is a personal virtue and that it is in concord with humility in the domain of personal relationships, both human-human and human-divine. (shrink)

For many people the existence of God is by no means a sufficiently clear feature of reality. This problem, the fact of divine hiddenness, has been a source of existential concern and has sometimes been taken as a rationale for support of atheism or agnosticism. In this collection of essays, a distinguished group of philosophers of religion explore the question of divine hiddenness in considerable detail. The issue is approached from several perspectives including Jewish, Christian, atheist and agnostic. There is (...) coverage of the historical treatment of divine hiddenness as found in the work of Maimonides, St. John of the Cross, Jonathan Edwards, Kierkegaard, and various Biblical writers. A substantial introduction clarifies the main problems of and leading solutions to divine hiddenness. Primarily directed at philosophers of religion, theologians, and scholars of religious studies, this collection could also serve as a textbook for upper-level courses in philosophy of religion. (shrink)

In another paper, one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what is expected: often, what is expected from a theory of the system's microscopic constituents. We take reduction as deduction, aided by appropriate definitions. Then the main idea of our reconciliation of emergence (...) and reduction is that one makes the deduction after taking a limit of an appropriate parameter $N$. Thus our first main claim will be that in some situations, one can deduce a novel behaviour, by taking a limit $N\to\infty$. Our main illustration of this will be Lee-Yang theory. But on the other hand, this does not show that the $N=\infty$ limit is physically real. For our second main claim will be that in such situations, there is a logically weaker, yet still vivid, novel behaviour that occurs before the limit, i.e. for finite $N$. And it is this weaker behaviour which is physically real. Our main illustration of this will be the renormalization group description of cross-over phenomena. (shrink)

Faith in God conflicts with reason—or so we’re told. We focus on two arguments for this conclusion. After evaluating three criticisms of them, we identify an assumption they share, namely that faith in God requires belief that God exists. Whether the assumption is true depends on what faith is. We sketch a theory of faith that allows for both faith in God without belief that God exists, and faith in God while in belief-cancelling doubt God’s existence. We then argue that (...) our theory, unlike the theory of Thomas Aquinas, makes sense of four central items of faith-data: (i) pístis in the Synoptics, (ii) ʾemunāh in the Hebrew scriptures, (iii) exemplars of faith in God, including Abraham, Jesus, and Mother Teresa, and (iv) the widespread experience of people of faith today. We close by assessing revisions of the two arguments we began with, revisions that align with our theory of faith, and find them dubious, at best. (shrink)

Infallibilism is the view that a belief cannot be at once warranted and false. In this essay we assess three nonpartisan arguments for infallibilism, arguments that do not depend on a prior commitment to some substantive theory of warrant. Three premises, one from each argument, are most significant: (1) if a belief can be at once warranted and false, then the Gettier Problem cannot be solved; (2) if a belief can be at once warranted and false, then its warrant can (...) be transferred to an accidentally true belief; (3) if a belief can be at once warranted and false, then it can be warranted and accidentally true. We argue that each of these is either false or no more plausible than its denial. Along the way, we offer a solution to the Gettier Problem that is compatible with fallibilism. (shrink)

Abstract: This paper assesses the Everettian approach to the measurement problem, especially the version of that approach advocated by Simon Saunders and David Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than technical ones; but I include an introductory exposition of decoherence. In particular, I discuss whether---as these authors maintain---it is acceptable to have no precise definition of 'branch' (in the Everettian kind of sense). (A version of this paper will appear in a CTNS/Vatican Observatory volume on Quantum Theory and (...) Divine Action, ed. Robert Russell et al.). (shrink)

This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical (...) issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics. (shrink)

We might be tempted to think that, necessarily, if God unsurpassably loves such created persons as there may be, then for any capable created person S and time t, God is at t open to being in a positively meaningful and reciprocal conscious relationship with S at t, where one is open to relationship with another only if one never does anything (by commission or omission) that would have the result that the other was prevented from being able, just by (...) trying, to participate in that relationship. I argue that we should resist the temptation. (shrink)

Niche construction theory (NCT) can be applied to examine the influence of culturally constructed learning environments on the acquisition and retention of beliefs, values, role expectations, and skills. Thus, NCT provides a quantitative framework to account for cultural-historical contingency affecting development and cultural evolution. Learning in a culturally constructed environment is of central concern to many sociologists, cognitive scientists, and sociocultural anthropologists, albeit often from different perspectives. This article summarizes four pertinent theories from these fields—situated learning, activity theory, practice theory, (...) and distributed cognition. As a basis for interdisciplinary investigation, the article considers how these theories may be addressed using a cultural niche-construction framework, including the utility of an embedded model that explicitly accounts for effects of the constructed learning environment on within-individual learning dynamics in an evolutionary framework. (shrink)

This essay is aimed at a theistic audience, mainly those who are new to thinking hard about the problem of evil.

