Results for 'Richard Keynes'

981 found
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  1. John Maynard Keynes and Ludwig von Mises on Probability.Ludwig van den Hauwe - 2010 - Journal of Libertarian Studies 22 (1):471-507.
    The economic paradigms of Ludwig von Mises on the one hand and of John Maynard Keynes on the other have been correctly recognized as antithetical at the theoretical level, and as antagonistic with respect to their practical and public policy implications. Characteristically they have also been vindicated by opposing sides of the political spectrum. Nevertheless the respective views of these authors with respect to the meaning and interpretation of probability exhibit a closer conceptual affinity than has been acknowledged in (...)
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  2. Materialised Identities: Cultural Identity, Collective Memory, and Artifacts.Richard Heersmink - 2021 - Review of Philosophy and Psychology:1-17.
    This essay outlines one way to conceptualise the relation between cultural identity, collective memory, and artifacts. It starts by characterising the notion of cultural identity as our membership to cultural groups and briefly explores the relation between cultural and narrative identity (section 2). Next, it presents how human memory is conceptualised on an individual and collective level (section 3) and then distinguishes between small-scale and large-scale collective memory (section 4). Having described cultural identity and collective memory, it argues that cultural (...)
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  3. Keynes, Uncertainty and Interest Rates.Brian Weatherson - 2002 - Cambridge Journal of Economics 26 (1):47-62.
    Uncertainty plays an important role in The General Theory, particularly in the theory of interest rates. Keynes did not provide a theory of uncertainty, but he did make some enlightening remarks about the direction he thought such a theory should take. I argue that some modern innovations in the theory of probability allow us to build a theory which captures these Keynesian insights. If this is the right theory, however, uncertainty cannot carry its weight in Keynes’s arguments. This (...)
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  4. Labeled calculi and finite-valued logics.Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach - 1998 - Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...)
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  5. Choosing for Changing Selves.Richard Pettigrew - 2019 - Oxford, UK: Oxford University Press.
    What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.
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  6. The problem of closure and questioning attitudes.Richard Teague - 2022 - Synthese 200 (5):1-19.
    The problem of closure for the traditional unstructured possible worlds model of attitudinal content is that it treats belief and other cognitive states as closed under entailment, despite apparent counterexamples showing that this is not a necessary property of such states. One solution to this problem, which has been proposed recently by several authors (Schaffer 2005; Yalcin 2018; Hoek forthcoming), is to restrict closure in an unstructured setting by treating propositional attitudes as question-sensitive. Here I argue that this line of (...)
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  7. Aggregating agents with opinions about different propositions.Richard Pettigrew - 2022 - Synthese 200 (5):1-25.
    There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...)
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  8. On the Expected Utility Objection to the Dutch Book Argument for Probabilism.Richard Pettigrew - 2021 - Noûs (1):23-38.
    The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...)
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  9. Pandemic ethics: the case for risky research.Richard Yetter Chappell & Peter Singer - 2020 - Research Ethics 16 (3-4):1-8.
    There is too much that we do not know about COVID-19. The longer we take to find it out, the more lives will be lost. In this paper, we will defend a principle of risk parity: if it is permissible to expose some members of society (e.g. health workers or the economically vulnerable) to a certain level of ex ante risk in order to minimize overall harm from the virus, then it is permissible to expose fully informed volunteers to a (...)
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  10. Sustainable development in the shadow of climate change.Richard Sťahel - 2019 - Civitas, Porto Alegre 19 (2):337-353.
    Development plans at different levels – from local to global – aspire to eliminate poverty, famine, to make health care accessible, to create better access to education, to improve transportation, employment, and the quality of life, all within next decades. Yet, these plans collide with the reality of climate change, more precisely the Anthropocene, which already creates high-dimensional conflicts. These will only intensify within decades because climate change and other consequences of the environment global devastation lead to a real decrease (...)
