Results for 'causal set theory'

998 found
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  1.  47
    Causal Set Theory and Growing Block? Not Quite.Marco Forgione - manuscript
    In this contribution, I explore the possibility of characterizing the emergence of time in causal set theory (CST) in terms of the growing block universe (GBU) metaphysics. I show that although GBU seems to be the most intuitive time metaphysics for CST, it leaves us with a number of interpretation problems, independently of which dynamics we choose to favor for the theory —here I shall consider the Classical Sequential Growth and the Covariant model. Discrete general covariance of (...)
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  2. Causation as Constraints in Causal Set Theory.Marco Forgione - manuscript
    Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory (...)
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  3. Out of Nowhere: Spacetime from causality: causal set theory.Christian Wüthrich & Nick Huggett - manuscript
    This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory.
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  4. Causal Theories of Spacetime.Sam Baron & Baptiste Le Bihan - 2024 - Noûs 58 (1):202-224.
    We develop a new version of the causal theory of spacetime. Whereas traditional versions of the theory seek to identify spatiotemporal relations with causal relations, the version we develop takes causal relations to be the grounds for spatiotemporal relations. Causation is thus distinct from, and more basic than, spacetime. We argue that this non-identity theory, suitably developed, avoids the challenges facing the traditional identity theory.
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  5. Aptness and means-end coherence: a dominance argument for causal decision theory.J. Robert G. Williams - 2023 - Synthese 201 (2):1-19.
    Why should we be means-end rational? Why care whether someone’s mental states exhibit certain formal patterns, like the ones formalized in causal decision theory? This paper establishes a dominance argument for these constraints in a finite setting. If you violate the norms of causal decision theory, then your desires will be aptness dominated. That is, there will be some alternative set of desires that you could have had, which would be more apt (closer to the actual (...)
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  6. Quantum mechanics and consciousness: Thoughts on a causal correspondence theory.Ian J. Thompson - 2017 - In S. Gosh, B. D. Mundhra, K. Vasudeva Rao & Varun Agarwal (eds.), Quantum Physics & Consciousness - Thoughts of Founding Fathers of Quantum Physics and other Renowned Scholars. Bhaktivedanta Institute. pp. 173-185.
    Which way does causation proceed? The pattern in the material world seems to be upward: particles to molecules to organisms to brains to mental processes. In contrast, the principles of quantum mechanics allow us to see a pattern of downward causation. These new ideas describe sets of multiple levels in which each level influences the levels below it through generation and selection. Top-down causation makes exciting sense of the world: we can find analogies in psychology, in the formation of our (...)
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  7. Causal Theory of Reference of Saul Kripke.Nicolae Sfetcu - manuscript
    Since the 1960s, Kripke has been a central figure in several fields related to mathematical logic, language philosophy, mathematical philosophy, metaphysics, epistemology and set theory. He had influential and original contributions to logic, especially modal logic, and analytical philosophy, with a semantics of modal logic involving possible worlds, now called Kripke semantics. In Naming and Necessity, Kripke proposed a causal theory of reference, according to which a name refers to an object by virtue of a causal (...)
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  8. Natural Agency: An Essay on the Causal Theory of Action.John Bishop - 1989 - New York: Cambridge University Press.
    From a moral point of view we think of ourselves as capable of responsible actions. From a scientific point of view we think of ourselves as animals whose behaviour, however highly evolved, conforms to natural scientific laws. Natural Agency argues that these different perspectives can be reconciled, despite the scepticism of many philosophers who have argued that 'free will' is impossible under 'scientific determinism'. This scepticism is best overcome, according to the author, by defending a causal theory of (...)
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  9. The causal structure of natural kinds.Olivier Lemeire - 2021 - Studies in History and Philosophy of Science Part A 85:200-207.
    One primary goal for metaphysical theories of natural kinds is to account for their epistemic fruitfulness. According to cluster theories of natural kinds, this epistemic fruitfulness is grounded in the regular and stable co- occurrence of a broad set of properties. In this paper, I defend the view that such a cluster theory is insufficient to adequately account for the epistemic fruitfulness of kinds. I argue that cluster theories can indeed account for the projectibility of natural kinds, but not (...)
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  10. Causal Projectivism, Agency, and Objectivity.Elena Popa - 2016 - International Studies in the Philosophy of Science 30 (2):147-163.