It is common for young Christians to go off to college assured in their beliefs but, in the course of their first year or two, they meet what appears to them to be powerful defenses of scientific naturalism and crushing critiques of the basic Christian story (BCS), and many are thrown into doubt. They think to themselves something like this: "To be honest, I am troubled about the BCS. While the problem of evil, the apparent cultural basis for the diversity (...) of religions, the explanatory breadth of contemporary science, naturalistic explanations of religious experience and miracle reports, and textual and historical criticism of the Bible, among other things, don’t make me believe the BCS is false , I am in serious doubt about it, so much so that I lack belief of it. In that case, how can I have Christian faith? And if I don’t have faith, how can I keep on praying, attending church, affirming the creed, confessing my sins, taking the sacraments, singing the hymns and songs, and so on? I can’t, unless I’m a hypocrite. So integrity requires me to drop the whole thing and get out." Of course, our student is not alone. Many Christians find themselves for some portion of their lives somewhere on the trajectory from doubt to getting out. Indeed, Christians in the West struggle with intellectual doubt more than they used to, especially university-educated Christians. What should we say to them? Some will say “Get out!,” welcoming the development as a path to liberation. We explore a different response in this essay. (shrink)

A brief article on faith as a psychological attitude.

“Divine hiddenness”, as the phrase suggests, refers, most fundamentally, to the hiddenness of God, i.e., the alleged fact that God is hidden, absent, silent. In religious literature, there is a long history of expressions of annoyance, anxiety, and despair over divine hiddenness, so understood. For example, ancient Hebrew texts lament God’s failure to show up in experience or to show proper regard for God’s people or some particular person, and two Christian Gospels portray Jesus, in his cry of dereliction on (...) the cross, as experiencing abandonment by God, whom he regarded as “Abba, Father”, an experience shared by many mystics, saints, and ordinary folk of all theistic traditions, described at its worst as “the dark night of the soul”. Understood in this way, divine hiddenness poses an existential problem for those who have such experiences. -/- However, “divine hiddenness” refers to something else in recent philosophical literature, especially since the publication of J.L. Schellenberg’s landmark book, Divine Hiddenness and Human Reason (1993). In this context, it refers to alleged facts about the absence of belief of God, on the basis of which one might think there is no God. For example, Schellenberg argues that, since there are nonbelievers who are capable of a personal relationship with God and who do not resist it, there is no perfectly loving God, while Stephen Maitzen argues that naturalism better explains the “demographics” of nonbelief than theism and Jason Marsh argues that naturalism better explains “natural nonbelief” than theism. Understood in this way, divine hiddenness constitutes putative evidence for atheism. -/- Although some of the recent philosophical literature addresses the problem understood in the first way (e.g., DeWeese-Boyd 2016; Garcia 2002), this entry focuses on divine hiddenness understood in the second way. The first section discusses the relationships between nonbelief and another source of alleged evidence for atheism: evil. The second section states and defends the argument from nonresistant nonbelief. The third section sketches attempts to explain nonresistant nonbelief from a theistic perspective. The fourth section states other responses to the argument from nonresistant nonbelief. The fifth section discusses the argument from the demographics of nonbelief and the sixth section discusses the argument from natural nonbelief. (shrink)

This 9,000+ word entry briefly assesses five models of the Trinity, those espoused by (i) Richard Swinburne, (ii) William Lane Craig, (iii) Brian Leftow, (iv) Jeff Brower and Michael Rea, and (v) Peter van Inwagen.

Picturing is a poorly understood element of Sellars’s philosophical project. We diagnose the problem with picturing as follows: on the one hand, it seems that it must be connected with action in order for it to do its job. On the other hand, the representational states of a picturing system are characterized in descriptive and seemingly static terms. How can static terms be connected with action? To solve this problem, we adopt a concept from recent work in Sellarsian metaethics: the (...) idea of a material practical inference, which (we argue) features centrally in how we picture. The key distinction is that the picturing of nonhuman animals involves only Humean material practical inference, in which representational states are corrected only by feedback from the environment and not from discursive interactions. The resulting view shows that Sellars’s contributions to practical philosophy (especially theory of action and metaethics) cannot be separated from his contributions to philosophy of mind, language, and cognitive science. Further, the view makes it clear that picturing is neither a version of the Given, nor is it a fifth wheel to inferential role in explaining representation, but is essential to Sellars’s model of how animals—including humans—represent their environment. (shrink)

The purpose of this paper is to think about the various methods of attempting to make money in the capital markets (“investing”). I suggest that though running a betting system on a Roulette wheel is silly, running a betting system on the capital markets may be a good idea.

