Results for 'Richard Eduard Leibbrandt'

920 found
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  1. The Priority of Epistemology in Early Neo-Kantianism.Kevin J. Harrelson - 2015 - History of Philosophy Quarterly 32 (1):57-77.
    This essay examines the argumentative context in which early Neo-Kantian philosophers defined and defended "epistemology." The paper defends Richard Rorty's claim that the priority of epistemology influenced how the history of modern philosophy was written but corrects his story by showing that epistemology was defended mainly via antifoundational arguments. The essay begins with a few programmatic arguments by Kuno Fischer and Eduard Zeller but focuses mainly on Otto Liebmann's Kant und die Epigonen. I argue that Liebmann completes the (...)
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  2. Wagner und Hanslick. Kurze Geschichte einer Feindschaft.Christian Jung - 2012 - Österreichische Musikzeitschrift 67 (6):14-21.
    The controversy between Richard Wagner and his critic Eduard Hanslick is well known, but rarely looked at in detail. It is mostly believed that Hanslick was unable to see Wagner's genius, stuck deeply in an antiquated aesthetical world. By reassessing Wagner's and Hanslick's letters and publications it can be seen, however, that Hanslick's detailed criticism (and also appreciation) was much more objective and less spiteful than is often assumed.
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  3. Minds Online: The Interface between Web Science, Cognitive Science, and the Philosophy of Mind.Paul Smart, Robert William Clowes & Richard Heersmink - 2017 - Foundations and Trends in Web Science 6 (1-2):1-234.
    Alongside existing research into the social, political and economic impacts of the Web, there is a need to study the Web from a cognitive and epistemic perspective. This is particularly so as new and emerging technologies alter the nature of our interactive engagements with the Web, transforming the extent to which our thoughts and actions are shaped by the online environment. Situated and ecological approaches to cognition are relevant to understanding the cognitive significance of the Web because of the emphasis (...)
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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. Elimination of Cuts in First-order Finite-valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
    A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
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  6. Systematic construction of natural deduction systems for many-valued logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Unknown (ed.), Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. IEEE Press. pp. 208-213.
    A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
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  7. Evolution of Individuality: A Case Study in the Volvocine Green Algae.Erik R. Hanschen, Dinah R. Davison, Zachariah I. Grochau-Wright & Richard E. Michod - 2017 - Philosophy, Theory, and Practice in Biology 9 (3).
    All disciplines must define their basic units and core processes. In evolutionary biology, the core process is natural selection and the basic unit of selection and adaptation is the individual. To operationalize the theory of natural selection we must count individuals, as they are the bearers of fitness. While canonical individuals have often been taken to be multicellular organisms, the hierarchy of life shows that new kinds of individuals have evolved. A variety of criteria have been used to define biological (...)
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  8. Ethical Leadership as a Balance Between Opposing Neural Networks.Kylie C. Rochford, Anthony I. Jack, Richard E. Boyatzis & Shannon E. French - 2017 - Journal of Business Ethics 144 (4):755-770.
    In this article, we explore the implications of opposing domains theory for developing ethical leaders. Opposing domains theory highlights a neurological tension between analytic reasoning and socioemotional reasoning. Specifically, when we engage in analytic reasoning, we suppress our ability to engage in socioemotional reasoning and vice versa. In this article, we bring together the domains of neuroscience, psychology, and ethics, to inform our theorizing around ethical leadership. We propose that a key issue for ethical leadership is achieving a healthy balance (...)
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  9. On the Decisional Nature of Faith.Richard Oxenberg - 2023 - Interreligious Insight 21 (2):40-46.
    On what basis should we embrace a religious belief? In this article I argue that religious faith should be viewed, not as a conclusion we arrive at after reviewing the evidence, but as an existential decision we make through which we define ourselves.
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  10. Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...)
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  11. An improved ontological representation of dendritic cells as a paradigm for all cell types.Anna Maria Masci, Cecilia N. Arighi, Alexander D. Diehl, Anne E. Liebermann, Chris Mungall, Richard H. Scheuermann, Barry Smith & Lindsay Cowell - 2009 - BMC Bioinformatics 10 (1):70.
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  12. 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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  13. An improved ontological representation of dendritic cells as a paradigm for all cell types.Masci Anna Maria, N. Arighi Cecilia, D. Diehl Alexander, E. Lieberman Anne, Mungall Chris, H. Scheuermann Richard, Barry Smith & G. Cowell Lindsay - 2009 - BMC Bioinformatics 10 (1):70.
