Results for 'Richard Eduard Leibbrandt'

999 found
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  1. Logic in mathematics and computer science.Richard Zach - forthcoming - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...)
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  2. Hilbert's program then and now.Richard Zach - 2006 - In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  3. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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  4. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective).Richard Zach - 2015 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...)
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  5. Incompleteness and Computability: An Open Introduction to Gödel's Theorems.Richard Zach - 2019 - Open Logic Project.
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  6. Reflection as a Deliberative and Distributed Practice: Assessing Neuro-Enhancement Technologies via Mutual Learning Exercises.Hub Zwart, Jonna Brenninkmeijer, Peter Eduard, Lotte Krabbenborg, Sheena Laursen, Gema Revuelta & Winnie Toonders - 2017 - NanoEthics 11 (2):127-138.
    In 1968, Jürgen Habermas claimed that, in an advanced technological society, the emancipatory force of knowledge can only be regained by actively recovering the ‘forgotten experience of reflection’. In this article, we argue that, in the contemporary situation, critical reflection requires a deliberative ambiance, a process of mutual learning, a consciously organised process of deliberative and distributed reflection. And this especially applies, we argue, to critical reflection concerning a specific subset of technologies which are actually oriented towards optimising human cognition. (...)
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  7. Consequences of Calibration.Robert Williams & Richard Pettigrew - forthcoming - British Journal for the Philosophy of Science:14.
    Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...)
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  8. Climate Change Assessments: Confidence, Probability, and Decision.Richard Bradley, Casey Helgeson & Brian Hill - 2017 - Philosophy of Science 84 (3):500–522.
    The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.
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  9. The Concept of Innateness as an Object of Empirical Enquiry.Richard Samuels - 2016 - In Wesley Buckwalter & Justin Sytsma (eds.), Blackwell Companion to Experimental Philosophy. Malden, MA: Blackwell. pp. 504-519.
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  10. 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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  11. Reasonable religious disagreements.Richard Feldman - 2010 - In Louise M. Antony (ed.), Philosophers Without Gods: Meditations on Atheism and the Secular Life. Oup Usa. pp. 194-214.
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  12. 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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  13. Disagreement.Richard Feldman & Ted A. Warfield (eds.) - 2010 - Oxford, GB: Oxford University Press.
    Disagreement is common: even informed, intelligent, and generally reasonable people often come to different conclusions when confronted with what seems to be the same evidence. Can the competing conclusions be reasonable? If not, what can we reasonably think about the situation? This volume examines the epistemology of disagreement. Philosophical questions about disagreement arise in various areas, notably politics, ethics, aesthetics, and the philosophy of religion: but this will be the first book focusing on the general epistemic issues arising from informed (...)
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  14. 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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  15. Completeness before Post: Bernays, Hilbert, and the development of propositional logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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  16. 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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  17. What, if anything, renders all humans morally equal?Richard J. Arneson - 1999 - In . Blackwell. pp. 103-28.
    All humans have an equal basic moral status. They possess the same fundamental rights, and the comparable interests of each person should count the same in calculations that determine social policy. Neither supposed racial differences, nor skin color, sex, sexual orientation, ethnicity, intelligence, nor any other differences among humans negate their fundamental equal worth and dignity. These platitudes are virtually universally affirmed. A white supremacist racist or an admirer of Adolf Hitler who denies them is rightly regarded as beyond the (...)
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  18. Nonconceptual content and the "space of reasons".Richard G. Heck - 2000 - Philosophical Review 109 (4):483-523.
    In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.
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  19. Deprioritizing the A Priori Arguments against Physicalism.Richard Brown - 2010 - Journal of Consciousness Studies 17 (3-4):47-69.
    In this paper I argue that a priori arguments fail to present any real problem for physicalism. They beg the question against physicalism in the sense that the argument will only seem compelling if one is already assuming that qualitative properties are nonphysical. To show this I will present the reverse-zombie and reverse-knowledge arguments. The only evidence against physicalism is a priori arguments, but there are also a priori arguments against dualism of exactly the same variety. Each of these parity (...)
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  20. 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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  21. Epimorphism between Fine and Ferguson’s Matrices for Angell’s AC.Richard Zach - 2023 - Logic and Logical Philosophy 32 (2):161-179.
    Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.
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  22. Counterfactual Desirability.Richard Bradley & H. Orii Stefansson - 2017 - British Journal for the Philosophy of Science 68 (2):485-533.
    The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. (...)
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  23. 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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  24. Knowing What Matters.Richard Yetter Chappell - 2017 - In Peter Singer (ed.), Does Anything Really Matter? Essays on Parfit on Objectivity. Oxford University Press. pp. 149-167.
    Parfit's On What Matters offers a rousing defence of non-naturalist normative realism against pressing metaphysical and epistemological objections. He addresses skeptical arguments based on (i) the causal origins of our normative beliefs, and (ii) the appearance of pervasive moral disagreement. In both cases, he concedes the first step to the skeptic, but draws a subsequent distinction with which he hopes to stem the skeptic's advance. I argue, however, that these distinctions cannot bear the weight that Parfit places on them. A (...)
