Results for 'four‐dimensionalism'

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  1. Four-Dimensionalism, Evil, and Christian Belief.Ryan Mullins - 2014 - Philosophia Christi 16 (1):117-137.
    Four-dimensionalism and eternalism are theories on time, change, and persistence. Christian philosophers and theologians have adopted four-dimensional eternalism for various reasons. In this paper I shall attempt to argue that four-dimensional eternalism conflicts with Christian thought. Section I will lay out two varieties of four-dimensionalism—perdurantism and stage theory—along with the typically associated ontologies of time of eternalism and growing block. I shall contrast this with presentism and endurantism. Section II will look at some of the purported theological benefits of adopting (...)
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  2. Why Four-Dimensionalism Explains Coincidence.Maya Eddon - 2010 - Australasian Journal of Philosophy 88 (4):721-728.
    In "Does Four-Dimensionalism Explain Coincidence" Mark Moyer argues that there is no reason to prefer the four-dimensionalist (or perdurantist) explanation of coincidence to the three-dimensionalist (or endurantist) explanation. I argue that Moyer's formulations of perdurantism and endurantism lead him to overlook the perdurantist's advantage. A more satisfactory formulation of these views reveals a puzzle of coincidence that Moyer does not consider, and the perdurantist's treatment of this puzzle is clearly preferable.
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  3. Ought a Four-Dimensionalist to Believe in Temporal Parts?Kristie Miller - 2009 - Canadian Journal of Philosophy 39 (4):pp. 619-646.
    This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...)
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  4. Ought a Four-Dimensionalist To Believe in Temporal Parts?Kristie Miller - 2009 - Canadian Journal of Philosophy 39 (4):619-646.
    This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...)
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  5. Why Counterpart Theory and Four-Dimensionalism Are Incompatible.Jim Stone - 2005 - Analysis 65 (4):329-333.
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  6. Critical Notice of Theodore Sider, Four Dimensionalism.Matthew Davidson - 2004 - Philosophical Books 45 (1):17-33.
    This is a critical notice of Theodore Sider's book, _Four-Dimensionalism_.
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  7.  37
    Four-Dimensionalism, Eternalism, and Deprivationist Accounts of the Evil of Death.Andrew Brenner - forthcoming - Synthese:1-18.
    Four-dimensionalists think that we persist over time by having different temporal parts at each of the times at which we exist. Eternalists think that all times are equally real. Deprivationists think that death is an evil for the one who dies because it deprives them of something. I argue that four-dimensionalist eternalism, conjoined with a standard deprivationist account of the evil of death, has surprising implications for what we should think about the evil of death. In particular, given these assumptions, (...)
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  8. Two Arguments From Sider’s Four-Dimensionalism. [REVIEW]Ned Markosian - 2004 - Philosophy and Phenomenological Research 68 (3):665–673.
    In this essay for a PPR book symposium on Theodore Sider's _Four-Dimensionalism<D>, I focus on two of Sider's arguments for four-dimensionalism: (i) his argument from vagueness, and (ii) his argument from time travel. Concerning (i), I first show that Sider's argument commits him to certain strange consequences that many four-dimensionalists may not endorse, and then I discuss an objection that involves appealing to 'brutal composition', the view that there is no informative answer to Peter van Inwagen's 'special composition question'. Concerning (...)
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  9.  38
    Persistence as a Four-Dimensionalist: Perdurantism Vs. Exdurantism.Richard Callais - forthcoming - Dialogue.
    The debate over persistence currently involves three competing theories—one three-dimensionalist theory called “endurantism” and two four-dimensionalist theories called “perdurantism” and “exdurantism.” This inner debate between the latter two persistence theories is what I aim to clarify, and ultimately, I argue that perdurantism is superior to exdurantism because exdurantism is too extravagant in counting ordinary objects in the world. Extravagant for the reason that objects in their entirety are bound to their momentary stages, and there is practically an interminable number of (...)
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  10. Reply to Stone on Counterpart Theory and Four-Dimensionalism.Antony Eagle - 2007 - Analysis 67 (2):159 - 162.
    Recently, Jim Stone has argued that counterpart theory is incompatible with the existence of temporal parts. I demonstrate that there is no such incompatibility.
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  11. Review of Four-Dimensionalism. [REVIEW]Josh Parsons - manuscript
    “The truth,” Quine says, “is that you can bathe in the same river twice, but not in the same river stage. You can bathe in two river stages which are stages of the same river, and this is what constitutes bathing in the same river twice. A river is a process through time, and the river stages are its momentary parts.” (Quine 1953, p. 65) Quine’s view is four-dimensionalism, and that is what Theodore Sider’s book is about. In Sider’s usage, (...)
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  12.  90
    No Hope in the Dark: Problems for Four-Dimensionalism.Jonathan J. Loose - 2019 - European Journal for Philosophy of Religion 11 (3):31-47.