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  11. On the pragmatic and epistemic virtues of inference to the best explanation.Richard Pettigrew - 2021 - Synthese 199 (5-6):12407-12438.
    In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.
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  12. Should longtermists recommend hastening extinction rather than delaying it?Richard Pettigrew - 2024 - The Monist 107 (2):130-145.
    Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...)
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  13. Preserving narrative identity for dementia patients: Embodiment, active environments, and distributed memory.Richard Heersmink - 2022 - Neuroethics 15 (8):1-16.
    One goal of this paper is to argue that autobiographical memories are extended and distributed across embodied brains and environmental resources. This is important because such distributed memories play a constitutive role in our narrative identity. So, some of the building blocks of our narrative identity are not brain-bound but extended and distributed. Recognising the distributed nature of memory and narrative identity, invites us to find treatments and strategies focusing on the environment in which dementia patients are situated. A second (...)
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  14. How should your beliefs change when your awareness grows?Richard Pettigrew - forthcoming - Episteme:1-25.
    Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...)
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  15. Nothing, Inc.Richard Oxenberg - manuscript
    A short story about an encounter with . . . nothing.
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  16.  96
    Nietzsche’s Physiology of Aesthetics, and the Aesthetics of Physiology.Richard J. Elliott - 2024 - Studi di Estetica 27 (3):71 - 90.
    Nietzsche announces his intentions to publish a “physiology of aesthetics”, namely a naturalistic explanation for how aesthetic judgements are grounded in the physiology of both the one experiencing the work, and the creator of it. But as well as the physiological reduction of aesthetic judgements, Nietzsche in many places across his oeuvre frames the apparatus of physiology, especially the prescriptive dimension of self-cultivation, in terms amenable to being treated as ‘aesthetic’. The first section will mount a (re-) defense of the (...)
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  17. Pandemic Ethics and Status Quo Risk.Richard Yetter Chappell - 2022 - Public Health Ethics 15 (1):64-73.
    Conservative assumptions in medical ethics risk immense harms during a pandemic. Public health institutions and public discourse alike have repeatedly privileged inaction over aggressive medical interventions to address the pandemic, perversely increasing population-wide risks while claiming to be guided by ‘caution’. This puzzling disconnect between rhetoric and reality is suggestive of an underlying philosophical confusion. In this paper, I argue that we have been misled by status quo bias—exaggerating the moral significance of the risks inherent in medical interventions, while systematically (...)
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  18. Distributed learning: Educating and assessing extended cognitive systems.Richard Heersmink & Simon Knight - 2018 - Philosophical Psychology 31 (6):969-990.
    Extended and distributed cognition theories argue that human cognitive systems sometimes include non-biological objects. On these views, the physical supervenience base of cognitive systems is thus not the biological brain or even the embodied organism, but an organism-plus-artifacts. In this paper, we provide a novel account of the implications of these views for learning, education, and assessment. We start by conceptualising how we learn to assemble extended cognitive systems by internalising cultural norms and practices. Having a better grip on how (...)
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  19. Pooling, Products, and Priors.Richard Pettigrew & Jonathan Weisberg -
    We often learn the opinions of others without hearing the evidence on which they're based. The orthodox Bayesian response is to treat the reported opinion as evidence itself and update on it by conditionalizing. But sometimes this isn't feasible. In these situations, a simpler way of combining one's existing opinion with opinions reported by others would be useful, especially if it yields the same results as conditionalization. We will show that one method---upco, also known as multiplicative pooling---is specially suited to (...)
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  20. Human uniqueness in using tools and artifacts: flexibility, variety, complexity.Richard Heersmink - 2022 - Synthese 200 (6):1-22.
    The main goal of this paper is to investigate whether humans are unique in using tools and artifacts. Non-human animals exhibit some impressive instances of tool and artifact-use. Chimpanzees use sticks to get termites out of a mound, beavers build dams, birds make nests, spiders create webs, bowerbirds make bowers to impress potential mates, etc. There is no doubt that some animals modify and use objects in clever and sophisticated ways. But how does this relate to the way in which (...)