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  25. Fittingness: The sole normative primitive.Richard Yetter Chappell - 2012 - Philosophical Quarterly 62 (249):684 - 704.
    This paper draws on the 'Fitting Attitudes' analysis of value to argue that we should take the concept of fittingness (rather than value) as our normative primitive. I will argue that the fittingness framework enhances the clarity and expressive power of our normative theorising. Along the way, we will see how the fittingness framework illuminates our understanding of various moral theories, and why it casts doubt on the Global Consequentialist idea that acts and (say) eye colours are normatively on a (...)
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  26. Dimensions of integration in embedded and extended cognitive systems.Richard Heersmink - 2015 - Phenomenology and the Cognitive Sciences 14 (3):577-598.
    The complementary properties and functions of cognitive artifacts and other external resources are integrated into the human cognitive system to varying degrees. The goal of this paper is to develop some of the tools to conceptualize this complementary integration between agents and artifacts. It does so by proposing a multidimensional framework, including the dimensions of information flow, reliability, durability, trust, procedural transparency, informational transparency, individualization, and transformation. The proposed dimensions are all matters of degree and jointly they constitute a multidimensional (...)
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  27. 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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  28. 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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  29. Distributed selves: Personal identity and extended memory systems.Richard Heersmink - 2017 - Synthese 194 (8):3135–3151.
    This paper explores the implications of extended and distributed cognition theory for our notions of personal identity. On an extended and distributed approach to cognition, external information is under certain conditions constitutive of memory. On a narrative approach to personal identity, autobiographical memory is constitutive of our diachronic self. In this paper, I bring these two approaches together and argue that external information can be constitutive of one’s autobiographical memory and thus also of one’s diachronic self. To develop this claim, (...)
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  30. Dimensions of integration in embedded and extended cognitive systems.Richard Heersmink - 2015 - Phenomenology and the Cognitive Sciences 13 (3):577-598.
    The complementary properties and functions of cognitive artifacts and other external resources are integrated into the human cognitive system to varying degrees. The goal of this paper is to develop some of the tools to conceptualize this complementary integration between agents and artifacts. It does so by proposing a multidimensional framework, including the dimensions of information flow, reliability, durability, trust, procedural transparency, informational transparency, individualization, and transformation. The proposed dimensions are all matters of degree and jointly they constitute a multidimensional (...)
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  31. A phenomenology and epistemology of large language models: Transparency, trust, and trustworthiness.Richard Heersmink, Barend de Rooij, María Jimena Clavel Vázquez & Matteo Colombo - forthcoming - Ethics and Information Technology.
    This paper analyses the phenomenology and epistemology of chatbots such as ChatGPT and Bard. The computational architecture underpinning these chatbots are large language models (LLMs), which are generative AI (Artificial Intelligence) systems trained on a massive dataset of text extracted from the Web. We conceptualise these LLMs as multifunctional computational cognitive artifacts, used for various cognitive tasks such as translating, summarizing, answering questions, information-seeking, and much more. Phenomenologically, LLMs can be experienced as a “quasi-other”; when that happens, users anthropomorphise them. (...)
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  32. 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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  33. 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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  34. Logical ignorance and logical learning.Richard Pettigrew - 2021 - 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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  35. Factors Associated with Mathematics Performance.Grace Abalde & Richard Oco - 2023 - Asian Research Journal of Mathematics 19 (6):45-60.
    Aims: The purpose of this study is to identify the factors associated with the academic performance of Grade 10 students during their First Quarter of school as well as the significant correlation between the factors and student academic performance in Mathematics. -/- Study Design: Descriptive Correlation Design. -/- Place and Duration of Study: The study was conducted at Agusan National High School in Cagayan de Or City's East 1 District during the school year: 2022 – 2023. -/- Methodology: The respondents (...)
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  36. Rumfitt on truth-grounds, negation, and vagueness.Richard Zach - 2018 - Philosophical Studies 175 (8):2079-2089.
    In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.
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  37. Introduction: Know thyself.Richard Gipps & Michael Lacewing - 2019 - In Richard G. T. Gipps & Michael Lacewing (eds.), Oxford Handbook of Philosophy and Psychoanalysis. Oxford, UK: Oxford University Press. pp. 1-22.
    In this introduction to the Oxford Handbook of Philosophy and Psychoanalysis, we provide an overview of the promise and problems of connecting philosophy and psychoanalysis through a focus on the age-old theme central to both disciplines, 'know thyself'.
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  38. The internet, cognitive enhancement, and the values of cognition.Richard Heersmink - 2016 - Minds and Machines 26 (4):389-407.
