The supertasks described by Perez Laraudogoitia, involving the dynamics of a system containing an infinite number of particles in a bounded region of space, are characterized by the nonconservation of energy and by the spontaneous motion of particles. We argue that these features arise from the inadequacy of the local, particle-by-particle description used to analyze the supertasks. A global analysis, involving embeddings in Hilbert spaces, clarifies these supertasks and avoids what we regard as their nonphysical features.

In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...) the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks. (shrink)

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...) discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time. (shrink)

A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton's laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in a (...) Banach space, to determine the origin of the strange behavior. This paper provides a common framework for the discussion of both the local and global methods of analysis. Using this single framework, the areas of disagreement and agreement are made explicit. Further examples of supertasks are proposed to illuminate various aspects of the discussion. (shrink)

A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton''s laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in a (...) Banach space, to determine the origin of the strange behavior. This paper provides a common framework for the discussion of both the local and global methods of analysis. Using this single framework, the areas of disagreement and agreement are made explicit. Further examples of supertasks are proposed to illuminate various aspects of the discussion. (shrink)

In the “Appendix” to the Treatise, Hume claims that he has discovered a “very considerable” mistake in his earlier discussion of the self. Hume's expression of the problem is notoriously opaque, leading to a vast scholarly debate as to exactly what problem he identified in his earlier account of the self. I propose a new solution to this interpretive puzzle. I argue that a tension generated by Hume's conceptual skepticism about real “principles of union” and his account of fictions of (...) the imagination is the defect identified in the “Appendix.”. (shrink)

The past decade has witnessed a surge of pricing innovations in the U.S. telecommunications industry. This book systematically reviews recent innovations in the economic theory of pricing and extends results to the conditions which characterise telecommunications markets. The implementation of normative pricing theory is examined in selected US telephone tariffs, providing a rich and diverse data base and laboratory for examining the practical consequences of pricing innovations. The authors develop and illuminate the relationships between the normative economic theory of pricing (...) - with its objectives of social welfare, economic efficiency, and fairness - and telecommunications pricing as it is practised by business and regulators. The general theoretical pricing principles and lessons of US pricing experience discussed are directly applicable to telecommunications services in other countries, and to numerous other industries including electricity, gas, rail and air transport, and postal services, as well as economists studying the economic theory of pricing. (shrink)

Hume’s claim that we project necessity onto objects we take to be causally related has been influential in contemporary discussions of modality, inspiring deflationary accounts of our modal commitments. Hume is commonly understood as holding that modal projection explains our judging that an effect must follow its cause. This misunderstands the role of projection in Hume’s discussions of causation and causal judgement. Projection is a diagnosis of a distinctively philosophical confusion: the commitment to mind-independent necessary connections. In arguing for this, (...) I provide an account of the psychological process that, in Hume’s view, underlies projection. This account resolves problems with Hume’s projectivism identified by his commentators. (shrink)

This paper aims to clarify Locke’s distinction between simple and complex ideas. I argue that Locke accepts what I call the “compositional criterion of simplicity.” According to this criterion, an idea is simple just in case it does not have another idea as a proper part. This criterion is prima facie inconsistent with Locke’s view that there are simple ideas of extension. This objection was presented to Locke by his French translator, Pierre Coste, on behalf of Jean Barbeyrac. Locke responded (...) to Barbeyrac’s objection, but his response, along with a passage from Chapter XV of Book II of the Essay, “Of Duration and Expansion, considered together,” has been taken to show that he did not accept the compositional criterion. I examine these passages and argue that they are not in tension with but rather affirm that criterion. (shrink)

Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, when (...) one side of the argument gets things wrong, it necessarily gets them wrong. As we consider both sides of one of these philosophical arguments, we will at some point think about something that’s impossible. Yet most philosophical accounts of meaning and content hold that we can’t meaningfully think or reason about the impossible. -/- In The Impossible, Jago argues that we often gain new information, new beliefs, and, sometimes, fresh knowledge through logic, mathematics, and philosophy. That is why logic, mathematics, and philosophy are useful. We therefore require accounts of knowledge and belief, of information and content, and of meaning which allow space for the impossible. Jago’s aim in this book is to provide such accounts. He gives a detailed analysis of the concept of hyperintensionality, whereby logically equivalent contents may be distinct, and develops a theory in terms of possible and impossible worlds. Along the way, he provides a theory of what those worlds are and how they feature in our analysis of normative epistemic concepts: knowledge, belief, information, and content. (shrink)

Online data collection methods are expanding the ease and access of developmental research for researchers and participants alike. While its popularity among developmental scientists has soared during the COVID-19 pandemic, its potential goes beyond just a means for safe, socially distanced data collection. In particular, advances in video conferencing software has enabled researchers to engage in face-to-face interactions with participants from nearly any location at any time. Due to the novelty of these methods, however, many researchers still remain uncertain about (...) the differences in available approaches as well as the validity of online methods more broadly. In this article, we aim to address both issues with a focus on moderated data collected using video-conferencing software. First, we review existing approaches for designing and executing moderated online studies with young children. We also present concrete examples of studies that implemented choice and verbal measures and looking time across both in-person and online moderated data collection methods. Direct comparison of the two methods within each study as well as a meta-analysis of all studies suggest that the results from the two methods are comparable, providing empirical support for the validity of moderated online data collection. Finally, we discuss current limitations of online data collection and possible solutions, as well as its potential to increase the accessibility, diversity, and replicability of developmental science. (shrink)

The Molyneux problem is one of the major questions addressed by early modern authors. Whereas Locke’s response to Molyneux’s question has been the subject of extensive scholarly discussion, Leibniz’s response has received comparatively little attention. This paper defends an interpretation of Leibniz’s nuanced response to the problem and criticizes a competing interpretation that has recently been proposed.

That Socrates took himself to possess a divine sign is well attested by ancient sources. Both Plato and Xenophon mention Socrates’ daimonion on numerous occasions. What is problematic for contemporary scholars is that Socrates unfailingly obeys the warnings of his sign. Scholars have worried that Socrates seems to ascribe greater epistemic authority to his sign than his own critical reasoning. Moreover, he never so much as questions the authority of his sign to guide his actions, much less its divine nature. (...) Socrates’ unquestioning obedience to his sign thus appears to be in conflict with another of Socrates’ defining characteristics: namely, his relentless rationality. However, Socrates does not seem to recognize such inconsistency. The problem of the daimonion, then, is this: is Socrates’ professed commitment to rationality consistent with his unquestioning deference to his daimonion’s warnings? And if so, how? In this paper, I first discuss several solutions to the problem of the daimonion. I aim to show that none of the accounts of Socrates’ sign that have appeared in the scholarly literature are adequate. I then propose a new account of the daimonion, which, I argue, secures the rationality of Socrates’ obedience to his divine sign. (shrink)

It is time to bring the rich resources of these traditions into the contemporary debate about the nature of self. This volume is the first of its kind.

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.