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  21. What is a brain state?Richard Brown - 2006 - Philosophical Psychology 19 (6):729-742.
    Philosophers have been talking about brain states for almost 50 years and as of yet no one has articulated a theoretical account of what one is. In fact this issue has received almost no attention and cognitive scientists still use meaningless phrases like 'C-fiber firing' and 'neuronal activity' when theorizing about the relation of the mind to the brain. To date when theorists do discuss brain states they usually do so in the context of making some other argument with the (...)
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  22. Die innere Dynamik von selbst- und umweltbezogenen Tugenden im tugendhaften Akteur. Systematische Überlegungen im Ausgang von Erich Fromm.Richard Friedrich Runge - 2022 - Zeitschrift Für Ethik Und Moralphilosophie 5 (1):37-59.
    Die eudaimonistische Tugendethik sieht sich, was ihre innere Struktur anbelangt, standardmäßig mit den Vorwürfen des Egoismus und Anthropozentrismus konfrontiert, was auch das Projekt einer ökologischen Tugendethik zu gefährden scheint. Der vorliegende Artikel versucht, ausgehend von der Tugendethik Erich Fromms, eine neue Perspektive auf diese Standardvorwürfe zu entwickeln, indem er den theoretischen Implikationen nachgeht, die die Anerkennung der Biophilie – der Liebe zum Leben – als eine der Tugenden des Menschen für den Frommschen Ansatz hat. Die zunächst noch exegetisch ausgerichtete Diskussion (...)
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  23. History and normativity in political theory: the case of Rawls.Richard Bourke - 2023 - In Richard Bourke & Quentin Skinner (eds.), History in the humanities and social sciences. New York: Cambridge University Press.
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  24. Environmetalism as a Political Philosophy for the Anthropocene.Richard Sťahel - 2020 - Anthropocenica. Revista De Estudos Do Antropoceno E Ecocritica 1 (1):3-22.
    The political philosophy originates from the reflections of crisis, risks and threats which society faces to. The author understands environmentalism as a tendency of current political philosophy which starts from the reflections of causes and possible effects of global environmental crisis as one of the most serious threats to the existential preconditions of current political system and global civilization at all. Considering the changes in social, technological and environmental starting conditions of the existence of economic-political system – that are consequences (...)
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  25. Clinician Perspectives on Opioid Treatment Agreements: A Qualitative Analysis of Focus Groups.Nathan Richards, Martin Fried, Larisa Svirsky, Nicole Thomas, Patricia J. Zettler & Dana Howard - 2023 - AJOB Empirical Bioethics (ahead of print):1-12.
    BACKGROUND Patients with chronic pain face significant barriers in finding clinicians to manage long-term opioid therapy (LTOT). For patients on LTOT, it is increasingly common to have them sign opioid treatment agreements (OTAs). OTAs enumerate the risks of opioids, as informed consent documents would, but also the requirements that patients must meet to receive LTOT. While there has been an ongoing scholarly discussion about the practical and ethical implications of OTA use in the abstract, little is known about how clinicians (...)
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  26. Bayesian updating when what you learn might be false.Richard Pettigrew - 2023 - Erkenntnis 88 (1):309-324.
    Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...)
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  27. Logical ignorance and logical learning.Richard Pettigrew - 2020 - Synthese 198 (10):9991-10020.
    According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...)
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  28. Why Not Effective Altruism?Richard Yetter Chappell - 2024 - Public Affairs Quarterly 38 (1):3-21.
    Effective altruism sounds so innocuous—who could possibly be opposed to doing good more effectively? Yet it has inspired significant backlash in recent years. This paper addresses some common misconceptions and argues that the core “beneficentric” ideas of effective altruism are both excellent and widely neglected. Reasonable people may disagree on details of implementation, but all should share the basic goals or values underlying effective altruism.