    This paper has two distinct but related goals: (1) to identify some of the potential consequences of the Internet for our cognitive abilities and (2) to suggest an approach to evaluate these consequences. I begin by outlining the Google effect, which (allegedly) shows that when we know information is available online, we put less effort into storing that information in the brain. Some argue that this strategy is adaptive because it frees up internal resources which can then be used for (...)
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  39. 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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  40. Are there different kinds of content?Richard Heck - 2007 - In Brian P. McLaughlin & Jonathan D. Cohen (eds.), Contemporary Debates in Philosophy of Mind. Blackwell. pp. 117-138.
    In an earlier paper, "Non-conceptual Content and the 'Space of Reasons'", I distinguished two forms of the view that perceptual content is non-conceptual, which I called the 'state view' and the 'content view'. On the latter, but not the former, perceptual states have a different kind of content than do cognitive states. Many have found it puzzling why anyone would want to make this claim and, indeed, what it might mean. This paper attempts to address these questions.
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  41. Extended mind and cognitive enhancement: Moral aspects of cognitive artifacts.Richard Heersmink - 2017 - Phenomenology and the Cognitive Sciences 16 (1):17-32.
    This article connects philosophical debates about cognitive enhancement and situated cognition. It does so by focusing on moral aspects of enhancing our cognitive abilities with the aid of external artifacts. Such artifacts have important moral dimensions that are addressed neither by the cognitive enhancement debate nor situated cognition theory. In order to fill this gap in the literature, three moral aspects of cognitive artifacts are singled out: their consequences for brains, cognition, and culture; their moral status; and their relation to (...)
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  42. Value Receptacles.Richard Yetter Chappell - 2015 - Noûs 49 (2):322-332.
    Utilitarianism is often rejected on the grounds that it fails to respect the separateness of persons, instead treating people as mere “receptacles of value”. I develop several different versions of this objection, and argue that, despite their prima facie plausibility, they are all mistaken. Although there are crude forms of utilitarianism that run afoul of these objections, I advance a new form of the view—‘token-pluralistic utilitarianism’—that does not.
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  43. Willpower Satisficing.Richard Yetter Chappell - 2019 - Noûs 53 (2):251-265.
    Satisficing Consequentialism is often rejected as hopeless. Perhaps its greatest problem is that it risks condoning the gratuitous prevention of goodness above the baseline of what qualifies as "good enough". I propose a radical new willpower-based version of the view that avoids this problem, and that better fits with the motivation of avoiding an excessively demanding conception of morality. I further demonstrate how, by drawing on the resources of an independent theory of blameworthiness, we may obtain a principled specification of (...)
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  44. The metaphysics of cognitive artifacts.Richard Heersmink - 2016 - Philosophical Explorations 19 (1):78-93.
    This article looks at some of the metaphysical properties of cognitive artefacts. It first identifies and demarcates the target domain by conceptualizing this class of artefacts as a functional kind. Building on the work of Beth Preston, a pluralist notion of functional kind is developed, one that includes artefacts with proper functions and system functions. Those with proper functions have a history of cultural selection, whereas those with system functions are improvised uses of initially non-cognitive artefacts. Having identified the target (...)
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  45. Overriding Virtue.Richard Y. Chappell - 2019 - In Hilary Greaves & Theron Pummer (eds.), Effective Altruism: Philosophical Issues. Oxford University Press. pp. 218-226.
    If you focus your charitable giving on global causes where it will do the most good, how should you feel about passing by the local soup kitchen? Would the ideally virtuous agent have their (local) empathy still activated, but simply overridden by the recognition that distant others are in even greater need, leaving the agent feeling torn? Or would their empathetic impulses be wholeheartedly redirected towards the greatest needs? This chapter suggests a way to revise an outdated conception of moral (...)
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  46. Extended mind and artifactual autobiographical memory.Richard Heersmink - 2020 - Mind and Language 36:1-15.
    In this paper, I describe how artifacts and autobiographical memory are integrated into new systemic wholes, allowing us to remember our personal past in a more reliable and detailed manner. After discussing some empirical work on lifelogging technology, I elaborate on the dimension of autobiographical dependency, which is the degree to which we depend on an object to be able to remember a personal experience. When this dependency is strong, we integrate information in the embodied brain and in an object (...)
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  47. Numbers and functions in Hilbert's finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...)
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  48. Number Concepts: An Interdisciplinary Inquiry.Richard Samuels & Eric Snyder - 2024 - Cambridge University Press.
    This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...)
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  49. Mathematical Cognition: A Case of Enculturation.Richard Menary - 2015 - Open Mind.
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  50. Do demonstratives have senses?Richard Heck - 2002 - Philosophers' Imprint 2:1-33.
    Frege held that referring expressions in general, and demonstratives and indexicals in particular, contribute more than just their reference to what is expressed by utterances of sentences containing them. Heck first attempts to get clear about what the essence of the Fregean view is, arguing that it rests upon a certain conception of linguistic communication that is ultimately indefensible. On the other hand, however, he argues that understanding a demonstrative (or indexical) utterance requires one to think of the object denoted (...)
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