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Mark Greenberg
University of California, Los Angeles
Gabriel Greenberg
University of California, Los Angeles
Alexander Greenberg
University College London
2 more
  1. Universals of Language.J. H. GREENBERG - 1963
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  2. Beyond Resemblance.Gabriel Greenberg - 2013 - Philosophical Review 122 (2):215-287.
    What is it for a picture to depict a scene? The most orthodox philosophical theory of pictorial representation holds that depiction is grounded in resemblance. A picture represents a scene in virtue of being similar to that scene in certain ways. This essay presents evidence against this claim: curvilinear perspective is one common style of depiction in which successful pictorial representation depends as much on a picture's systematic differences with the scene depicted as on the similarities; it cannot be analyzed (...)
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  3.  74
    Memory Reconsolidation, Emotional Arousal, and the Process of Change in Psychotherapy: New Insights From Brain Science.Richard D. Lane, Lee Ryan, Lynn Nadel & Leslie Greenberg - 2015 - Behavioral and Brain Sciences 38:1-80.
    Since Freud, clinicians have understood that disturbing memories contribute to psychopathology and that new emotional experiences contribute to therapeutic change. Yet, controversy remains about what is truly essential to bring about psychotherapeutic change. Mounting evidence from empirical studies suggests that emotional arousal is a key ingredient in therapeutic change in many modalities. In addition, memory seems to play an important role but there is a lack of consensus on the role of understanding what happened in the past in bringing about (...)
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  4. Semantics of Pictorial Space.Gabriel Greenberg - 2021 - Review of Philosophy and Psychology 1 (4):847-887.
    A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes from recent (...)
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  5.  57
    Manifestations of Genericity.Yael Greenberg - 2003 - Routledge.
    In this book, Yael Greenberg discusses and clarifies a number of controversial issues and phenomena in the generic literature, including the existence of ...
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  6. Conventions of Viewpoint Coherence in Film.Samuel Cumming, Gabriel Greenberg & Rory Kelly - 2017 - Philosophers' Imprint 17.
    This paper examines the interplay of semantics and pragmatics within the domain of film. Films are made up of individual shots strung together in sequences over time. Though each shot is disconnected from the next, combinations of shots still convey coherent stories that take place in continuous space and time. How is this possible? The semantic view of film holds that film coherence is achieved in part through a kind of film language, a set of conventions which govern the relationships (...)
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  7.  97
    How Facts Make Law.Mark Greenberg - 2004 - In Scott Hershovitz (ed.), Exploring Law's Empire: The Jurisprudence of Ronald Dworkin. Oxford University Press. pp. 157-198.
    I offer a new argument against the legal positivist view that non-normative social facts can themselves determine the content of the law. I argue that the nature of the determination relation in law is rational determination: the contribution of law-determining practices to the content of the law must be based on reasons. That is why it must be possible in principle to explain what makes the law have the content that it does. It follows, I argue, that non-normative facts about (...)
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  8. Introduction: Varieties of Iconicity.Valeria Giardino & Gabriel Greenberg - 2015 - Review of Philosophy and Psychology 6 (1):1-25.
    This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...)
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  9.  51
    Should I believe all the truths?Alexander Greenberg - 2020 - Synthese 197 (8):3279-3303.
    Should I believe something if and only if it’s true? Many philosophers have objected to this kind of truth norm, on the grounds that it’s not the case that one ought to believe all the truths. For example, some truths are too complex to believe; others are too trivial to be worth believing. Philosophers who defend truth norms often respond to this problem by reformulating truth norms in ways that do not entail that one ought to believe all the truths. (...)
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  10. Conceptual Role Semantics.Mark Greenberg & Gilbert Harman - 2006 - In Barry C. Smith (ed.), The Oxford Handbook of Philosophy of Language. Oxford University Press. pp. 295.
     
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  11. A New Map of Theories of Mental Content: Constitutive Accounts and Normative Theories.Mark Greenberg - 2005 - Philosophical Issues 15 (1):299-320.
