Results for 'Richard Sieb'

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  1. Space-Time Intervals Underlie Human Conscious Experience, Gravity, and a Theory of Everything.Richard Sieb - 2018 - Neuroquantology 16 (7):49-64.
    Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time intervals by the brain; (...)
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  2. The Emergence of Emotions.Richard Sieb - 2013 - Activitas Nervosa Superior 55 (4):115-145.
    Emotion is conscious experience. It is the affective aspect of consciousness. Emotion arises from sensory stimulation and is typically accompanied by physiological and behavioral changes in the body. Hence an emotion is a complex reaction pattern consisting of three components: a physiological component, a behavioral component, and an experiential (conscious) component. The reactions making up an emotion determine what the emotion will be recognized as. Three processes are involved in generating an emotion: (1) identification of the emotional significance of a (...)
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  3. Four-Dimensional Consciousness.Richard Allen Sieb - 2017 - Activitas Nervosa Superior 59 (2):(43-60).
    Conscious experience is the direct observation of conscious events. Human conscious experience is four-dimensional. Conscious events are linked (associated) by spacetime intervals to produce a coherent conscious experience. This explains why conscious experience appears to us the way it does. Conscious experience is an orientation in space and time, an understanding of the position of the observer in space and time. Causality, past-future relations, learning, memory, cognitive processing, and goal-directed actions all evolve from four-dimensional conscious experience. A neural correlate for (...)
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  4. CONSCIOUS EXPERIENCE, THE NEURAL MECHANISM.Richard A. Sieb - manuscript
    The physical basis of conscious experience is revealed by direct observation and analysis of any conscious experience. Human conscious experience has an invariant structural mode of organization based on the three types of space-time intervals (light-like, time-like, space-like). Sensory input activates the autonomic nervous system, endocrine system, and ascending reticular activating system to produce the awake conscious state. The dorsal and ventral frontoparietal attention networks are activated. Dorsal and ventral cortical functional streams carry “what”, “where”, and “when” information to the (...)
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  5. Human Conscious Experience is Four-Dimensional and has a Neural Correlate Modeled by Einstein's Special Theory of Relativity.Richard Sieb - 2016 - Neuroquantology 14 (4):630-644.
    In humans, knowing the world occurs through spatial-temporal experiences and interpretations. Conscious experience is the direct observation of conscious events. It makes up the content of consciousness. Conscious experience is organized in four dimensions. It is an orientation in space and time, an understanding of the position of the observer in space and time. A neural correlate for four-dimensional conscious experience has been found in the human brain which is modeled by Einstein’s Special Theory of Relativity. Spacetime intervals are fundamentally (...)
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  6. Space-Time Intervals Underlie Human Conscious Experience, Gravity, and Everything.Richard Sieb - 2019 - Neuroquantology 17 (5):87-89.
    This short commentary discusses the importance of space-time intervals in scientific study. Space-time intervals underlie special relativity, general relativity, and quantum field theory. In doing so, space-time intervals underlie human conscious experience, gravity, and a theory of everything. Space-time intervals also explain many puzzling scientific phenomena: quantum phenomena, dark matter, dark energy, the origin and evolution of the universe, and the life force. The importance of space-time intervals cannot be overestimated. Two articles published in Neuroquantology explain how all this was (...)
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  7. Definition by Induction in Frege's Grundgesetze der Arithmetik.Richard Heck - 1995 - In William Demopoulos (ed.), Frege's philosophy of mathematics. Cambridge: Harvard University Press.
    This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.
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  8. 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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  9. 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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  10. Some Remarks on Wittgenstein’s Philosophy of Mathematics.Richard Startup - 2020 - Open Journal of Philosophy 10 (1):45-65.
    Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...)
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  11. Introduction: Advances in Experimental Philosophy of Science.Richard Samuels & Daniel Wilkenfeld - 2019 - In Richard Samuels & Daniel A. Wilkenfeld (eds.), Advances in Experimental Philosophy of Science. London: Bloomsbury. pp. 1-12.
    In this chapter we explain what experimental philosophy of science is, how it relates to the philosophy of science, and STS more broadly, and what sorts of contributions is can make to ongoing research in the philosophy of science.
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  12. Counterfactual Desirability.Richard Bradley & H. Orri 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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  13. 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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  14. 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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  15. 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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  16. Ernest Becker and Emmanuel Levinas: Surprising Convergences.Richard Colledge - 2002 - In Daniel Liechty (ed.), Death and denial: interdisciplinary perspectives on the legacy of Ernest Becker. Westport, Conn.: Praeger. pp. 175-184.
    After a brief introduction and orientation (section I), this dialogue between Levinasian and Beckerian thought is approached along the lines of two major themes concerning consciousness which emerge in very different contexts and registers in their work (sections II and III), and one tantalizing question that is raised with great force by the dialogue (section IV). The two themes revolve around the subtle dialectical interplay that runs throughout the thought of both Levinas and Becker – the switching between internality and (...)
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  17. Why Care About Non-Natural Reasons?Richard Yetter Chappell - 2019 - American Philosophical Quarterly 56 (2):125-134.
    Are non-natural properties worth caring about? I consider two objections to metaethical non-naturalism. According to the intelligibility objection, it would be positively unintelligible to care about non-natural properties that float free from the causal fabric of the cosmos. According to the ethical idlers objection, there is no compelling motivation to posit non-natural normative properties because the natural properties suffice to provide us with reasons. In both cases, I argue, the objection stems from misunderstanding the role that non-natural properties play in (...)
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  18. 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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  19.  34
    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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  20. Rights, Property and Politics: Hume to Hegel.Richard Bourke - forthcoming - In The Cambridge History of Rights, Volume IV. Cambridge University Press.
