Results for 'Downward Exclusion'

973 found
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  1. Causal Exclusion and Downward Counterfactuals.Tuomas K. Pernu - 2016 - Erkenntnis 81 (5):1031-1049.
    One of the main line of responses to the infamous causal exclusion problem has been based on the counterfactual account of causation. However, arguments have begun to surface to the effect that the counterfactual theory is in fact ill-equipped to solve the exclusion problem due to its commitment to downward causation. This argumentation is here critically analysed. An analysis of counterfactual dependence is presented and it is shown that if the semantics of counterfactuals is taken into account (...)
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  2. Downward Causation Defended.James Woodward - 2021 - In Jan Voosholz & Markus Gabriel, Top-Down Causation and Emergence. Cham: Springer Verlag. pp. 217-251.
    This paper defends the notion of downward causation. I will seek to elucidate this notion, explain why it is a useful way of thinking, and respond to criticisms attacking its intelligibility. My account of downward causation will be in many respects similar to the account recently advanced by Ellis. The overall framework I will adopt is the interventionist treatment of causation I have defended elsewhere: X causes Y when Y changes under a suitable manipulation of X. When X (...)
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  3. Causation, exclusion, and the special sciences.Panu Raatikainen - 2010 - Erkenntnis 73 (3):349-363.
    The issue of downward causation (and mental causation in particular), and the exclusion problem is discussed by taking into account some recent advances in the philosophy of science. The problem is viewed from the perspective of the new interventionist theory of causation developed by Woodward. It is argued that from this viewpoint, a higher-level (e.g., mental) state can sometimes truly be causally relevant, and moreover, that the underlying physical state which realizes it may fail to be such.
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  4.  63
    Experiment, Downward Causation, and Interventionist Levels of Explanation.Veli-Pekka Parkkinen - 2016 - International Studies in the Philosophy of Science 30 (3):245-261.
    This article considers interventionist arguments for downward causation and non-fundamental level causal explanation from the point of view of inferring causation from experiments. Several authors have utilised the interventionist theory of causal explanation to argue that the causal exclusion argument is moot and that higher-level as well as downward causation is real. I show that this argument can be made when levels are understood as levels of grain, leaving us with a choice between causal explanations pitched at (...)
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  5. Counterfactuals, Autonomy and Downward Causation: Reply to Zhong.Dwayne Moore - 2013 - Philosophia 41 (3):831-839.
    In recent papers, Lei Zhong argues that the autonomy solution to the causal exclusion problem is unavailable to anyone that endorses the counterfactual model of causation. The linchpin of his argument is that the counterfactual theory entails the downward causation principle, which conflicts with the autonomy solution. In this note I argue that the counterfactual theory does not entail the downward causation principle, so it is possible to advocate for the autonomy solution to the causal exclusion (...)
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  6. Nonreductive physicalism and the limits of the exclusion principle.Christian List & Peter Menzies - 2009 - Journal of Philosophy 106 (9):475-502.
    It is often argued that higher-level special-science properties cannot be causally efficacious since the lower-level physical properties on which they supervene are doing all the causal work. This claim is usually derived from an exclusion principle stating that if a higher-level property F supervenes on a physical property F* that is causally sufficient for a property G, then F cannot cause G. We employ an account of causation as difference-making to show that the truth or falsity of this principle (...)
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  7. From Multilevel Explanation to Downward Causation.David Yates - 2024 - In Katie Robertson & Alastair Wilson, Levels of Explanation. Oxford University Press.
    The causal closure of the physical poses a familiar causal exclusion problem for the special sciences that stems from the idea that if closure is true, then fundamental physical properties do all the causal work involved in bringing about physical effects. In this paper I aim to show that the strongest causal closure principle that is not ruled out by some simple physics in fact allows for a certain kind of downward causation, which in turn makes room for (...)
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  8.  76
    Three Grades of Downward Causation.Francesco Orilia & Michele Paolini Paoletti - 2017 - In Michele Paolini Paoletti & Francesco Orilia, Philosophical and Scientific Perspectives on Downward Causation. New York: Routledge. pp. 25-41.
    Kim has argued that in the layered model of reality shared by nonreductive physicalism and by emergentism, the assumed dependence of the mental level on the physical level leaves no room for downward causation. In his analysis Kim assumes that causal relata are events, conceived of as exemplifications of properties by particulars at a certain time. But if causal relata are conceived of in different ways and causation is appropriately understood, one can find room in the layered model for (...)