Nondescriptivist views in many areas of philosophy have long been associated with the commitment that in contrast to other domains of discourse, there are no propositions in their particular domain. For example, the ‘no truth conditions’ theory of conditionals1 is understood as the view that conditionals don’t express propositions, noncognitivist expressivism in metaethics is understood as advocating the view that there are not really moral propositions,2 and expressivism about epistemic modals is thought of as the view that there is no (...) such thing as the proposition that Jack might be at home, over and above the proposition that Jack is at home.3 Of course, it is nearly always acknowledged that advocates of a nondescriptivist theory need not deny that there are conditional, moral, or modal propositions ‘at the end of the day’ – for if they also endorse a deflationary reading of talk about propositions, as famously advocated by Simon Blackburn, then they can employ such deflationary talk just as much as the rest of us. They just don’t appeal to propositions to do any of the work in their theories. Rather, they ‘earn the right’ to talk about propositions.4 It is the aim of this paper to upset this way of thinking about the proper attitude of nondescriptivists toward propositions, and to advocate a more constructive and in some ways more radical alternative on behalf of the nondescriptivist. I will begin by introducing and developing a set of problems that are faced by any nondescriptivist theory which tries to do without propositions. All of these problems are easily solved by any view which postulates propositions across the board, but none of them are solved by merely deflationary talk about propositions – their most promising solutions require propositions to do real theoretical work, and therefore the problems themselves remind us of and illustrate some of the important reasons why it is worth positing propositions in the first place.. (shrink)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...) epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, which defenders (...) of the ‘possible worlds’ approach are frequently critical of. (shrink)

We argue that the interaction of biased media coverage and widespread employment of the recognition heuristic can produce epistemic injustices. First, we explain the recognition heuristic as studied by Gerd Gigerenzer and colleagues, highlighting how some of its components are largely external to, and outside the control of, the cognitive agent. We then connect the recognition heuristic with recent work on the hypotheses of embedded, extended, and scaffolded cognition, arguing that the recognition heuristic is best understood as an instance of (...) scaffolded cognition. In section three, we consider the double-edged sword of cognitive scaffolding. On the one hand, scaffolds can reduce the internal processing demands on cognitive agents while increasing their access to information. On the other hand, the use of scaffolding leaves cognitive agents increasingly vulnerable to forming false beliefs or failing to form beliefs at all about particular topics. With respect to the recognition heuristic, agents rely on third parties (such as the media) to report not just what’s true but also what’s important or valuable. This makes cognitive agents relying on these third parties vulnerable to two erroneous influences: 1) because they don’t recognize something, it isn’t important or valuable, and 2) because they do recognize something, it is important or valuable. Call the latter the Kardashian Inference and the former the Darfur Inference. In section four, we use Fricker’s (2007) concept of epistemic injustice to characterize the nature and harm of these false inferences, with special emphasis on the Darfur Inference. In section five, we use data-mining and an empirical study to show how Gigerenzer’s population estimation task is liable to produce Darfur Inferences. We conclude with some speculative remarks on more important Darfur Inferences, and how to avoid them by scaffolding better. One primary way to accomplish this it to shift the burden of embodying the virtue of epistemic justice from the hearer or consumer of media to the media themselves. (shrink)

First published in 1902, William James's Varieties of Religious Experience is considered a classic in religious studies and the psychology of religion. But how has James's classic study weathered decades of development in psychology and behavioral sciences?

The aim of this article is to demonstrate a methodology that ‘writes across’ the separation between theory and practice. It refers to French feminist writers of the 1970s and 1980s, often categorized under the heading of ‘écriture féminine’, who were concerned with how language operates and with the relationship between language and the formation of the self. The article consists of a short preface introducing a piece of autobiographical writing driving home. The piece brings into collision incidents, objects and time (...) frames in an attempt to dissolve the borders between fact and fiction, personal and impersonal, private and public, poetic writing and analysis. In the act of writing driving home the author also attempts to generate knowledge. driving home searches within the anecdotal and autobiographical for methodological indicators. The how and why of the author’s writing practice run across, over and around each other, acting as short and inconclusive pathways within the investigative structure of the whole. (shrink)

