Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new (...) model introduced here. (shrink)

John Norton has proposed a position of “material induction” that denies the existence of a universal inductive inference schema behind scientific reasoning. In this vein, Norton has recently presented a “dome scenario” based on Newtonian physics that, in his understanding, is at variance with Bayesianism. The present note points out that a closer analysis of the dome scenario reveals incompatibilities with material inductivism itself.

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an (...) application I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013). (shrink)

If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle’s equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics—that of Norton’s dome—and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is (...) preferred. Instead of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold. (shrink)

Newton’s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, (...) PA 15260; e‐mail: [email protected]. (shrink)

In my contribution to the Symposium ("On the Vagaries of Determinism and Indeterminism"), I will identify several issues that arise in trying to decide whether Newtonian particle mechanics qualifies as a deterministic theory. I'll also give a mini-tutorial on the geometry and dynamical properties of Norton's dome surface. The goal is to better understand how his example works, and better appreciate just how wonderfully strange it is.

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance (...) with Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

In this article, we argue that the application of mathematics in the construction of physical theories constrains the form of our scientific understanding. Specifically, we discuss the constraints that the mathematical structure of the differential calculus imposes on the understanding of the structure of the world within a Newtonian worldview. In the first section of the paper, we develop the formal structure of the differential calculus. In the second section, we provide a discussion of the constraints that the differential calculus (...) imposes on the application of Newton's second law. In the final section, we present a case study of a thought experiment by John Norton, simply called `the dome'. We argue that the pathological nature of Norton's dome cannot serve as an argument to sustain the claim that Newton's second law is indeterministic because the constraints of the differential calculus dictate that Newton's second law cannot be well-defined in the infinitesimal neighbourhood of the apex of Norton's dome. (shrink)

Norton’s and Myrvold’s recent analyses of fluctuations and Landauer’s principle are compatible.

Bentham and J. S. Mill can be regarded as utilitarian tax-reformers distinguished from political economists who were simply averse to taxation. The purpose of this paper is to elucidate the difference between Bentham's and Mill's tax reform programmes. Bentham proposed the law of escheat and a tax on bankers' and stock dealers' profits, subject to the principle of least sacrifice of enjoyment. He also planned to correct the inequality of the land tax by extending it into a general income tax. (...) Mill proposed an income tax on the basis of the principle of equal sacrifice of enjoyment. He also proposed a progressive inheritance tax and a variable land tax, regarding unearned income as a fit subject for a special tax. Consequently, Mill used Bentham's ideas and tools to take a step towards a more egalitarian programme. (shrink)

Many prescriptions offered in the literature for enhancing creativity and innovation in organizations raise ethical concerns, yet creativity researchers rarely discuss ethics. We identify four categories of behavior proffered as a means for fostering creativity that raise serious ethical issues: (1) breaking rules and standard operating procedures; (2) challenging authority and avoiding tradition; (3) creating conflict, competition and stress; and (4) taking risks. We discuss each category, briefly identifying research supporting these prescriptions for fostering creativity and then we delve into (...) ethical issues associated with engaging in the prescribed behavior. These four rubrics illustrate ethical issues that need to be incorporated into the creativity and innovation literature. Recommendations for how organizations can respond to the ethical issues are offered based on practices of exemplary organizations and theories of organizational ethics. A research agenda for empirically investigating the ethical impact these four categories of behavior have on organizations concludes the article. (shrink)

The focus of Norton's book is the distinction between objectives and values in developing environmental policies. Norton argues that environmentalism is a coalition of many groups working toward common objectives, but unlike other social action movements the environmental coalition does not have shared moral principles.

We describe a case of indeterminacy in general relativity for homogeneous and isotropic cosmologies for a class of dark energy fluids. The cosmologies are parametrized by an equation of state variable, with one instance giving the same solution as Norton’s mechanical dome. Our example goes beyond previously studied cases in that indeterminacy lies in the evolution of spacetime itself: the onset of the Big Bang is indeterminate. We show further that the indeterminacy is resolved if the dynamics is (...) viewed relationally. (shrink)

Supertasks recently discussed in the literature purport to display a failure ofenergy conservation and determinism in Newtonian mechanics. We debatewhether these supertasks are admissible as Newtonian systems, with Earmanand Norton defending the affirmative and Alper and Bridger the negative.