    The Cell Ontology (CL) is designed to provide a standardized representation of cell types for data annotation. Currently, the CL employs multiple is_a relations, defining cell types in terms of histological, functional, and lineage properties, and the majority of definitions are written with sufficient generality to hold across multiple species. This approach limits the CL’s utility for cross-species data integration. To address this problem, we developed a method for the ontological representation of cells and applied this method to develop a (...)
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  14. Individual Differences in Moral Behaviour: A Role for Response to Risk and Uncertainty?Colin J. Palmer, Bryan Paton, Trung T. Ngo, Richard H. Thomson, Jakob Hohwy & Steven M. Miller - 2012 - Neuroethics 6 (1):97-103.
    Investigation of neural and cognitive processes underlying individual variation in moral preferences is underway, with notable similarities emerging between moral- and risk-based decision-making. Here we specifically assessed moral distributive justice preferences and non-moral financial gambling preferences in the same individuals, and report an association between these seemingly disparate forms of decision-making. Moreover, we find this association between distributive justice and risky decision-making exists primarily when the latter is assessed with the Iowa Gambling Task. These findings are consistent with neuroimaging studies (...)
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  15. 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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  16. VO: Vaccine Ontology.Yongqun He, Lindsay Cowell, Alexander D. Diehl, H. L. Mobley, Bjoern Peters, Alan Ruttenberg, Richard H. Scheuermann, Ryan R. Brinkman, Melanie Courtot, Chris Mungall, Barry Smith & Others - 2009 - In Barry Smith (ed.), ICBO 2009: Proceedings of the First International Conference on Biomedical Ontology. Buffalo: NCOR.
    Vaccine research, as well as the development, testing, clinical trials, and commercial uses of vaccines involve complex processes with various biological data that include gene and protein expression, analysis of molecular and cellular interactions, study of tissue and whole body responses, and extensive epidemiological modeling. Although many data resources are available to meet different aspects of vaccine needs, it remains a challenge how we are to standardize vaccine annotation, integrate data about varied vaccine types and resources, and support advanced vaccine (...)
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  17. Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Voronkov Andrei & Parigot Michel (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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  18. Review of Daniel J. Singer, Right Belief and True Belief, OUP, 2023. [REVIEW]Richard Pettigrew - manuscript
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  19. 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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  20. Completeness of a first-order temporal logic with time-gaps.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - Theoretical Computer Science 160 (1-2):241-270.
    The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.
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  21. 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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  22. Completeness of a Hypersequent Calculus for Some First-order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In Baaz Matthias, Preining Norbert & Zach Richard (eds.), 36th Interna- tional Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
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  23.  63
    FACTORS THAT CONTRIBUTE TO REPORT WRITING PROFICIENCY IN AMERICAN LAW ENFORCEMENT: A THEMATIC LITERATURE REVIEW.Richard Segovia - 2024 - International Journal of Police Science 3 (1).
    Purpose: This thematic literature review explores the critical role of competent writing skills in law enforcement, examining its impact on career progression, agency reputation, and legal proceedings. The purpose is to synthesize existing literature to identify research gaps and suggest directions for future studies. Methods: Google Scholar, ERIC, and the Jerry Falwell Library searches were conducted to capture a broad range of studies involving police report writing, its impact on officers, law enforcement agencies, and the criminal justice system, and writing (...)
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  24. Incompleteness of a first-order Gödel logic and some temporal logics of programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Kleine Büning Hans (ed.), Computer Science Logic. CSL 1995. Selected Papers. Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...)
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  25. 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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  26. The Question of Idealism.Richard Gaskin (ed.) - forthcoming
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  27. 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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  28. Narrative niche construction: Memory ecologies and distributed narrative identities.Richard Heersmink - 2020 - Biology and Philosophy 35 (5):1-23.
    Memories of our personal past are the building blocks of our narrative identity. So, when we depend on objects and other people to remember and construct our personal past, our narrative identity is distributed across our embodied brains and an ecology of environmental resources. This paper uses a cognitive niche construction approach to conceptualise how we engineer our memory ecology and construct our distributed narrative identities. It does so by identifying three types of niche construction processes that govern how we (...)
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  29. 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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  30. 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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  31. The cultural evolution of mind-modelling.Richard Moore - 2020 - Synthese 199 (1):1751-1776.