    In this paper, I propose a new way of understanding the space of possibilities in the field of mental content. The resulting map assigns separate locations to theories of content that have generally been lumped together on the more traditional map. Conversely, it clusters together some theories of content that have typically been regarded as occupying opposite poles. I make my points concrete by developing a taxonomy of theories of mental content, but the main points of the paper concern not (...)
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  12.  60
    The Standard Picture and its Discontents.Mark Greenberg - 2011 - In Leslie Green & Brian Leiter (eds.), Oxford Studies in Philosophy of Law. Oxford University Press.
    In this paper, I argue that there is a picture of how law works that most legal theorists are implicitly committed to and take to be common ground. This Standard Picture (SP, for short) is generally unacknowledged and unargued for. SP leads to a characteristic set of concerns and problems and yields a distinctive way of thinking about how law is supposed to operate. I suggest that the issue of whether SP is correct is a fundamental one for the philosophy (...)
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  13.  25
    The Semiotic Spectrum.Gabriel Greenberg - 2011 - Dissertation,
    Because humans cannot know one another’s minds directly, every form of communication is a solution to the same basic problem: how can privately held information be made publicly accessible through manipulations of the physical environment? Language is by far the best studied response to this challenge. But there are a diversity of non-linguistic strategies for representation with external signs as well, from facial expressions and fog horns to chronological graphs and architectural renderings. The general thesis of this dissertation is that (...)
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  14.  1
    Real Existence, Ideal Necessity: Kant's Compromise, and the Modalities Without the Compromise.Robert Greenberg - unknown - Berlin, Germany: De Gruyter.
    In his Critique of Pure Reason, Kant argues that we can know what the existing world must be like, but only if it is considered idealistically, which for Kant means relative to our senses. Analytic philosophy, however, tends to be skeptical that the world of our senses must be like anything at all. This book defends Kant in terms of techniques that belong to analytic philosophy itself, in particular, to its philosophy of language. In addition, the book first abstracts and (...)
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  15.  59
    Whistleblowing Intentions of Lower-Level Employees: The Effect of Reporting Channel, Bystanders, and Wrongdoer Power Status.Jingyu Gao, Robert Greenberg & Bernard Wong-On-Wing - 2015 - Journal of Business Ethics 126 (1):85-99.
    It has been suggested that a reporting channel administered by a third-party may represent a stronger procedural safeguard of anonymity and avoids the appearance of impropriety. This study examines whistleblowing intentions among lower-tier employees, specifically examines whether an externally-administered reporting channel increases whistleblowing intentions compared to an internally-administered one. In contrast to the findings of an earlier study by Kaplan et al. :273–288, 2009), our results suggest that whistle-blowing intentions are higher when the reporting channel is administered externally than when (...)
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  16.  61
    Content and Target in Pictorial Representation.Gabriel Greenberg - 2018 - Ergo: An Open Access Journal of Philosophy 5.
    This essay argues for a model of pictorial representation which aims to explain the relationship between pictorial content and pictorial accuracy. Focusing on cases where pictures are intended to convey accurate information, the model distinguishes between two fundamental representational relations: on one hand, a picture expresses a content; on the other, it aims at a target scene. Such a picture is accurate when the content it expresses fits the target scene it aims at. In addition, the model follows the traditional (...)
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  17.  14
    A Dual-Process Model of Defense Against Conscious and Unconscious Death-Related Thoughts: An Extension of Terror Management Theory.Tom Pyszczynski, Jeff Greenberg & Sheldon Solomon - 1999 - Psychological Review 106 (4):835-845.
  18.  60
    Exceptions to Generics: Where Vagueness, Context Dependence and Modality Interact.Yael Greenberg - 2007 - Journal of Semantics 24 (2):131-167.