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  9. Downward causation and supervenience: the non-reductionist’s extra argument for incompatibilism.Joana Rigato - 2018 - Philosophical Explorations 21 (3):384-399.
    Agent-causal theories of free will, which rely on a non-reductionist account of the agent, have traditionally been associated with libertarianism. However, some authors have recently argued in favor of compatibilist agent-causal accounts. In this essay, I will show that such accounts cannot avoid serious problems of implausibility or incoherence. A careful analysis of the implications of non-reductionist views of the agent (event-causal or agent-causal as they may be) reveals that such views necessarily imply either the denial of the principle of (...)
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  10. Intervening on the Causal Exclusion Problem for Integrated Information Theory.Matthew Baxendale & Garrett Mindt - 2018 - Minds and Machines 28 (2):331-351.
    In this paper, we examine the causal framework within which integrated information theory of consciousness makes it claims. We argue that, in its current formulation, IIT is threatened by the causal exclusion problem. Some proponents of IIT have attempted to thwart the causal exclusion problem by arguing that IIT has the resources to demonstrate genuine causal emergence at macro scales. In contrast, we argue that their proposed solution to the problem is damagingly circular as a result of inter-defining (...)
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  11.  54
    Mental Causation and Exclusion: Why the Difference-making Account of Causation is No Help.José Luis Bermúdez & Arnon Cahen - 2015 - Humana Mente 8 (29).
    Peter Menzies has developed a novel version of the exclusion principle that he claims to be compatible with the possibility of mental causation. Menzies proposes to frame the exclusion principle in terms of a difference-making account of causation, understood in counterfactual terms. His new exclusion principle appears in two formulations: upwards exclusion — which is the familiar case in which a realizing event causally excludes the event that it realizes — and, more interestingly, downward (...), in which an event causally excludes its realizer. This paper shows that one consequence of Menzies’s proposed solution to the problem of mental causation is a ubiquitous violation of the principle of closure — a fact that forces him into a trilemma to which we see no satisfactory response. (shrink)
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  12. Interventionist Causal Exclusion and Non‐reductive Physicalism.Michael Baumgartner - 2009 - International Studies in the Philosophy of Science 23 (2):161-178.
    The first part of this paper presents an argument showing that the currently most highly acclaimed interventionist theory of causation, i.e. the one advanced by Woodward, excludes supervening macro properties from having a causal influence on effects of their micro supervenience bases. Moreover, this interventionist exclusion argument is demonstrated to rest on weaker premises than classical exclusion arguments. The second part then discusses a weakening of interventionism that Woodward suggests. This weakened version of interventionism turns out either to (...)
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  13. The Causal Exclusion Argument.Jesper Kallestrup - 2006 - Philosophical Studies 131 (2):459-485.
    Jaegwon Kim’s causal exclusion argument says that if all physical effects have sufficient physical causes, and no physical effects are caused twice over by distinct physical and mental causes, there cannot be any irreducible mental causes. In addition, Kim has argued that the nonreductive physicalist must give up completeness, and embrace the possibility of downward causation. This paper argues first that this extra argument relies on a principle of property individuation, which the nonreductive physicalist need not accept, and (...)
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  14.  52
    Models of Downward Causation.Max Kistler - 2021 - In Jan Voosholz & Markus Gabriel, Top-Down Causation and Emergence. Cham: Springer Verlag. pp. 305-326.
    Two conceptual frameworks – in terms of phase space and in terms of structural equations – are sketched, in which downward causal influence of higher-level features on lower-level features is possible. The “Exclusion” principle, which is a crucial premise of the argument against the possibility of downward causation, is false in models constructed within both frameworks. Both frameworks can be supplemented with conceptual tools that make it possible to explain why downward causal influence is not only (...)
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  15.  36
    Supervenience and the problem of downward causation.Wilson Mendonça - 2002 - Manuscrito 25 (3):251-270.
    It seems that higher-level, nonbasic properties can only manifest their causal powers by exerting causal influence on lower-level, physically basic phenomena in the first place. A very influential line of reasoning conceives of this form of downward causation as either reducible to causation by physical properties or as ultimately untenable, because incompatible with the causal closure of physical reality. The paper argues that this is not so. It examines, first, why it is that a recent attempt by Noordhof to (...)