    This article examines how specific realist and projectivist versions of manipulability theories of causation deal with the problem of objectivity. Does an agent-dependent concept of manipulability imply that conflicting causal claims made by agents with different capacities can come out as true? In defence of the projectivist stance taken by the agency view, I argue that if the agent’s perspective is shown to be uniform across different agents, then the truth-values of causal claims do not vary arbitrarily and, (...)
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  11. Causal relevance and thought content.Kirk A. Ludwig - 1994 - Philosophical Quarterly 44 (176):334-353.
    It is natural to think that our ordinary practices in giving explanations for our actions, for what we do, commit us to claiming that content properties are causally relevant to physical events such as the movements of our limbs and bodies, and events which these in turn cause. If you want to know why my body ambulates across the street, or why my arm went up before I set out, we suppose I have given you an answer when I say (...)
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  12. Hierarchies, Networks, and Causality: The Applied Evolutionary Epistemological Approach.Nathalie Gontier - 2021 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 52 (2):313-334.
    Applied Evolutionary Epistemology is a scientific-philosophical theory that defines evolution as the set of phenomena whereby units evolve at levels of ontological hierarchies by mechanisms and processes. This theory also provides a methodology to study evolution, namely, studying evolution involves identifying the units that evolve, the levels at which they evolve, and the mechanisms and processes whereby they evolve. Identifying units and levels of evolution in turn requires the development of ontological hierarchy theories, and examining mechanisms and processes (...)
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  13. Unspecific Evidence and Normative Theories of Decision.Rhys Borchert - forthcoming - Episteme:1-23.
    The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I (...)
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  14. Causal Specificity, Biological Possibility and Non-parity about Genetic Causes.Marcel Weber - manuscript
    Several authors have used the notion of causal specificity in order to defend non-parity about genetic causes (Waters 2007, Woodward 2010, Weber 2017, forthcoming). Non-parity in this context is the idea that DNA and some other biomolecules that are often described as information-bearers by biologists play a unique role in life processes, an idea that has been challenged by Developmental Systems Theory (e.g., Oyama 2000). Indeed, it has proven to be quite difficult to state clearly what the alleged (...)
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  15. Actual Causation: Apt Causal Models and Causal Relativism.Jennifer McDonald - 2022 - Dissertation, The Graduate Center, Cuny
    This dissertation begins by addressing the question of when a causal model is apt for deciding questions of actual causation with respect to some target situation. I first provide relevant background about causal models, explain what makes them promising as a tool for analyzing actual causation, and motivate the need for a theory of aptness as part of such an analysis (Chapter 1). I then define what it is for a model on a given interpretation to be (...)
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  16. Experimental effects and causal representations.Vadim Keyser - 2017 - Synthese:1-32.
    In experimental settings, scientists often “make” new things, in which case the aim is to intervene in order to produce experimental objects and processes—characterized as ‘effects’. In this discussion, I illuminate an important performative function in measurement and experimentation in general: intervention-based experimental production (IEP). I argue that even though the goal of IEP is the production of new effects, it can be informative for causal details in scientific representations. Specifically, IEP can be informative about causal relations in: (...)
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  17. Egan and agents: How evidential decision theory can deal with Egan’s dilemma.Daniel Dohrn - 2015 - Synthese 192 (6):1883-1908.
    Andy Egan has presented a dilemma for decision theory. As is well known, Newcomb cases appear to undermine the case for evidential decision theory. However, Egan has come up with a new scenario which poses difficulties for causal decision theory. I offer a simple solution to this dilemma in terms of a modified EDT. I propose an epistemological test: take some feature which is relevant to your evaluation of the scenarios under consideration, evidentially correlated with the (...)
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  18. Wand/Set Theories: A realization of Conway's mathematicians' liberation movement, with an application to Church's set theory with a universal set.Tim Button - forthcoming - Journal of Symbolic Logic.
    Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...)
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  19. Tournament decision theory.Abelard Podgorski - 2020 - Noûs 56 (1):176-203.
    The dispute in philosophical decision theory between causalists and evidentialists remains unsettled. Many are attracted to the causal view’s endorsement of a species of dominance reasoning, and to the intuitive verdicts it gets on a range of cases with the structure of the infamous Newcomb’s Problem. But it also faces a rising wave of purported counterexamples and theoretical challenges. In this paper I will describe a novel decision theory which saves what is appealing about the causal (...)