    This paper deals with the exceptions-tolerance property of generic sentences with indefinite singular and bare plural subjects (IS and BP generics, respectively) and with the way this property is connected to some well-known observations about felicity differences between the two types of generics (e.g. Lawler's 1973, Madrigals are popular vs. #A madrigal is popular). I show that whereas both IS and BP generics tolerate exceptional and contextually irrelevant individuals and situations in a strikingly similar way, which indicates the existence of (...)
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  19.  22
    A Revised, Gradability-Based Semantics for Even.Yael Greenberg - 2018 - Natural Language Semantics 26 (1):51-83.
    This paper concentrates on giving precise content to the general wisdom on the scalar presupposition of even, according to which the prejacent of even, p, is stronger than its relevant focus alternatives, q. To that end I first examine both familiar challenges for the popular ‘comparative likelihood’ view of the ‘stronger than’ relation, as well as novel challenges, having to do with the context dependency of even and with its sensitivity to standards of comparison. To overcome these challenges and to (...)
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  20. Legislation as Communication? Legal Interpretation and the Study of Linguistic Communication.Mark Greenberg - 2011 - In Andrei Marmor & Scott Soames (eds.), Philosophical Foundations of Language in the Law. Oxford University Press, Usa.
     
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  21. Studies in the Stream of Consciousness: Experimental Enhancement and Suppression of Spontaneous Cognitive Processes.J. S. Antrobus, Jerome L. Singer & Sean Greenberg - 1966 - Perceptual and Motor Skills 23:399-417.
  22.  93
    The Six Most Essential Questions in Psychiatric Diagnosis: A Pluralogue Part 1: Conceptual and Definitional Issues in Psychiatric Diagnosis. [REVIEW]James Phillips, Allen Frances, Michael A. Cerullo, John Chardavoyne, Hannah S. Decker, Michael B. First, Nassir Ghaemi, Gary Greenberg, Andrew C. Hinderliter, Warren A. Kinghorn, Steven G. LoBello, Elliott B. Martin, Aaron L. Mishara, Joel Paris, Joseph M. Pierre, Ronald W. Pies, Harold A. Pincus, Douglas Porter, Claire Pouncey, Michael A. Schwartz, Thomas Szasz, Jerome C. Wakefield, G. Scott Waterman, Owen Whooley & Peter Zachar - 2012 - Philosophy, Ethics, and Humanities in Medicine 7:1-29.
    In face of the multiple controversies surrounding the DSM process in general and the development of DSM-5 in particular, we have organized a discussion around what we consider six essential questions in further work on the DSM. The six questions involve: 1) the nature of a mental disorder; 2) the definition of mental disorder; 3) the issue of whether, in the current state of psychiatric science, DSM-5 should assume a cautious, conservative posture or an assertive, transformative posture; 4) the role (...)
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  23. Kant’s Theory of A Priori Knowledge.Robert Greenberg - 2001 - Pennsylvania State University Press.
    The prevailing interpretation of Kant’s _First Critique _in Anglo-American philosophy views his theory of a priori knowledge as basically a theory about the possibility of empirical knowledge, or the a priori conditions for that possibility. Instead, Robert Greenberg argues that Kant is more fundamentally concerned with the possibility of a priori knowledge—the very possibility of the possibility of empirical knowledge in the first place. Greenberg advances four central theses: the _Critique_ is primarily concerned about the possibility, or relation to objects, (...)
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  24.  4
    “Help! I Need Somebody”: Music as a Global Resource for Obtaining Wellbeing Goals in Times of Crisis.Roni Granot, Daniel H. Spitz, Boaz R. Cherki, Psyche Loui, Renee Timmers, Rebecca S. Schaefer, Jonna K. Vuoskoski, Ruth-Nayibe Cárdenas-Soler, João F. Soares-Quadros, Shen Li, Carlotta Lega, Stefania La Rocca, Isabel Cecilia Martínez, Matías Tanco, María Marchiano, Pastora Martínez-Castilla, Gabriela Pérez-Acosta, José Darío Martínez-Ezquerro, Isabel M. Gutiérrez-Blasco, Lily Jiménez-Dabdoub, Marijn Coers, John Melvin Treider, David M. Greenberg & Salomon Israel - 2021 - Frontiers in Psychology 12.