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  16. How I (freely) Raised My Arm. Downward, Structural, Substance Causation.Michele Paolini Paoletti - 2016 - Mind and Matter 14 (2):203-228.
    I develop and defend a model of downward causation denoted as downward, structural, substance causation. This model is based on the idea that higher-level, strongly emergent substances can cause something at lower levels by imposing certain structures on lower-level goings-on. After providing a sketch of the model and of its ontological assumptions, I apply it to the analysis of how free mental causes can structure neural goings-on. I defend three theses following from such an analysis, and I test (...)
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  17. Can Counterfactuals Solve the Exclusion Problem?Lei Zhong - 2010 - Philosophy and Phenomenological Research 83 (1):129-147.
    A quite popular approach to solving the Causal Exclusion Problem is to adopt a counterfactual theory of causation. In this paper, I distinguish three versions of the Causal Exclusion Argument. I argue that the counterfactualist approach can block the first two exclusion arguments, because the Causal Inheritance Principle and the Upward Causation Principle upon which the two arguments are based respectively are problematic from the perspective of the counterfactual account of causation. However, I attempt to show that (...)
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  18. Interventions on causal exclusion.Tuomas K. Pernu - 2014 - Philosophical Explorations 17 (2):255-263.
    Two strains of interventionist responses to the causal exclusion argument are reviewed and critically assessed. On the one hand, one can argue that manipulating supervenient mental states is an effective strategy for manipulating the subvenient physical states, and hence should count as genuine causes to the subvenient physical states. But unless the supervenient and subvenient states manifest some difference in their manipulability conditions, there is no reason to treat them as distinct, which in turn goes against the basic assumption (...)
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  19.  49
    Sequence Data, Phylogenetic Inference, and Implications of Downward Causation.Kirk Fitzhugh - 2016 - Acta Biotheoretica 64 (2):133-160.
    Framing systematics as a field consistent with scientific inquiry entails that inferences of phylogenetic hypotheses have the goal of producing accounts of past causal events that explain differentially shared characters among organisms. Linking observations of characters to inferences occurs by way of why-questions implied by data matrices. Because of their form, why-questions require the use of common-cause theories. Such theories in phylogenetic inferences include natural selection and genetic drift. Selection or drift can explain ‘morphological’ characters but selection cannot be causally (...)
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  20. Why the Counterfactualist Should Still Worry About Downward Causation.Lei Zhong - 2015 - Erkenntnis 80 (1):159-171.
    In Zhong (Philos Phenomenol Res 83:129–147, 2011; Analysis 72:75–85, 2012), I argued that, contrary to what many people might expect, the counterfactual theory of causation will generate (rather than solve) the exclusion problem. Recently some philosophers raise an incisive objection to this argument. They contend that my argument fails as it equivocates between different notions of a physical realizer (see Christensen and Kallestrup in Analysis 72:513–517, 2012). However, I find that their criticism doesn’t threaten the central idea of my (...)
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  21. Does same-level causation entail downward causation?Neil Campbell - 2015 - Abstracta 8 (2).
    I argue that Jaegwon Kim’s supervenience argument does not generalize to all special science properties by undermining his central intuition, employed in stage 1 of the argument, that there is a tension between horizontal causation and vertical determination. First, I challenge Kim’s treatment of the examples he employs to support this intuition, then I appeal to Kim’s own work on the metaphysics of explanation in order to dissipate the alleged tension.
     
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  22. Emergent Causation.Simon Prosser - 2012 - Philosophical Studies 159 (1):21-39.
    Downward causation is commonly held to create problems for ontologically emergent properties. In this paper I describe two novel examples of ontologically emergent properties and show how they avoid two main problems of downward causation, the causal exclusion problem and the causal closure problem. One example involves an object whose colour does not logically supervene on the colours of its atomic parts. The other example is inspired by quantum entanglement cases but avoids controversies regarding quantum mechanics. These (...)
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  23.  89
    Contrastive mental causation.Walter Sinnott-Armstrong - 2019 - Synthese 198 (Suppl 3):861-883.
    Any theory of mind needs to explain mental causation. Kim’s exclusion argument concludes that non-reductive physicalism cannot meet this challenge. One classic reply is that mental properties capture the causally relevant level of generality, because they are insensitive to physical realization. However, this reply suggests downward exclusion, contrary to physicalism’s assumption of closure. This paper shows how non-reductive physicalists can solve this problem by introducing a contrastive account of causation with non-exhaustive contrasts. That view has independent justification, (...)