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  20. Causal Decision Theory, Context, and Determinism.Calum McNamara - forthcoming - Philosophy and Phenomenological Research.
    The classic formulation of causal decision theory (CDT) appeals to counterfactuals. It says that you should aim to choose an option that would have a good outcome, were you to choose it. However, this version of CDT faces trouble if the laws of nature are deterministic. After all, the standard theory of counterfactuals says that, if the laws are deterministic, then if anything—including the choice you make—were different in the present, either the laws would be violated or (...)
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  21. Wants and Acts: Logical, Causal and Material Connections.Edward Allen Francisco - 1974 - Dissertation, Purdue University
    This inquiry is addressed to two questions: (1) what if any logical relations might exist between the concepts of desire and action (as they and the distinctions to which they commit us are ensconced in ordinary parlance), and (2) what if any causal or significant non-causal (i.e., material) relations might ever exist between instances of desire and action? -/- It is held that any credible move to deal with such questions must initially, and at some length, specify the (...)
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  22. Chrysippus' Theory of Causes.Susanne Bobzien - 1998 - In Katerina Ierodiakonou (ed.), Topics in stoic philosophy. New York: Oxford University Press.
    ABSTRACT: A systematic reconstruction of Chrysippus’ theory of causes, grounded on the Stoic tenets that causes are bodies, that they are relative, and that all causation can ultimately be traced back to the one ‘active principle’ which pervades all things. I argue that Chrysippus neither developed a finished taxonomy of causes, nor intended to do so, and that he did not have a set of technical terms for mutually exclusive classes of causes. Rather, the various adjectives which he used (...)
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  23. The Central Dogma as a Thesis of Causal Specificity.Marcel Weber - 2006 - History and Philosophy of the Life Sciences 28 (4):595-610.
    I present a reconstruction of F.H.C. Crick's two 1957 hypotheses "Sequence Hypothesis" and "Central Dogma" in terms of a contemporary philosophical theory of causation. Analyzing in particular the experimental evidence that Crick cited, I argue that these hypotheses can be understood as claims about the actual difference-making cause in protein synthesis. As these hypotheses are only true if restricted to certain nucleic acids in certain organisms, I then examine the concept of causal specificity and its potential to counter (...)
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  24.  20
    Defending the pure causal-historical theory of reference fixing for natural kind terms.Jaakko Tapio Reinikainen - 2024 - Synthese 203 (131):1-15.
    According to the causal-historical theory of reference, natural kind terms refer in virtue of complicated causal relations the speakers have to their environment. A common objection to the theory is that purely causal relations are insufficient to fix reference in a determinate fashion. The so-called hybrid view holds that what is also needed for successful fixing are true descriptions associated in the mind of the speaker with the referent. The main claim of this paper is (...)
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  25. An Essentialist Theory of the Meaning of Slurs.Eleonore Neufeld - 2019 - Philosophers' Imprint 19.
    In this paper, I develop an essentialist model of the semantics of slurs. I defend the view that slurs are a species of kind terms: Slur concepts encode mini-theories which represent an essence-like element that is causally connected to a set of negatively-valenced stereotypical features of a social group. The truth-conditional contribution of slur nouns can then be captured by the following schema: For a given slur S of a social group G and a person P, S is true of (...)
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  26. Incommensurability and Theory Change.Howard Sankey - 2011 - In Steven D. Hales (ed.), A Companion to Relativism. Oxford: Wiley-Blackwell. pp. 456-474.
    The paper explores the relativistic implications of the thesis of incommensurability. A semantic form of incommensurability due to semantic variation between theories is distinguished from a methodological form due to variation in methodological standards between theories. Two responses to the thesis of semantic incommensurability are dealt with: the first challenges the idea of untranslatability to which semantic incommensurability gives rise; the second holds that relations of referential continuity eliminate semantic incommensurability. It is then argued that methodological incommensurability poses little risk (...)
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  27.  93
    Phenomenology of Anomaluos Causality.Nijaz Ibrulj - 2017 - In Ivo Komšić (ed.), The Theory of Social Pulsation. Peter Lang Publishing, Inc.,. pp. 89-136.
    The conceptual framework that emerged in relation to Komsic’s theory of social pulsations is composed of notions we will deem convenient in the reception of this theory: the anomalous character of social causation, implicit normative inferentialism, projective semantics of social relations, projective sociology, projective social phenomenology, inferential explication of social relations, social inferentialism, and many others. This conceptual framework is part of a “partial doctrine” itself, or a counter-factual position within sociological theory that could legitimately be called (...)