    Music can reduce stress and anxiety, enhance positive mood, and facilitate social bonding. However, little is known about the role of music and related personal or cultural variables in maintaining wellbeing during times of stress and social isolation as imposed by the COVID-19 crisis. In an online questionnaire, administered in 11 countries, participants rated the relevance of wellbeing goals during the pandemic, and the effectiveness of different activities in obtaining these goals. Music was found to be the most effective activity (...)
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  25.  38
    Establishing the Role of Empirical Studies of Organizational Justice in Philosophical Inquiries Into Business Ethics.Jerald Greenberg & Robert J. Bies - 1992 - Journal of Business Ethics 11 (5-6):433-444.
    The present article attempts to evaluate various tenets of moral philosophy by reviewing empirical data from the field of organizational justice bearing on: (a) people''s concerns about fairness in organizations, and (b) the consequences of following or not following rules of justice. With respect to concerns about fairness in organizations, utilitarian claims that people believe that fairness requires distributions of reward based on merit were assessed. Similarly, evidence was reviewed bearing on the claim of psychological egoists that judgments of fairness (...)
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  26. Lethal Consumption: Death-Denying Materialism.Sheldon Solomon, Jeff Greenberg & Thomas A. Pyszczynski - 2004 - In Tim Kasser & Allen D. Kanner (eds.), Psychology and Consumer Culture: The Struggle for a Good Life in a Materialistic World. American Psychological Association. pp. 127--146.
     
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  27.  92
    The Six Most Essential Questions in Psychiatric Diagnosis: A Pluralogue Part 3: Issues of Utility and Alternative Approaches in Psychiatric Diagnosis. [REVIEW]Peter Zachar, Owen Whooley, GScott Waterman, Jerome C. Wakefield, Thomas Szasz, Michael A. Schwartz, Claire Pouncey, Douglas Porter, Harold A. Pincus, Ronald W. Pies, Joseph M. Pierre, Joel Paris, Aaron L. Mishara, Elliott B. Martin, Steven G. LoBello, Warren A. Kinghorn, Andrew C. Hinderliter, Gary Greenberg, Nassir Ghaemi, Michael B. First, Hannah S. Decker, John Chardavoyne, Michael A. Cerullo, Allen Frances & James Phillips - 2012 - Philosophy, Ethics, and Humanities in Medicine 7 (1):9-.
    In face of the multiple controversies surrounding the DSM process in general and the development of DSM-5 in particular, we have organized a discussion around what we consider six essential questions in further work on the DSM. The six questions involve: 1) the nature of a mental disorder; 2) the definition of mental disorder; 3) the issue of whether, in the current state of psychiatric science, DSM-5 should assume a cautious, conservative posture or an assertive, transformative posture; 4) the role (...)
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  28.  3
    Punctual Categoricity and Universality.Rod Downey, Noam Greenberg, Alexander Melnikov, Keng Meng Ng & Daniel Turetsky - 2020 - Journal of Symbolic Logic 85 (4):1427-1466.
    We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is ${\text {PA}}$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is $0''$. We also prove that, with a bit of work, the latter result can be pushed beyond $\Delta ^1_1$, thus showing that punctually categorical structures can (...)
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  29.  32
    Benign Cost Functions and Lowness Properties.Noam Greenberg & André Nies - 2011 - Journal of Symbolic Logic 76 (1):289 - 312.
    We show that the class of strongly jump-traceable c.e. sets can be characterised as those which have sufficiently slow enumerations so they obey a class of well-behaved cost functions, called benign. This characterisation implies the containment of the class of strongly jump-traceable c.e. Turing degrees in a number of lowness classes, in particular the classes of the degrees which lie below incomplete random degrees, indeed all LR-hard random degrees, and all ω-c.e. random degrees. The last result implies recent results of (...)