    I argue that uniquely human forms of ‘Theory of Mind’ are a product of cultural evolution. Specifically, propositional attitude psychology is a linguistically constructed folk model of the human mind, invented by our ancestors for a range of tasks and refined over successive generations of users. The construction of these folk models gave humans new tools for thinking and reasoning about mental states—and so imbued us with abilities not shared by non-linguistic species. I also argue that uniquely human forms of (...)
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  32. 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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  33. 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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  34. 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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  35. 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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  36. Wondering and Epistemic Desires.Richard Teague - forthcoming - Philosophical Quarterly.
    This paper explores the relationship between the questioning attitude of wondering and a class of attitudes I call 'epistemic desires'. Broadly, these are desires to improve one's epistemic position on some question. A common example is the attitude of wanting to know the answer to some question. I argue that one can have any kind of epistemic desire towards any question, Q, without necessarily wondering Q, but not conversely. That is, one cannot wonder Q without having at least some epistemic (...)
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  37. How should your beliefs change when your awareness grows?Richard Pettigrew - 2024 - Episteme 21 (3):733-757.
    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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  38. Review of Gerhard Schurz's Optimality Justifications (2024, OUP). [REVIEW]Richard Pettigrew - manuscript
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  39. A Cartesian Argument for Substance Dualism.Richard Swinburne - 2023 - Belgrade Philosophical Annual 36 (1):33-47.
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  40. A phenomenology and epistemology of large language models: transparency, trust, and trustworthiness.Richard Heersmink, Barend de Rooij, María Jimena Clavel Vázquez & Matteo Colombo - 2024 - Ethics and Information Technology 26 (3):1-15.
    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 artificial intelligence (AI) 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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  41. The Basic Laws of Cardinal Number.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 1-30.
    An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.
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  42.  99
    Jeffrey Pooling.Richard Pettigrew & Jonathan Weisberg - forthcoming - Philosophers' Imprint.
    How should your opinion change in light of an epistemic peer's? We show that the pooling rule known as "upco" is the unique answer satisfying some natural desiderata. If your revised opinion will impact your other views by Jeffrey conditionalization, then upco is the only standard pooling rule that ensures the order in which peers are consulted makes no difference. Popular alternatives like linear pooling, geometric pooling, and harmonic pooling cannot boast the same. In fact, no alternative can that possesses (...)
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  43. 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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  44. 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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  45. Should market harms be an exception to the Harm Principle?Richard Endörfer - 2022 - Economics and Philosophy 38 (2):221-241.
    Many proponents of the Harm Principle seem to implicitly assume that the principle is compatible with permitting the free exchange of goods and services, even if such exchanges generate so-called market harms. I argue that, as a result, proponents of the Harm Principle face a dilemma: either the Harm Principle’s domain cannot include a large number of non-market harm cases or market harms must be treated on par with non-market harms. I then go on to discuss three alternative arguments defending (...)
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  46. Thermal Perception and its Relation to Touch.Richard Gray - 2023 - Philosophers' Imprint 23 (25).
    Touch is standardly taken to be a proximal sense, principally constituted by capacities to detect proximal pressure and thermal stimulation, and contrasted with the distal senses of vision and audition. It has, however, recently been argued that the scope of touch extends beyond proximal perception; touch can connect us to distal objects. Hence touch generally should be thought of as a connection sense. In this paper, I argue that whereas pressure perception is a connection sense, thermal perception is not. Thermal (...)
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  47. 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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  48. What is the characteristic wrong of testimonial injustice?Richard Pettigrew - manuscript
    My aim in this paper is to identify the wrong that is done in all cases of testimonial injustice, if there is one. Miranda Fricker (2007) proposes one account of this distinctive wrong, and Gaile Pohlhaus Jr. (2014) offers another. I think neither works. Nor does an account based on giving due respect to the testifier's epistemic competence. Nor does an account based on exposing the testifier to substantial risk of harm. Rachel Fraser (2023) describes a further account, and the (...)
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  49. Frege, Thomae, and Formalism: Shifting Perspectives.Richard Lawrence - 2023 - Journal for the History of Analytical Philosophy 11 (2):1-23.
    Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...)
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  50. Frege, Hankel, and Formalism in the Foundations.Richard Lawrence - 2021 - Journal for the History of Analytical Philosophy 9 (11).
    Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...)
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