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  28. How Biological Technology Should Inform the Causal Selection Debate.Janella Baxter - 2019 - Philosophy, Theory, and Practice in Biology 11.
    Waters’s (2007) actual difference making and Weber’s (2013, 2017) biological normality approaches to causal selection have received many criticisms, some of which miss their target. Disagreement about whether Waters’s and Weber’s views succeed in providing criteria that uniquely singles out the gene as explanatorily significant in biology has led philosophers to overlook a prior problem. Before one can address whether Waters’s and Weber’s views successfully account for the explanatory significance of genes, one must ask whether either view satisfactorily meets (...)
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  29. Causal Decision Theory and Decision Instability.Brad Armendt - 2019 - Journal of Philosophy 116 (5):263-277.
    The problem of the man who met death in Damascus appeared in the infancy of the theory of rational choice known as causal decision theory. A straightforward, unadorned version of causal decision theory is presented here and applied, along with Brian Skyrms’ deliberation dynamics, to Death in Damascus and similar problems. Decision instability is a fascinating topic, but not a source of difficulty for causal decision theory. Andy Egan’s purported counterexample to causal (...)
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  30. Causal Decision Theory: A Counterexample.Arif Ahmed - 2013 - Philosophical Review 122 (2):289-306.
    The essay presents a novel counterexample to Causal Decision Theory (CDT). Its interest is that it generates a case in which CDT violates the very principles that motivated it in the first place. The essay argues that the objection applies to all extant formulations of CDT and that the only way out for that theory is a modification of it that entails incompatibilism. The essay invites the reader to find this consequence of CDT a reason to reject (...)
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  31. Using stable model semantics (SMODELS) in the causal calculator (CCALC).Semra Dogandag, F. Nur Alpaslan & Varol Akman - 2001 - In Proceedings of 10th Turkish Symposium on Artificial Intelligence and Neural Networks (TAINN).
    Action Languages are formal methods of talking about actions and their effects on fluents. One recent approach in planning is to define the domains of the planning problems using action languages. The aim of this research is to find a plan for a system defined in the action language C by translating it into a causal theory and then finding an equivalent logic program. The planning problem will then be reduced to finding the answer set (stable model) of (...)
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  32. A powerful theory of causation.Stephen Mumford & Rani Anjum - 2010 - In Anna Marmodoro (ed.), The Metaphysics of Powers: Their Grounding and Their Manifestations. Routledge. pp. 143--159.
    Hume thought that if you believed in powers, you believed in necessary connections in nature. He was then able to argue that there were none such because anything could follow anything else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations: rather, it disposes towards them in a way that is less than necessary but more than purely contingent. -/- In this paper a dispositional theory of causation is offered. Causes dispose towards their effects and often (...)
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  33. A New Theory of Free Will.Marcus Arvan - 2013 - Philosophical Forum 44 (1):1-48.
    This paper shows that several live philosophical and scientific hypotheses – including the holographic principle and multiverse theory in quantum physics, and eternalism and mind-body dualism in philosophy – jointly imply an audacious new theory of free will. This new theory, "Libertarian Compatibilism", holds that the physical world is an eternally existing array of two-dimensional information – a vast number of possible pasts, presents, and futures – and the mind a nonphysical entity or set of properties that (...)
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  34. Implications of Migration Theory for Distributive Justice.Alex Sager - 2012 - Global Justice: Theory, Practice, Rhetoric 5.
    This paper explores the implications of empirical theories of migration for normative accounts of migration and distributive justice. It examines neo-classical economics, world-systems theory, dual labor market theory, and feminist approaches to migration and contends that neo-classical economic theory in isolation provides an inadequate understanding of migration. Other theories provide a fuller account of how national and global economic, political, and social institutions cause and shape migration flows by actively affecting people's opportunity sets in source countries and (...)
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  35. An Embodied Predictive Processing Theory of Pain.Julian Kiverstein, Michael David Kirchhoff & Mick Thacker - 2022 - Review of Philosophy and Psychology 1 (1):1-26.