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  24.  85
    Can Western Monotheism Avoid Substance Dualism?Dennis Bielfeldt - 2001 - Zygon 36 (1):153-177.
    The problem of divine agency and action is analogous to the problem of human agency and action: How is such agency possible in the absence of a dualistic causal interaction between disparate orders of being? This paper explores nondualistic accounts of divine agency that assert the following: (1) physical monism, (2) antireductionism, (3) physical realization, and (4) divine causal realism. I conclude that a robustly causal deity is incompatible with nonddualism's affirmation of physical monism. Specifically, I argue the incoherence of (...)
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  25. Neural Synchrony and the Causal Efficacy of Consciousness.David Yates - 2020 - Topoi 39 (5):1057-1072.
    The purpose of this paper is to address a well-known dilemma for physicalism. If mental properties are type identical to physical properties, then their causal efficacy is secure, but at the cost of ruling out mentality in creatures very different to ourselves. On the other hand, if mental properties are multiply realizable, then all kinds of creatures can instantiate them, but then they seem to be causally redundant. The causal exclusion problem depends on the widely held principle that realized (...)
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  26. Taking Emergentism Seriously.Lei Zhong - 2019 - Australasian Journal of Philosophy 98 (1):31-46.
    The Exclusion Argument has afflicted non-reductionists for decades. In this article, I attempt to show that emergentism—the view that mental entities can downwardly cause physical entities in a non-overdetermining way—is the most plausible approach to solving the exclusion problem. The emergentist approach is largely absent in contemporary philosophy of mind, because emergentism rejects the Causal Closure of Physics, a doctrine embraced by almost all physicalists. This article, however, challenges the consensus on causal closure and defends a physicalist version (...)
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  27. Natural Selection and Multi-Level Causation.Maximiliano Martínez & Andrés Moya - 2011 - Philosophy, Theory, and Practice in Biology 3 (20130604).
    In this paper, using a multilevel approach, we defend the positive role of natural selection in the generation of organismal form. Despite the currently widespread opinion that natural selection only plays a negative role in the evolution of form, we argue, in contrast, that the Darwinian factor is a crucial (but not exclusive) factor in morphological organization. Analyzing some classic arguments, we propose incorporating the notion of ‘downward causation’ into the concept of ‘natural selection.’ In our opinion, this kind (...)
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  28. How properties emerge.Paul Humphreys - 1997 - Philosophy of Science 64 (1):1-17.
    A framework for representing a specific kind of emergent property instance is given. A solution to a generalized version of the exclusion argument is then provided and it is shown that upwards and downwards causation is unproblematical for that kind of emergence. One real example of this kind of emergence is briefly described and the suggestion made that emergence may be more common than current opinions allow.
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  29. A Defense of Emergence.Jason Megill - 2013 - Axiomathes 23 (4):597-615.
    I defend a physicalistic version of ontological emergence; qualia emerge from the brain, but are physical properties nevertheless. First, I address the following questions: what are the central tenets of physicalistic ontological emergentism; what are the relationships between these tenets; what is the relationship between physicalistic ontological emergentism and non-reductive physicalism; and can there even be a physicalistic version of ontological emergentism? This discussion is merely an attempt to clarify exactly what a physicalistic version of ontological emergentism must claim, and (...)
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  30.  66
    Quantity implicatures.Bart Geurts - 2010 - New York: Cambridge University Press.
    Gricean pragmatics. Saying vs. implicating ; Discourse and cooperation ; Conversational implicatures ; Generalised vs. particularised ; Cancellability ; Gricean reasoning and the pragmatics of what is said -- The standard recipe for Q-implicatures. The standard recipe ; Inference to the best explanation ; Weak implicatures and competence ; Relevance ; Conclusion -- Scalar implicatures. Horn scales and the generative view ; Implicatures and downward entailing environments ; Disjunction : exclusivity and ignorance ; Conclusion -- Psychological plausibility. Charges of (...)
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  31.  36
    Julian Johnson, Who Needs Classical Music? Cultural Choice and Musical Value. Oxford University Press, 2002.William M. Perrine - 2014 - Philosophy of Music Education Review 22 (1):96.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Who Needs Classical Music? Cultural Choice and Musical Value by Julian JohnsonWilliam M. PerrineJulian Johnson, Who Needs Classical Music? Cultural Choice and Musical Value. Oxford University Press, 2002.In Who Needs Classical Music? Cultural Choice and Musical Value, British musicologist and composer Julian Johnson defends the value of classical music in a commercialized culture fixated on the immediate gratification of popular music. At 130 pages divided into six chapters, (...)