I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical (...) mechanics with metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke’s (Mod Schoolman 78:1–8, 2000 ) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia’s (Synthese 148:433–441, 2006 ) rebuttal of it. (shrink)

Reply to Steven Lestition's article, "Countering, Transposing, or Negating the Enlightenment? A Response to Robert Norton," published in the Journal of the History of Ideas(2007), pp. 659-81.

The empirical study of grace, a relational virtue, is in its beginning stages. The purpose of this study was to provide rich, context-based, qualitative data to describe Mainline Protestants’ (a) experiences of, and (b) beliefs about, divine grace. Interviews were conducted with 28 community adults who were affiliated with Mainline Protestant Churches. Results indicated that Mainline Protestant Christians have varying beliefs about divine grace and how it is related to both the present moment and the afterlife. Divine grace was often (...) defined as, or associated with, other relational virtues (e.g., forgiveness and love), and participants occasionally defined grace as a gift. In addition, divine grace was also reported to be difficult to accept at times for a variety of reasons, but the effects of divine grace have direct associations with participants’ overall well-being. Divine grace was also associated with beliefs about heaven or the afterlife, yet participants had varying beliefs about how grace is applied to non-Christians. Limitations and future directions for research are discussed in light of the present empirical literature on divine grace. (shrink)

Disparities in maternal morbidity and mortality for Latinx populations are a paradigmatic example of the now widely acknowledged structural racism in U.S. health care that predisposed minorities to...

Context: This paper outlines how radical constructivist theory has led to a particular methodological technique, developing second-order models of student thinking, that has helped mathematics educators to be more effective teachers of their students. Problem: The paper addresses the problem of how radical constructivist theory has been used to explain and engender more viable adaptations to the complexities of teaching and learning. Method: The paper presents empirical data from teaching experiments that illustrate the process of second-order model building. Results: The (...) result of the paper is an illustration of how second-order models are developed and how this process, as it progresses, supports teachers to be more effective. Implications: This paper has the implication that radical constructivism has the potential to impact practice. Key Words: Second-order model, radical constructivism, teaching, mathematics education. (shrink)

Introduction Herder's status within German intellectual history has largely rested on the premise that he, along with his friend Johann Georg Hamann, ...

Bryan Norton’s 2005 book Sustainability describes a pragmatic approach to environmental philosophy that stresses philosophy’s role as one of mediating between scientific and ordinary language. But on two topics, Norton’s approach is not pragmatic enough. In the case of his discussion of risk, he accedes to a scientific notion that fails to acknowledge the way that ordinary usage of the word risk involves pragmatic links to human action and moral responsibility. With respect to the word sustainability, his analysis (...) fails to acknowledge important scientific work that characterizes the functional integrity of system cycling, opting instead for usage grounded either in economic accounting or in an even less substantive sense of a broad social movement for environmental improvement. On each of these topics, adherence to the pragmatic orientation of Norton’s philosophy results in a different analysis of the concepts in question. (shrink)

Responding to a major pandemic and planning for allocation of scarce resources under crisis standards of care requires coordination and cooperation across federal, state and local governments in tandem with the larger societal infrastructure. Maryland remains one of the few states with no state-endorsed ASR plan, despite having a plan published in 2017 that was informed by public forums across the state. In this article, we review strengths and weaknesses of Maryland’s response to COVID-19 and the role of the Maryland (...) Healthcare Ethics Committee Network in bridging gaps in the state’s response to prepare health care facilities for potential implementation of ASR plans. Identified “lessons learned” include: Deliberative Democracy Provided a Strong Foundation for Maryland’s ASR Framework; Community Consensus is Informative, Not Normative; Hearing Community Voices Has Inherent Value; Lack of Transparency & Political Leadership Gaps Generate a Fragmented Response; Pandemic Politics Requires Diplomacy & Persistence; Strong Leadership is Needed to Avoid Implementing ASR … And to Plan for ASR; An Effective Pandemic Response Requires Coordination and Information-Sharing Beyond the Acute Care Hospital; and The Ability to Correct Course is Crucial: Reconsidering No-visitor Policies. (shrink)