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  29. Varieties of artifacts: Embodied, perceptual, cognitive, and affective.Richard Heersmink - 2021 - Topics in Cognitive Science (4):1-24.
    The primary goal of this essay is to provide a comprehensive overview and analysis of the various relations between material artifacts and the embodied mind. A secondary goal of this essay is to identify some of the trends in the design and use of artifacts. First, based on their functional properties, I identify four categories of artifacts co-opted by the embodied mind, namely (1) embodied artifacts, (2) perceptual artifacts, (3) cognitive artifacts, and (4) affective artifacts. These categories can overlap and (...)
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  30. Varieties of the extended self.Richard Heersmink - 2020 - Consciousness and Cognition 85:103001.
    This article provides an overview and analysis of recent work on the extended self, demonstrating that the boundaries of selves are fluid, shifting across biological, artifactual, and sociocultural structures. First, it distinguishes the notions of minimal self, person, and narrative self. Second, it surveys how philosophers, psychologists, and cognitive scientists argue that embodiment, cognition, emotion, consciousness, and moral character traits can be extended and what that implies for the boundaries of selves. It also reviews and responds to various criticisms and (...)
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  31. Testability and Viability: Is Inflationary Cosmology “Scientific”?Richard Dawid & Casey McCoy - 2023 - European Journal for Philosophy of Science 13 (4):51.
    We provide a philosophical reconstruction and analysis of the debate on the scientific status of cosmic inflation that has played out in recent years. In a series of critical papers, Ijjas et al. have questioned the scientificality of the current views on cosmic inflation. Proponents of cosmic inflation have in turn defended the scientific credentials of their approach. We argue that, while this defense, narrowly construed, is successful against Ijjas et al., the latter's reasoning does point to a significant epistemic (...)
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  32. A virtue epistemology of the Internet: Search engines, intellectual virtues and education.Richard Heersmink - 2018 - Social Epistemology 32 (1):1-12.
    This paper applies a virtue epistemology approach to using the Internet, as to improve our information-seeking behaviours. Virtue epistemology focusses on the cognitive character of agents and is less concerned with the nature of truth and epistemic justification as compared to traditional analytic epistemology. Due to this focus on cognitive character and agency, it is a fruitful but underexplored approach to using the Internet in an epistemically desirable way. Thus, the central question in this paper is: How to use the (...)
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  33. Hegel and the French Revolution.Richard Bourke - 2023 - History of European Ideas 49 (4):757-768.
    G. W. F. Hegel (1770–1831) has commonly been seen as Europe’s leading philosopher since Kant. His influence extended across the globe down to the Second World War – not least through his dissident disciple, Karl Marx. Since then, despite intermittent revivals, his importance has tended to be eclipsed by a rising tide of anti-modernist polemic, extending from Heidegger to postmodernism. Central to Hegel’s political thought was his view of the French Revolution. But notwithstanding its pivotal role in the development of (...)
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  34.  90
    The Question of Idealism.Richard Gaskin (ed.) - forthcoming
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  35. Independent alternatives: Ross’s puzzle and free choice.Richard Jefferson Booth - 2022 - Philosophical Studies 179 (4):1241-1273.
    Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...)
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  36. Opposites and Explanations in Heraclitus.Richard Neels - forthcoming - Oxford Studies in Ancient Philosophy.
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  37. Self-limitation as the basis of environmentally sustainable care of the self.Richard Sťahel - 2017 - Human Affairs 27 (4):444-454.
    When we abandon the neoliberal fiction that one is independent on the grounds that it is a-historic and antisocial, we realize that everyone is dependent and interdependent. In a media-driven society the self-identity of the individual is formed within the framework of the culture-ideology of consumerism from early childhood. As a result, both the environmental and social destruction have intensified. In the global era, or in the era of the global environmental crisis, self-identity as a precondition for environmentally sustainable care (...)