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  30. Hartian Positivism and Normative Facts : How Facts Make Law II.Mark Greenberg - 2006 - In Scott Hershovitz (ed.), Exploring Law's Empire: The Jurisprudence of Ronald Dworkin. Oxford University Press.
    In this paper, I deploy an argument that I have developed in a number of recent papers in the service of three projects. First, I show that the most influential version of legal positivism – that associated with H.L.A. Hart – fails. The argument’s engine is a requirement that a constitutive account of legal facts must meet. According to this rational-relation requirement, it is not enough for a constitutive account of legal facts to specify non-legal facts that modally determine the (...)
     
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  31.  14
    There is No (Sui Generis) Norm of Assertion.Alexander Greenberg - 2020 - Philosophy 95 (3):337 - 362.
    There are norms on action and norms on assertion. That is, there are things we should and shouldn't do, and things we should and shouldn't say. How do these two kinds of norm relate? Are norms on assertion reducible to norms on action? Many philosophers think they are not. These philosophers claim there is a sui generis norm specific to assertion, a norm which is also often claimed to be constitutive of assertion. Both claims, I argue, should be rejected. The (...)
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  32. Incomplete Understanding, Deference, and the Content of Thought.Mark Greenberg - unknown
    Tyler Burge’s influential arguments have convinced most philosophers that a thinker can have a thought involving a particular concept without fully grasping or having mastery of that concept. In Burge’s (1979) famous example, a thinker who lacks mastery of the concept of arthritis nonetheless has thoughts involving that concept. It is generally supposed, however, that this phenomenon – incomplete understanding, for short – does not require us to reconsider in a fundamental way what it is for a thought to involve (...)
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  33.  43
    Comment on "Detecting Awareness in the Vegetative State".Daniel L. Greenberg - 2007 - Science 315 (5816).
  34.  41
    Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.
    We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.
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  35. Descartes on the Passions: Function, Representation, and Motivation.Sean Greenberg - 2007 - Noûs 41 (4):714–734.
  36. Moral Concepts and Motivation.Mark Greenberg - 2009 - Philosophical Perspectives 23 (1):137-164.
  37.  24
    Epistemic Responsibility and Criminal Negligence.Alexander Greenberg - 2020 - Criminal Law and Philosophy 14 (1):91-111.
    We seem to be responsible for our beliefs in a distinctively epistemic way. We often hold each other to account for the beliefs that we hold. We do this by criticising other believers as ‘gullible’ or ‘biased’, and by trying to persuade others to revise their beliefs. But responsibility for belief looks hard to understand because we seem to lack control over our beliefs. In this paper, I argue that we can make progress in our understanding of responsibility for belief (...)
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  38.  74
    Counterfactuals and Modality.Gabriel Greenberg - 2021 - Linguistics and Philosophy 1 (6):1-26.
    This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...)
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  39.  16
    Anti-Complex Sets and Reducibilities with Tiny Use.Johanna N. Y. Franklin, Noam Greenberg, Frank Stephan & Guohua Wu - 2013 - Journal of Symbolic Logic 78 (4):1307-1327.
  40.  20
    Computing K-Trivial Sets by Incomplete Random Sets.Laurent Bienvenu, Adam R. Day, Noam Greenberg, Antonín Kučera, Joseph S. Miller, André Nies & Dan Turetsky - 2014 - Bulletin of Symbolic Logic 20 (1):80-90.
    EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.
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  41.  32
    Lowness for Kurtz Randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
    We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...)
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  42.  23
    A Prospective Study of the Impact of Transcranial Alternating Current Stimulation on EEG Correlates of Somatosensory Perception.Danielle D. Sliva, Christopher J. Black, Paul Bowary, Uday Agrawal, Juan F. Santoyo, Noah S. Philip, Benjamin D. Greenberg, Christopher I. Moore & Stephanie R. Jones - 2018 - Frontiers in Psychology 9.