This book offers a systematic framework for thinking about the relationship between language and technology and an argument for interweaving thinking about technology with thinking about language. The main claim of philosophy of technology—that technologies are not mere tools and artefacts not mere things, but crucially and significantly shape what we perceive, do, and are—is re-thought in a way that accounts for the role of language in human technological experiences and practices. Engaging with work by Wittgenstein, Heidegger, McLuhan, Searle, Ihde, (...) Latour, Ricoeur, and many others, the author critically responds to, and constructs a synthesis of, three "extreme", idealtype, untenable positions: only humans speak and neither language nor technologies speak, only language speaks and neither humans nor technologies speak, and only technology speaks and neither humans nor language speak. The construction of this synthesis goes hand in hand with a narrative about subjects and objects that become entangled and constitute one another. Using Words and Things thus draws in central discussions from other subdisciplines in philosophy, such as philosophy of language, epistemology, and metaphysics, to offer an original theory of the relationship between language and technology centered on use, performance, and narrative, and taking a transcendental turn. (shrink)

In this paper, I describe some of what I take to be the more interesting features of friendship, then explore the extent to which other virtues can be reconstructed as sharing those features. I use trustworthiness as my example throughout, but I think that other virtues such as generosity & gratitude, pride & respect, and the producer’s & consumer’s sense of humor can also be analyzed with this model. The aim of the paper is not to demonstrate that all moral (...) virtues are exactly like friendship in all important respects, but rather to articulate a fruitful model in which to explore the virtues. Section 2 explores the relational nature of friendship, drawing on Aristotle’s discussion of friendship in the Nicomachean Ethics. Section 3 catalogues four motivations for taking seriously the friendship model of virtue. Section 4 applies the friendship model in depth to the virtue of trustworthiness. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 (...) when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

Bringing together the latest scientific advances and some of the most enduring subtle philosophical puzzles and problems, this book collects original historical and contemporary sources to explore the wide range of issues surrounding the nature of life. Selections ranging from Aristotle and Descartes to Sagan and Dawkins are organised around four broad themes covering classical discussions of life, the origins and extent of natural life, contemporary artificial life creations and the definition and meaning of 'life' in its most general form. (...) Each section is preceded by an extensive introduction connecting the various ideas discussed in individual chapters and providing helpful background material for understanding them. With its interdisciplinary perspective, this fascinating collection is essential reading for scientists and philosophers interested in astrobiology, synthetic biology and the philosophy of life. (shrink)

From his earliest work on personal identity to his last on the value of truthfulness, the ideas and arguments of Bernard Williams - in the metaphysics of personhood, in the history of philosophy, but especially in ethics and moral psychology - have proved sometimes controversial, often influential, and always worth studying. This book provides a comprehensive account of Williams's many significant contributions to contemporary philosophy. Topics include personal identity, various critiques of moral theory, practical reasoning and moral motivation, truth and (...) objectivity, and the relevance of ancient Greece to modern life. It not only positions Williams among these important philosophical topics, but also with regard to the views of other philosophers, including prominent forerunners such as Hume and Nietzsche and contemporary thinkers such as, Nagel, McDowell, MacIntyre and Taylor. The fragmentary nature of Williams's work is addressed and recurring themes and connections within his work are brought to light. (shrink)

Debates over health care have focused for so long on economics that the proper goals for medicine seem to be taken for granted; yet problems in health care stem as much from a lack of agreement about the goals and priorities of medicine as from the way systems function. This book asks basic questions about the purposes and ends of medicine and shows that the answers have practical implications for future health care delivery, medical research, and the education of medical (...) students. The Hastings Center coordinated teams of physicians, nurses, public health experts, philosophers, theologians, politicians, health care administrators, social workers, and lawyers in fourteen countries to explore these issues. In this volume, they articulate four basic goals of medicine — prevention of disease, relief of suffering, care of the ill, and avoidance of premature death — and examine them in light of the cultural, political, and economic pressures under which medicine functions. In reporting these findings, the contributors touch on a wide range of diverse issues such as genetic technology, Chinese medicine, care of the elderly, and prevention and public health. The Goals of Medicine clearly demonstrates the importance of clarifying the purposes of medicine before attempting to change the economic and organizational systems. It warns that without such examination, any reform efforts may be fruitless. (shrink)