Until recently, psychologists have conceptualised and studied trust in God (TIG) largely in isolation from contemporary work in theology, philosophy, history, and biblical studies that has examined the topic with increasing clarity. In this article, we first review the primary ways that psychologists have conceptualised and measured TIG. Then, we draw on conceptualizations of TIG outside the psychology of religion to provide a conceptual map for how TIG might be related to theorised predictors and outcomes. Finally, we provide a research (...) agenda for future empirical work in this area, as well as practical applications for counsellors and religious leaders. (shrink)

I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...) denying transworld identity for points: I prefer the latter. (shrink)

No contemporary compatibilist account of free will can be complete unless it engages with the consequence argument. I will argue that Wilfrid Sellars offered an ingenious version of compatibilism that can be used to refute the consequence argument. Unfortunately, owing to the opacity of Sellars’s writings on free will, his solution has been neglected. I will reconstruct his view here, demonstrating how it represents a powerful challenge to the consequence argument and tying it to some recent developments in the compatibilist (...) literature. (shrink)

This collection of essays is dedicated to William Rowe, with great affection, respect, and admiration. The philosophy of religion, once considered a deviation from an otherwise analytically rigorous discipline, has flourished over the past two decades. This collection of new essays by twelve distinguished philosophers of religion explores three broad themes: religious attitudes of faith, belief, acceptance, and love; human and divine freedom; and the rationality of religious belief. Contributors include: William Alston, Robert Audi, Jan Cover, Martin Curd, Peter van (...) Inwagen, Norman Kretzmann, George Nakhnikian, John Hawthorne, Philip Quinn, James Ross, Eleonore Stump, and William Wainwright. (shrink)

In the book Exploiting Hope: How the Promise of New Medical Interventions Sustains Us—and Makes Us Vulnerable, Jeremy Snyder takes on the dominant theory that exploitation in research ethics involves culpable inequity in transactions between parties. He rightly dismisses that economic explanation as inadequate. His theory of exploitation argues that it happens when those who have a duty of beneficence to someone take advantage of their hope. Exploitation is not just an unfair transaction; it is a betrayal of an (...) obligation owed to the vulnerable, weak, or dependent to protect them. Snyder is persuasive. But only to a point. He helps us understand the betrayal involved in exploiting hope. But much more remains to be debated about hope and exploitation. Exploitation in health care is not just a matter of schemers and ne'er‐do‐wells playing fast and loose with ever‐hopeful patients. Sometimes it involves patient groups looking for the right to try any intervention, no matter how dangerous or outlandish, at government expense. (shrink)

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations (...) could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. (shrink)

According to Agnosticism with a capital A, even if we don’t see how any reason we know of would justify God in permitting all the evil in the world and even if we lack evidential and non-evidential warrant for theism, we should not infer that there probably is no reason that would justify God. That’s because, under those conditions, we should be in doubt about whether the goods we know of constitute a representative sample of all the goods there are, (...) among relevantly similar things. In my "Epistemic Humility, Arguments from Evil, and Moral Skepticism" (2009), I defended Agnosticism against the charge that it leaves us in doubt about whether we are obligated to intervene to prevent horrific suffering we can prevent at no risk to ourselves. In his “Agnosticism, Skeptical Theism, and Moral Obligation” (2014), Stephen Maitzen argues that, in light of my defense, Agnosticism is at odds with commonsense morality’s insistence that we have an obligation to intervene in such cases. In the present essay, I argue that the moral principle Maitzen seems to impute to commonsense (it's hard to tell what principle he has in mind) is false and that a moral principle much more in keeping with commonsense is compatible with Agnosticism and my defense of it. Along the way, I mention multiple misrepresentations Maitzen makes of Agnosticism and my defense of it. (shrink)

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: (...) i.e. on what an ascription of a property implies about other times. Therefore, I also discussed the metaphysical debate whether persistence should be understood as endurance or perdurance. In this paper, I focus instead on spatial extrinsicality: i.e. on what an ascription of a property implies about other places. The main idea will be that the classical mechanics of continuous media involves a good deal of spatial extrinsicality---which seems not to have been noticed by philosophers, even those who have no inclination to pointillisme. I begin by describing my wider campaign. Then I present some elementary aspects of stress, strain and elasticity---emphasising the kinds of spatial extrinsicality they each involve. I conduct the discussion entirely in the context of `Newtonian' ideas about space and time. But my arguments carry over to relativistic physics. (shrink)

This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic coordinates, (...) is the rectification of vector fields afforded by the local existence and uniqueness of solutions to ordinary differential equations. For the Hamiltonian theorem, the main extra ingredients are the asymmetry of the Poisson bracket, and the fact that a vector field generates canonical transformations iff it is Hamiltonian. (shrink)

This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational (...) principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that any actual truth, in particular an actual law, is made true by actual facts. Though this threat can be avoided, at least for simple mechanical systems, it repays scrutiny; not least because it leads to some open questions. (shrink)

The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman’s chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy (...) of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, ‘t Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers. (shrink)