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  21. 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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  22. 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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  23.  76
    Exchange on "Truth as convenient friction".Richard Rorty & Huw Price - 2010 - In Mario De Caro & David Macarthur (eds.), Naturalism and Normativity. Cambridge University Press.
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  24. 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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  25. 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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  26. Rethinking the Asymmetry.Richard Yetter Chappell - 2017 - Canadian Journal of Philosophy 47 (2):167-177.
    According to the Asymmetry, we’ve strong moral reason to prevent miserable lives from coming into existence, but no moral reason to bring happy lives into existence. This procreative asymmetry is often thought to be part of commonsense morality, however theoretically puzzling it might prove to be. I argue that this is a mistake. The Asymmetry is merely prima facie intuitive, and loses its appeal on further reflection. Mature commonsense morality recognizes no fundamental procreative asymmetry. It may recognize some superficially similar (...)
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  27. The Right Wrong‐Makers.Richard Yetter Chappell - 2020 - Philosophy and Phenomenological Research 103 (2):426-440.
    Right- and wrong-making features ("moral grounds") are widely believed to play important normative roles, e.g. in morally apt or virtuous motivation. This paper argues that moral grounds have been systematically misidentified. Canonical statements of our moral theories tend to summarize, rather than directly state, the full range of moral grounds posited by the theory. Further work is required to "unpack" a theory's criterion of rightness and identify the features that are of ground-level moral significance. As a result, it is not (...)
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  28. 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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  29. 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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  30. 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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  31. The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck - 1998 - In Matthias Schirn (ed.), The Philosophy of mathematics today. New York: Clarendon Press.
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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  32. Moral Error Theory and the Argument from Epistemic Reasons.Richard Rowland - 2012 - Journal of Ethics and Social Philosophy 7 (1):1-24.
    In this paper I defend what I call the argument from epistemic reasons against the moral error theory. I argue that the moral error theory entails that there are no epistemic reasons for belief and that this is bad news for the moral error theory since, if there are no epistemic reasons for belief, no one knows anything. If no one knows anything, then no one knows that there is thought when they are thinking, and no one knows that they (...)
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  33. 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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  34. 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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  35. The HOROR Theory of Phenomenal Consciousness.Richard Brown - 2015 - Philosophical Studies 172 (7):1783-1794.
    One popular approach to theorizing about phenomenal consciousness has been to connect it to representations of a certain kind. Representational theories of consciousness can be further sub-divided into first-order and higher-order theories. Higher-order theories are often interpreted as invoking a special relation between the first-order state and the higher-order state. However there is another way to interpret higher-order theories that rejects this relational requirement. On this alternative view phenomenal consciousness consists in having suitable higher-order representations. I call this ‘HOROR’ (‘Higher-Order (...)
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  36. 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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  37. 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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  38. The Sense of Communication.Richard Heck - 1995 - Mind 104 (413):79 - 106.
    Many philosophers nowadays believe Frege was right about belief, but wrong about language: The contents of beliefs need to be individuated more finely than in terms of Russellian propositions, but the contents of utterances do not. I argue that this 'hybrid view' cannot offer no reasonable account of how communication transfers knowledge from one speaker to another and that, to do so, we must insist that understanding depends upon more than just getting the references of terms right.
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  39.  11
    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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  40. 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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  41. 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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  42. 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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  43. The Brain and its States.Richard Brown - 2012 - In Shimon Edelman, Tomer Fekete & Neta Zach (eds.), Being in Time: Dynamical Models of Phenomenal Experience. John Benjamins. pp. 211-238.
    In recent times we have seen an explosion in the amount of attention paid to the conscious brain from scientists and philosophers alike. One message that has emerged loud and clear from scientific work is that the brain is a dynamical system whose operations unfold in time. Any theory of consciousness that is going to be physically realistic must take account of the intrinsic nature of neurons and brain activity. At the same time a long discussion on consciousness among philosophers (...)
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  44. 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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  45. 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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  46. Public Health and Normative Public Goods.Richard H. Dees - 2018 - Public Health Ethics 11 (1):20-26.
    Public health is concerned with increasing the health of the community at whole. Insofar as health is a ‘good’ and the community constitutes a ‘public’, public health by definition promotes a ‘public good’. But ‘public good’ has a particular and much more narrow meaning in the economics literature, and some commentators have tried to limit the scope of public health to this more narrow meaning of a ‘public good’. While such a move makes the content of public health less controversial, (...)
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  47. 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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  48. The Myth of Phenomenological Overflow.Richard Brown - 2012 - Consciousness and Cognition 21 (2):599-604.
    In this paper I examine the dispute between Hakwan Lau, Ned Block, and David Rosenthal over the extent to which empirical results can help us decide between first-order and higher-order theories of consciousness. What emerges from this is an overall argument to the best explanation against the first-order view of consciousness and the dispelling of the mythological notion of phenomenological overflow that comes with it.
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  49. The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard G. Heck - 1998 - In Matthias Schirn (ed.), The Philosophy of mathematics today. New York: Clarendon Press.
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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  50. Against ‘Saving Lives’: Equal Concern and Differential Impact.Richard Yetter Chappell - 2016 - Bioethics 30 (3):159-164.
    Bioethicists often present ‘saving lives’ as a goal distinct from, and competing with, that of extending lives by as much as possible. I argue that this usage of the term is misleading, and provides unwarranted rhetorical support for neglecting the magnitudes of the harms and benefits at stake in medical allocation decisions, often to the detriment of the young. Equal concern for all persons requires weighting equal interests equally, but not all individuals have an equal interest in ‘life-saving’ treatment.
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