Particularists in ethics emphasize that the normative is holistic, and invite us to infer with them that it therefore defies generalization. This has been supposed to present an obstacle to traditional moral theorizing, to have striking implications for moral epistemology and moral deliberation, and to rule out reductive theories of the normative, making it a bold and important thesis across the areas of normative theory, moral epistemology, moral psychology, and normative metaphysics. Though particularists emphasize the importance of the holism of (...) the normative, however, it is not something that they have been able to explain. In this paper I’ll show how to use a small number of simple and, I’ll argue, independently compelling assumptions in order to both predict and explain the holistic features of the normative with respect to the non-normative. The basic idea of the paper is simple. It is that normative claims are holistic because they are general, rather than because they defy generalization. (shrink)

The sense of smell occupies a peculiar intermediate position within Aristotle's theory of sense perception: odours, like colours and sounds, are perceived at a distance through an external medium of air or water; yet in their nature they are intimately related to flavours, the proper objects of taste, which for Aristotle is a form of touch. In this paper, I examine Aristotle's claims about odour and smell, especially in De Anima II.9 and De Sensu 5, to see what light they (...) shed on his theory of sense perception more generally. In the first half, I argue that neither of the two most influential recent ways of understanding Aristotle's theory of perception can adequately account for what he says about the sense of smell. In the second half, I offer my own positive account, considering and resolving various puzzles raised by Aristotle's claims about the nature of odour and its relation to flavour. Finally, I conclude that Aristotle's discussions of odour and smell suggest a plausible and interesting way of understanding the relationship, on his view, between ordinary, material changes in the sense organs and the activation of the capacity to perceive, considered merely as such. (shrink)

In this paper, I argue that there is a picture of how law works that most legal theorists are implicitly committed to and take to be common ground. This Standard Picture (SP, for short) is generally unacknowledged and unargued for. SP leads to a characteristic set of concerns and problems and yields a distinctive way of thinking about how law is supposed to operate. I suggest that the issue of whether SP is correct is a fundamental one for the philosophy (...) of law, more basic, for example, than the issue that divides legal positivists and anti-positivists, at least as the latter issue is ordinarily understood. The goals of the paper are fourfold: 1) to identify and articulate in some detail the Standard Picture; 2) to show that SP is widely held and has important consequences for other debates in the philosophy of law; 3) to show that SP leads to a serious theoretical problem; 4) to sketch an alternative picture that promises to avoid this problem. I emphasize the modesty of these goals in one respect. I make no claim to refute SP or to fully develop and defend an alternative picture. (shrink)

This article is a précis of Mark C. Murphy’s _Divine Holiness and Divine Action_ (Oxford University Press, 2021), which offers an account of God’s holiness and of the difference this view of God’s holiness should make to our understanding of divine action.

The Clarke/Rowe version of the Cosmological Argument is sound only if the Principle of Sufficient Reason is true, but many philosophers, including Rowe, think that there is not adequate evidence for the principle of sufficient reason. I argue that there may be indirect evidence for PSR on the grounds that if we do not accept it, we lose our best justification for an important principle of metaethics, namely, the Principle of Universalizability. To show this, I argue that all the other (...) justifications of the Principle of Universalizability on offer, including Richard Hare's, are inadequate. (shrink)

Quietist Moral Realists accept that there are moral facts and properties, while aiming to avoid many of the explanatory burdens thought to fall on traditional moral realists. This chapter examines the forms that Quietist Moral Realism has taken and the challenges it has faced, in order to better assess its prospects. The best hope, this chapter argues, lies in a pragmatist approach that distinguishes the different functions of diverse areas of discourse. This paves the way for a form of Quietism (...) that does not simply remain quiet about the explanatory demands of metaethics, but rather is able to diagnose where they go wrong. By combining a neopragmatic analysis of the discourse with an easy approach to ontology, , we can develop a form of Quietist Moral Realism that is far stronger than critics of quietism have appreciated. (shrink)