    This paper aims to provide a theoretical framework for explaining the subjective character of pain experience in terms of what we will call ‘embodied predictive processing’. The predictive processing (PP) theory is a family of views that take perception, action, emotion and cognition to all work together in the service of prediction error minimisation. In this paper we propose an embodied perspective on the PP theory we call the ‘embodied predictive processing (EPP) theory. The EPP theory (...)
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  36. Causal Decision Theory and EPR correlations.Arif Ahmed & Adam Caulton - 2014 - Synthese 191 (18):4315-4352.
    The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who (...)
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  37. Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In (...)
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  38. Concepts and Reference: Defending a Dual Theory of Natural Kind Concepts.Jussi Jylkkä - 2008 - Dissertation, University of Turku
    In this thesis I argue that the psychological study of concepts and categorisation, and the philosophical study of reference are deeply intertwined. I propose that semantic intuitions are a variety of categorisation judgements, determined by concepts, and that because of this, concepts determine reference. I defend a dual theory of natural kind concepts, according to which natural kind concepts have distinct semantic cores and non-semantic identification procedures. Drawing on psychological essentialism, I suggest that the cores consist of externalistic placeholder (...)
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  39. Theories of Epistemic Justification.Salah Ismail - 2000 - Arab Journal for the Humanities 18 (69):110-151.
    Knowledge is not only true belief, because some true beliefs are supported by lucky guesswork and hence do not describe knowledge. Knowledge requires possession of good reasons that elevates a true belief to the status of knowledge. This is justification condition. However, this concept of knowledge has been disputed by Gettier and requires modification. Some philosophers say that we must add the condition that the complete justification that a man has for what he believes must not depend on any false (...)
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  40. Law-Abiding Causal Decision Theory.Timothy Luke Williamson & Alexander Sandgren - 2023 - British Journal for the Philosophy of Science 74 (4):899-920.
    In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard (...)
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  41. An argument against causal decision theory.Jack Spencer - 2021 - Analysis 81 (1):52-61.
    This paper develops an argument against causal decision theory. I formulate a principle of preference, which I call the Guaranteed Principle. I argue that the preferences of rational agents satisfy the Guaranteed Principle, that the preferences of agents who embody causal decision theory do not, and hence that causal decision theory is false.
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  42. The Asymmetric Nature of Time.Vincent Grandjean - 2022 - Springer Nature.
    This open access monograph offers a detailed study and a systematic defense of a key intuition we typically have, as human beings, with respect to the nature of time: the intuition that the future is open, whereas the past is fixed. For example, whereas it seems unsettled whether there will be a fourth world war, it is settled that there was a first world war. -/- The book contributes, in particular, three major and original insights. First, it provides a coherent, (...)
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  43. Modal set theory.Christopher Menzel - 2018 - In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality. New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
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  44. Explanation in Descriptive Set Theory.Carolin Antos & Mark Colyvan - forthcoming - In Alastair Wilson & Katie Robertson (eds.), Levels of Explanation. Oxford University Press.
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  45. A foundation for causal decision theory.Brad Armendt - 1986 - Topoi 5 (1):3-19.
    The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already been given. (...)
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  46. Nonstandard set theories and information management.Varol Akman & Mujdat Pakkan - 1996 - Journal of Intelligent Information Systems 6:5-31.
    The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed.
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  47. Set Theory, Topology, and the Possibility of Junky Worlds.Thomas Mormann - 2014 - Notre Dame Journal of Formal Logic 55 (1): 79 - 90.
    A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...)
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  48. Set theory INC# based on intuitionistic logic with restricted modus ponens rule.Jaykov Foukzon (ed.) - 2021 - AP LAMBERT Academic Publishing (June 23, 2021).
    In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality. Similar results for paraconsistent set theories were obtained in author papers [13]-[16].
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  49.  66
    The Essences of Objects: Explicating a Theory of Essence in Object-Oriented Ontology.Stanford Howdyshell - 2020 - Open Philosophy 3 (1):01-10.
    In this paper, I will discuss the need for a theory of essences within Object-Oriented Ontology (OOO) and then formulate one. I will do so by drawing on Graham Harman’s work on OOO and Martin Heidegger’s thought on the essence of being, presented in his Introduction to Metaphysics. Harman touches on essences, describing them as the tension between a withdrawn object and its withdrawn qualities, but fails to distinguish between essential and inessential qualities within this framework. To fill in (...)
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  50. Set Theory INC# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper inductive definitions.Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (4):22.
    In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.
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