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  43. The Standard Picture and Its Discontents.Mark Greenberg - 2011 - In Leslie Green & Brian Leiter (eds.), Oxford Studies in Philosophy of Law: Volume 1. Oxford University Press.
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  44. The Theory of Social Situations: An Alternative Game-Theoretic Approach.Joseph Greenberg - 1990 - Cambridge University Press.
    This book, first published in 1991, offers an integrative approach to the study of formal models in the social and behavioural sciences. The theory presented here unifies both the representation of the social environment and the equilibrium concept. The theory requires that all alternatives that are available to the players be specified in an explicit and detailed manner, and this specification is defined as a social 'situation'. A situation, therefore, not only consists of the alternatives currently available to the players, (...)
     
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  45.  25
    I Am Not an Animal: Mortality Salience, Disgust, and the Denial of Human Creatureliness.Jamie L. Goldenberg, Tom Pyszczynski, Jeff Greenberg, Sheldon Solomon, Benjamin Kluck & Robin Cornwell - 2001 - Journal of Experimental Psychology: General 130 (3):427.
  46. The Six Most Essential Questions in Psychiatric Diagnosis: A Pluralogue Part 2: Issues of Conservatism and Pragmatism in Psychiatric Diagnosis. [REVIEW]James Phillips, Allen Frances, Michael A. Cerullo, John Chardavoyne, Hannah S. Decker, Michael B. First, Nassir Ghaemi, Gary Greenberg, Andrew C. Hinderliter, Warren A. Kinghorn, Steven G. LoBello, Elliott B. Martin, Aaron L. Mishara, Joel Paris, Joseph M. Pierre, Ronald W. Pies, Harold A. Pincus, Douglas Porter, Claire Pouncey, Michael A. Schwartz, Thomas Szasz, Jerome C. Wakefield, G. Waterman, Owen Whooley & Peter Zachar - 2012 - Philosophy, Ethics, and Humanities in Medicine 7:8-.
    In face of the multiple controversies surrounding the DSM process in general and the development of DSM-5 in particular, we have organized a discussion around what we consider six essential questions in further work on the DSM. The six questions involve: 1) the nature of a mental disorder; 2) the definition of mental disorder; 3) the issue of whether, in the current state of psychiatric science, DSM-5 should assume a cautious, conservative posture or an assertive, transformative posture; 4) the role (...)
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  47. Thoughts Without Masters Incomplete Understanding and the Content of Mind.Mark Greenberg - 2001
     
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  48.  11
    Parental Moral Distress and Moral Schism in the Neonatal ICU.Gabriella Foe, Jonathan Hellmann & Rebecca A. Greenberg - 2018 - Journal of Bioethical Inquiry 15 (3):319-325.
    Ethical dilemmas in critical care may cause healthcare practitioners to experience moral distress: incoherence between what one believes to be best and what occurs. Given that paediatric decision-making typically involves parents, we propose that parents can also experience moral distress when faced with making value-laden decisions in the neonatal intensive care unit. We propose a new concept—that parents may experience “moral schism”—a genuine uncertainty regarding a value-based decision that is accompanied by emotional distress. Schism, unlike moral distress, is not caused (...)
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  49. Some Men: Feminist Allies in the Movement to End Violence Against Women.Michael A. Messner, Max A. Greenberg & Tal Peretz - 2015 - Oup Usa.
    What does it mean for men to join with women in preventing sexual assault and domestic violence? This book, based on life history interviews with men and women anti-violence activists, illuminates both the promise of men's violence prevention work, as well as the strains and tensions that inhere, both for men as feminist allies, and for the women they work with.
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  50.  8
    A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.
    We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of${\rm{\Delta }}_2^0$functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees and the array noncomputable degrees. The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.
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