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  32. The acquisition of disjunction: Evidence for a grammatical view of scalar implicatures.Stephen Crain - manuscript
    This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic (...)
     
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  33. The Limitations of Kim’s Reductive Physicalism in Accounting for Living Systems and an Alternative Nonreductionist Ontology.Slobodan Perovic - 2007 - Acta Biotheoretica 55 (3):243-267.
    Jaegwon Kim’s exclusion argument is a general ontological argument, applicable to any properties deemed supervenient on a microproperty basis, including biological properties. It implies that the causal power of any higher-level property must be reducible to the subset of the causal powers of its lower-level properties. Moreover, as Kim’s recent version of the argument indicates, a higher-level property can be causally efficient only to the extent of the efficiency of its micro-basis. In response, I argue that the ontology that (...)
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  34. The Acquisition of Disjunction: Evidence for a Grammatical View of Scalar Implicatures.Luisa Meronib - unknown
    This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic (...)
     
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  35. Genuine Fortuitousness. Where Did That Click Come From?Ole Ulfbeck & Aage Bohr - 2001 - Foundations of Physics 31 (5):757-774.
    The paper presents a revised view of quantum mechanics centered on the notion (“genuine fortuitousness”) that the click in a counter is a totally lawless event, which comes by itself. A crucial point is the distinction between events on the spacetime scene and the content of the symbolic algorism. A revised conception of matrix variables emerges, by which such a variable, as part of a whole, does not have a value, under any circumstance. This conception is at variance with that (...)
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  36. Counterfactuals, Regularity and the Autonomy Approach.Lei Zhong - 2012 - Analysis 72 (1):75-85.
    Many philosophers insist that the most plausible solution to the exclusion problem is to adopt the so-called ‘autonomy approach’, which denies either upward or downward causation between mental and physical properties. But the question of whether the autonomy approach is compatible with respectable theories of causation has seldom been discussed in the literature. This paper considers two influential theories of causation, the counterfactual account and the regularity account. I argue that neither the counterfactual theory nor the regularity theory (...)
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  37.  67
    Building low level causation out of high level causation.Samuel Lee - 2021 - Synthese 199 (3-4):9927-9955.
    I argue that high level causal relationships are often more fundamental than low level causal relationships. My argument is based on some general principles governing when one causal relationship will metaphysically ground another—a phenomenon I term derivative causation. These principles are in turn based partly on our intuitive judgments concerning derivative causation in a series of representative examples, and partly on some powerful theoretical considerations in their favour. I show how these principles entail that low level causation can derive from (...)
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  38. At the semantics/pragmatics interface in child language.Stephen Crain - manuscript
    This paper investigates scalar implicatures and downward entailment in child English. In previous experimental work we have shown that adults’ computation of scalar implicatures is sensitive to entailment relations. For instance, when the disjunction operator or occurs in positive contexts, an implicature of exclusivity arises. By contrast when the disjunction operator occurs within the scope of a downward entailing linguistic expression, no implicature of exclusivity is computed. Investigations on children’s computation of scalar implicatures in the same contexts have (...)
     
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  39. At the Semantics/Pragmatics Interface in Child Language.Luisa Meronia - unknown
    This paper investigates scalar implicatures and downward entailment in child English. In previous experimental work we have shown that adults’ computation of scalar implicatures is sensitive to entailment relations. For instance, when the disjunction operator or occurs in positive contexts, an implicature of exclusivity arises. By contrast when the disjunction operator occurs within the scope of a downward entailing linguistic expression, no implicature of exclusivity is computed. Investigations on children’s computation of scalar implicatures in the same contexts have (...)
     
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  40. Object-Oriented France: The Philosophy of Tristan Garcia.Graham Harman - 2012 - Continent 2 (1):6-21.
    continent. 2.1 (2012): 6–21. The French philosopher and novelist Tristan Garcia was born in Toulouse in 1981. This makes him rather young to have written such an imaginative work of systematic philosophy as Forme et objet , 1 the latest entry in the MétaphysiqueS series at Presses universitaires de France. But this reference to Garcia’s youthfulness is not a form of condescension: by publishing a complete system of philosophy in the grand style, he has already done what none of us (...)