Landauer’s principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of k ln n in thermodynamic entropy. It can be formulated as a precise result in statistical mechanics, but for a restricted class of erasure processes that use a thermodynamically irreversible phase space expansion, which is the real origin of the law’s entropy cost and whose necessity has not been demonstrated. General arguments that purport to establish the unconditional validity of (...) the law fail. They turn out to depend on the illicit formation of a canonical ensemble from memory devices holding random data. To exorcise Maxwell’s demon one must show that all candidate devices—the ordinary and the extraordinary—must fail to reverse the second law of thermodynamics. The theorizing surrounding Landauer’s principle is too fragile and too tied to a few specific examples to support such general exorcism. Charles Bennett’s recent extension of Landauer’s principle to the merging of computational paths fails for the same reasons as trouble the original principle. (shrink)

In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein’s other statistical papers of 1905 had already developed and exploited the idea that the ideal (...) gas law is another macroscopic signature of finitely many, spatially localized, independent components and that these papers in turn drew on his first two, “worthless” papers of 1901 and 1902 on intermolecular forces. However, while the ideal gas law was a secure signature of independence, it was harder to use as an indicator that there are finitely many components and that they are spatially localized. Further, since his analysis of the ideal gas law depended on the assumption that the number of components was fixed, its use was precluded for heat radiation, whose component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to heat radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the number of quanta. (shrink)

Must a Maxwell demon must fail to reverse the second law of thermodynamics? Standard attempts to show it must fail make use of notions of information and computation. None of these attempts have succeeded. Worse they have distracted both supporters and opponents of these attempts from a much simpler demonstration of the necessary failure of a Maxwell's demon that employs no notions of information or computation. It requires only Liouville's theorem and its quantum analog.

In response to kenneth winkler's criticism of my suggestion (found in my "david hume: common sense moralist, sceptical metaphysician") that frances hutcheson embraced an interesting form of moral realism. i show important differences between hutcheson and locke, amplify my previous account of hutcheson's notion of concomitant ideas, and provide evidence that hutcheson's contemporaries, including his student adam smith, believed him to have maintained "that there is a real and essential distinction between vice and virtue". ("theory of moral sentiments").

Upshot: In reading the commentaries, we were struck by the fact that all of them were in some capacity related to what we consider a core principle of radical constructivism - interaction. We characterize interaction from a radical constructivist perspective, and then discuss how the authors of the commentaries address one kind of interaction.

In his new book, Sustainability: A Philosophy of Adaptive Ecosystem Management, Bryan G. Norton proposes an account of sustainability grounded in the deliberation of local communities as part of an adaptive management process. One can distinguish two different ways of justifying his account—resulting in “political” and “metaphysical” conceptions of sustainability—in much the same way that John Rawls famously distinguishes between political and metaphysical conceptions of justice. Whereas the metaphysical conception of sustainability depends on principles that are specific to American pragmatist (...) philosophical theory, the political conception draws on relatively uncontroversial elements of democratic political culture. Although Norton seems to lean toward a metaphysical conception of sustainability in his book, a political conception would actually be more compatible with the overarching aims of his project. Finally, the distinction between political and metaphysical conceptions could prove valuable as a model for thinking about how many of the current projects in environmental pragmatism relate to other strands of environmental philosophy. Thus, a potentially fruitful alteration to Norton’s recent work provides some conciliatory lessons for relating different projects in the field of environmental philosophy. (shrink)