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  38. Probability and arguments: Keynes’s legacy.William Peden - 2021 - Cambridge Journal of Economics 45 (5):933–950.
    John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of probability (...)
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  39. A taxonomy of cognitive artifacts: Function, information, and categories.Richard Heersmink - 2013 - Review of Philosophy and Psychology 4 (3):465-481.
    The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. In this (...)
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  40. Structuring a Philosophical Approach.Richard Startup - 2019 - Open Journal of Philosophy 9 (4):452-469.
    A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of (...)
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  41. What is justified credence?Richard Pettigrew - 2021 - Episteme 18 (1):16-30.
    In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...)
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  42. Nominalization, Specification, and Investigation.Richard Lawrence - 2017 - Dissertation, University of California, Berkeley
    Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...)
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  43. The narrative self, distributed memory, and evocative objects.Richard Heersmink - 2018 - Philosophical Studies 175 (8):1829-1849.
    In this article, I outline various ways in which artifacts are interwoven with autobiographical memory systems and conceptualize what this implies for the self. I first sketch the narrative approach to the self, arguing that who we are as persons is essentially our (unfolding) life story, which, in turn, determines our present beliefs and desires, but also directs our future goals and actions. I then argue that our autobiographical memory is partly anchored in our embodied interactions with an ecology of (...)
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  44. A Cartesian Argument for Substance Dualism.Richard Swinburne - 2023 - Belgrade Philosophical Annual 36 (1):33-47.
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  45. Understanding the Higher-Order Approach to Consciousness.Richard Brown, Hakwan Lau & Joseph E. LeDoux - 2019 - Trends in Cognitive Sciences 23 (9):754-768.
    Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized for over-intellectualizing consciousness. We show (...)
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  46. Nudging for changing selves.Richard Pettigrew - 2023 - Synthese 201 (1):1-21.
    When is it legitimate for a government to ‘nudge’ its citizens, in the sense described by Thaler and Sunstein (2008)? In their original work on the topic, Thaler and Sunstein developed the _‘as judged by themselves’ (or AJBT) test_ to answer this question (Thaler and Sunstein 2008, p. 5). In a recent paper, Paul and Sunstein (2019) raised a concern about this test: it often seems to give the wrong answer in cases in which we are nudged to make a (...)
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  47. What is conditionalization, and why should we do it?Richard Pettigrew - 2020 - Philosophical Studies 177 (11):3427-3463.
    Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...)
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  48. Why "All Joy Wills Eternity" for Nietzsche.Richard Elliott - 2022 - In Michael McNeal & Paul Kirkland (eds.), Joy and Laughter in Nietzsche's Philosophy. Bloomsbury Academic. pp. 85 - 102.
    Joy of a certain kind has an important affective role in demonstrating the overcoming of nihilism for Nietzsche. In this chapter I explore how one might arrive at a point where they too can give voice to Zarathustra’s proclamation that “all joy wills eternity.” There are consistent references to eternity and infinitude in passages of Nietzsche’s discussing nihilism. This is most obviously borne out in Nietzsche scholarship with reference to discussions of eternal recurrence. But eternal recurrence does not have a (...)
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  49. Wage Exploitation as Disequilibrium Price.Stanislas Richard - 2023 - Business Ethics Quarterly 33 (2):327-351.
    There are two opposing views concerning intuitive cases of wage exploitation. The first denies that they are cases of exploitation at all. It is based on the nonworseness claim: there is nothing wrong with a discretionary mutually beneficial employment relationship. The second is the reasonable view: some employment relationships can be exploitative even if employers have no duty towards their employees. This article argues that the reasonable view does not completely defeat defences of wage exploitation, because these do not rely (...)
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  50. Accuracy-First Epistemology Without Additivity.Richard Pettigrew - 2022 - Philosophy of Science 89 (1):128-151.
    Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.
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