     
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  41.  76
    From the universe of knowledge to the universe of concepts: The structural revolution in classification for information retrieval. [REVIEW]Clare Beghtol - 2008 - Axiomathes 18 (2):131-144.
    During the twentieth century, bibliographic classification theory underwent a structural revolution. The first modern bibliographic classifications were top-down systems that started at the universe of knowledge and subdivided that universe downward to minute subclasses. After the invention of faceted classification by S.R. Ranganathan, the ideal was to build bottom-up classifications that started with the universe of concepts and built upward to larger and larger faceted classes. This ideal has not been achieved, and the two kinds of classification systems are (...)
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  42.  31
    Loving God in and through the self: Trinitarian love in St. Augustine.Matthew Drever - 2017 - International Journal of Philosophy and Theology 78 (1-2):7-22.
    ABSTRACTAnders Nygren argues that Augustine’s adherence to a Platonist notion of eros undermines both his own and a wider Christian account of agape. On Nygren’s reading, eros, which is self-fulfilling love that originates in the soul’s movement toward God, stands in contradistinction to agape, which is self-denying love that originates in God and condescends to us through the sacrifice of Christ. While it is true that Platonism plays an important role for Augustine, he comes to interpret love through a lens (...)
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  43.  20
    Social Integration and Right-Wing Populist Voting in Germany: How Subjective Social Marginalization Affects Support for the AfD.Patrick Sachweh - 2020 - Analyse & Kritik 42 (2):369-398.
    Electoral support for right-wing populist parties is typically explained either by economic deprivation or cultural grievances. Attempting to bring economic and cultural explanations together, recent approaches have suggested to conceptualize right-wing populist support as a problem of social integration. Applying this perspective to the German case, this article investigates whether weak subjective social integration-or subjective social marginalization, respectively-is associated with the intention to vote for the AfD. Furthermore, it asks whether the strength of this association varies across income groups. Based (...)
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  44.  37
    Eros and Psyche. [REVIEW]A. R. E. - 1965 - Review of Metaphysics 19 (2):383-383.
    The basic theme is the development of the Platonic notion of Eros and its relation to the soul from the Platonic texts through the neo-Platonic and early Christian writers. Rist is concerned to modify Nygren's thesis that Eros is situated as a radically upward movement, while the downward movement of love is to be assigned exclusively to the Christian notion of Agape. He tries to show how Plato, and even more Plotinus, and finally Origen associated a downward movement (...)
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  45.  7
    52 Prices.Paul Downward - 2009 - In Jan Peil & Irene van Staveren, Handbook of economics and ethics. Northampton, MA: Edward Elgar. pp. 399.
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  46. Reorienting economics through triangulation of methods.Paul Downward & Andrew Mearman - 2009 - In Edward Fullbrook, Ontology and economics: Tony Lawson and his critics. New York: Routledge. pp. 130--141.
     
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  47. 14 Presenting demi-regularities: the case of Post Keynesian pricing1.Paul Downward & Andrew Mearman - 2003 - In Applied Economics and the Critical Realist Critique. New York: Routledge. pp. 247.
     
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  48.  18
    Symmetry and representation in a three dimensional space.Michael Downward - 2015 - Foundations of Chemistry 17 (3):275-287.
    Schoenflies point groups are presented in terms of spatial partitions and Laue classes based on abstract groups. A much simpler system using only a minimal set of generators for three dimensional groups is then presented in the same form. This simplified treatment allows group operations of a given Laue class to be correlated to a greatly simplified Mulliken-style notation for irreducible representations of that class. Transformation matrix representations of point groups in the simplified style can then be manipulated according to (...)
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  49.  50
    Transforming Economics Through Critical Realism — Themes and Issues.Paul Downward, Sheila Dowi & Steve Fleetwood - 2006 - Journal of Critical Realism 5 (1):139-182.
  50.  12
    Logic and Declarative Language.Michael Downward - 1998 - Routledge.
    Logic has acquired a reputation for difficulty, perhaps because many of the approaches adopted have been more suitable for mathematicians than computer scientists. This book shows that the subject is not inherently difficult and that the connections between logic and declarative language are straightforward. Many exercises have been included in the hope that these will lead to a much greater confidence in manual proofs, therefore leading to a greater confidence in automated proofs.
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