This paper defends the usefulness of the concept of philosophical progress and the common assumption that philosophy and science aim to make the same, or a comparable, kind of progress. It does so by responding to Yafeng Shan's (2022) arguments that the wealth of research on scientific progress is not applicable or useful to philosophy, and that philosophy doesn't need a concept of progress at all. It is ultimately argued that while Shan's arguments are not successful, they reveal the way (...) forward in developing accounts of philosophical progress. (shrink)

Einstein located the foundations of general relativity in simple and vivid physical principles: the principle of equivalence, an extended principle of relativity and Mach's principle. While these ideas played an important heuristic role in Einstein's thinking, they provide a dubious logical foundation for his final theory. Einstein was also guided to his final theory, I argue, by a second tier of more prosaic heuristics. I trace one strand among them. The principle of equivalence guided Einstein well until it led him (...) to a theory that contradicted the conservation of momentum. Einstein converted the requirement of conservation of energy and momentum into a procedure that he used repeatedly for finding gravitational field equations. That procedure survives in present day developments of general relativity. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

Thoreau believed that we can learn how to live by observing nature, a view that appeals to modem environmentalists. This doctrine is exemplified in Thoreau’s use of insect analogies to illustrate how humans, like butterflies, can be transformed from the “larval” stage, which relates to the physical world through consumption, to a “perfect” state in which consumption is less important, and in which freedom and contemplation are the ends of life. This transformational idea rests upon a theory of dynamic dualism (...) in which the animal and the spiritual self remain in tension, but in which the “maturity” of the individual-transcendence of economic demands as imposed by society-emerges through personal growth based on observation of nature. Thoreau’s dynamic theory of value, and its attractiveness to environmentalists, explains why environmentalists reject the mainstream, neoclassical economic paradigm. This paradigm accepts consumer preferences as “givens” and treats these preferences as thesource of all value in their model. Because Thoreau insists that there is value in transformations from one preference set to another, the neoclassical paradigm cannot capture this central value, and cannot account for the environmentalists’ emphasis on public “education” to reduce consunlptive demands of humans on their environment. (shrink)

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In his Rules for the Direction of the Mind, Descartes elevates arithmetic and geometry to the status of paradigms for all the sciences, because of the potential for certainty in their results. This emphasis on certainty is present throughout the Cartesian corpus, but in the Rules and other early works the substance dualism characteristic of Cartesian philosophy is not as obvious. However, when several key concepts from this early work are considered together, it becomes clear that Cartesian dualism necessarily follows. (...) The most important of these concepts are: Descartes’s rejection of the Scholastic theory of sense data in favor of a telecommunicative theory of perception; his innovative reconceptualization of mathematics in which he treats number and magnitude as interchangeable, making use of the symbolism of algebra; his frequent use of visual metaphors to describe perception in general, as well as other cognitive activity. It is in consideration of this third point that Descartes’s treatment of the imagination shows its importance, for the relationship of the imagination to the intellect parallels that of geometric figures to algebraic formulae. Though the role of the imagination in the Rules seems to make the status of a dualist ontology in this work more ambiguous, this paper will argue that in fact it is precisely in the treatment of imagination that one can find the traces of a fully developed substance dualism. (shrink)

In this paper we provide a psychological explanation for ‘grounding observations’—observations that are thought to provide evidence that there exists a relation of ground. Our explanation does not appeal to the presence of any such relation. Instead, it appeals to certain evolved cognitive mechanisms, along with the traditional modal relations of supervenience, necessitation and entailment. We then consider what, if any, metaphysical conclusions we can draw from the obtaining of such an explanation, and, in particular, if it tells us anything (...) about whether we ought to posit a relation of ground. (shrink)

Issues of interest, identity and values intertwine in environmental conflicts, creating challenges that cannot generally be overcome using rationalities grounded in generalised argumentation and abstraction. To address the growing need to engage interests and identities along with plural values in the conservation of biodiversity and ecological systems, we introduce the concept of ‘appropriateness of actions’ and ground it in a relational understanding of environmental ethics. A determination of appropriateness for actions comes from combining outputs from value elicitation with those of (...) interest and identity negotiation in ways that are salient to specific people and their relationships to specific places. Drawing on the Blue Mountain Forest Partnership in the Pacific Northwest, we propose factors of success for supporting appropriate actions: 1) understanding context and identifying key stakeholders; 2) surfacing a diversity of interests and building system-level trust; 3) building empathy for different identities grounded in specific places; 4) eliciting diverse values and seeking to understand their links to worldviews and knowledge systems and; 5) seeking out appropriate actions. (shrink)

David and Mary Norton present the definitive scholarly edition of one of the greatest philosophical works ever written. This second volume begins with their 'Historical Account' of the Treatise, an account that runs from the beginnings of the work to the period immediately following Hume's death in 1776, followed by an account of the Nortons' editorial procedures and policies and a record of the differences between the first-edition text of the Treatise and the critical text that follows. The volume continues (...) with an extensive set of 'Editors' Annotations', intended to illuminate Hume's texts; a four-part bibliography of materials cited in both volumes; and a comprehensive index. (shrink)

Preface: This volume originated in a conference on "The Place of Thought Experiments in Science and Philosophy" which was organized by us and held at the Center for Philosophy of Science at the University of Pittsburgh, April 18-20, 1986. The idea behind this conference was to encourage philosophers and scientists to talk to each other about the role of thought experiments in their various disciplines. These papers were either written for the conference, or were written after it by commentators and (...) other participants.... We hope that this volume will be of use to other philosophers and scientists who are interested in thought experiments, as well as inspire more work in this area.... (shrink)

A major part of Einstein’s 1905 light quantum paper is devoted to arguing that high frequency heat radiation bears the characteristic signature of a microscopic energy distribution of independent, spatially localized components. The content of his light quantum proposal was precarious in that it contradicted the great achievement of nineteenth century physics, the wave theory of light and its accommodation in electrodynamics. However the methods used to arrive at it were both secure and familiar to Einstein in 1905. A mainstay (...) of Einstein’s research in statistical physics, extending to his earliest publications of 1901 and 1902, had been the inferring of the microscopic constitution of systems from their macroscopic properties. In his statistical work of 1905, Einstein dealt with several thermal systems consisting of many, independent, spatially localized components. They were the dilute sugar solutions of his doctoral dissertation and suspended particles of his Brownian motion paper. (shrink)

To outward appearances, teleological description and explanation of human conduct have lately been regenerating themselves, phoenix-like, from the ashes to which they were reduced by positivism and behaviorism. In the words of Israel Scheffler, “Teleological explanations have, it is true, been largely expunged from the natural sciences, since it is no longer acceptable to attribute beliefs or purposes to physical objects. Such explanations are, however, of enduring relevance in the human sciences, history, literature, and everyday life, where the beliefs and (...) purposes of people are of major interest in characterizing and predicting their conduct.”. (shrink)

Modern readers turning to Einstein’s famous 1905 paper on special relativity may not find what they expect. Its title, “On the electrodynamics of moving bodies,” gives no inkling that it will develop an account of space and time that will topple Newton’s system. Even its first paragraph just calls to mind an elementary experimental result due to Faraday concerning the interaction of a magnet and conductor. Only then does Einstein get down to the business of space and time and lay (...) out a new theory in which rapidly moving rods shrink and clocks slow and the speed of light becomes an impassable barrier. This special theory of relativity has a central place in modern physics. As the first of the modern theories, it provides the foundation for particle physics and for Einstein’s general theory of relativity; and it is the last point of agreement between them. It has also received considerable attention outside physics. It is the first port of call for philosophers and other thinkers, seeking to understand what Einstein did and why it changed everything. It is often also their last port. The theory is arresting enough to demand serious reflection and, unlike quantum theory and general relativity, its essential content can be grasped fully by someone merely with a command of simple algebra. It contains Einstein’s analysis of simultaneity, probably the most celebrated conceptual analysis of the century. (shrink)