    Whether or not it is coherent to place hope in a future life beyond the grave has become a central question in the larger debate about whether a materialist view of human persons can accommodate Christian belief. Hud Hudson defends a four-dimensional account of resurrection in order to avoid persistent difficulties experienced by three-dimensionalist animalism. I present two difficulties unique to Hudson’s view. The first problem of counterpart hope is a manifestation of a general weakness of four-dimensional views to accommodate (...)
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  13. The Limit Decision Problem and Four-Dimensionalism.Costa Damiano - 2017 - Vivarium 55 (1-3):199-216.
    I argue that medieval solutions to the limit decision problem imply four-dimensionalism, i.e. the view according to which substances that persist through time are extended through time as well as through space, and have different temporal parts at different times.
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  14. There is No Invariant, Four-Dimensional Stuff.Hans Halvorson - manuscript
    Some philosophers say that in special relativity, four-dimensional stuff is invariant in some sense that three-dimensional stuff is not. I show that this claim is false.
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  15. From Spacetime to Space and Time: A Reply to Markosian.Baptiste Le Bihan - 2020 - Analysis 80 (3):456-462.
    In a recent article, Ned Markosian gives an argument against four-dimensionalism understood as the view that time is one of four identical dimensions that constitute a single four-dimensional manifold. In this paper, I show that Markosian attacks a straw man as his argument targets a theory known to be false on empirical grounds. Four-dimensionalism rightly conceived in no way entails that time is identical to space. I then address two objections raised by Markosian against four-dimensionalism rightly conceived.
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  16. Sparse Parts.Kristie Miller - 2006 - Sorites 17:31-48.
    Four dimensionalism, the thesis that persisting objects are four dimensional and thus extended in time as well as space, has become a serious contender as an account of persistence. While many four dimensionalists are mereological universalists, there are those who find mereological universalism both counterintuitive and ontologically profligate. It would be nice then, if there was a coherent and plausible version of four dimensionalism that was non-universalist in nature. I argue that unfortunately there is not. By its very nature four (...)
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  17. Neo-Aristotelian Plenitude.Ross Inman - 2014 - Philosophical Studies 168 (3):583-597.
    Plenitude, roughly, the thesis that for any non-empty region of spacetime there is a material object that is exactly located at that region, is often thought to be part and parcel of the standard Lewisian package in the metaphysics of persistence. While the wedding of plentitude and Lewisian four-dimensionalism is a natural one indeed, there are a hand-full of dissenters who argue against the notion that Lewisian four-dimensionalism has exclusive rights to plentitude. These ‘promiscuous’ three-dimensionalists argue that a temporalized version (...)
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  18. A New Definition of Endurance.Kristie Miller - 2005 - Theoria 71 (4):309-332.
    In this paper I present a new definition of endurance. I argue that the three-dimensionalist ought to adopt a different understanding from the four-dimensionalist, of what it is to have a part simpliciter. With this new understanding it becomes possible to define endurance in a manner that both preserves the central endurantist intuitions, whilst avoiding commitment to any controversial metaphysical theses. Furthermore, since this endurantist definition is a mereological one, there is an elegant symmetry between the definitions of endurance and (...)
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  19. A Modal Bundle Theory.Jiri Benovsky - 2006 - Metaphysica 7 (2).
    If ordinary particulars are bundles of properties, and if properties are said to be universals, then three well-known objections arise : no particular can change, all particulars have all of their properties essentially (even the most insignificant ones), and there cannot be two numerically distinct but qualitatively indiscernible particulars. In this paper, I try to make a little headway on these issues and see how the objections can be met, if one accepts a certain view about persistence through time and (...)
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  20.  41
    An Argument for Dualism From the Lived Experience of Being in Space.Steven Merle Duncan - manuscript
    In a sequel to the author's argument for dualism from the lived experience of time, this paper continues the line of though initiated by in that study a bit further by considering the implications of our experience of being in space for dualism. I conclude that four-dimensionalism cannot accommodate the facts of our experience of ourselves as being in time - localized in space but not located there after the manner of a material thing. Substance dualism, however, makes perfect sense (...)
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  21. La natura e l'identità degli oggetti materiali.Achille C. Varzi - 2007 - In Annalisa Coliva (ed.), Filosofia analitica. Temi e problemi. Carocci Editore. pp. 17–56.
    A critical survey of the main metaphysical theories concerning the nature of material objects (substratum theories, bundle theories, substance theories, stuff theories) and their identity conditions, both synchronic (monist vs. pluralist theories) and diachronic (three-dimensionalism, four-dimensionalism, sequentialism).
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  22. Momentum and Context.Hans Halvorson - manuscript
    A sentence's meaning may depend on the state of motion of the speaker. I argue that this context-sensitivity blocks the inference from special relativity to four-dimensionalism.
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  23. B-Theory and Time Biases.Sayid Bnefsi - 2019 - In Patrick Blackburn, Per Hasle & Peter Øhrstrøm (eds.), Logic and Philosophy of Time: Further Themes from Prior. Aalborg, Denmark: Aalborg University Press. pp. 41-52.
    We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...)
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  24. 3D Cohabitation.Simon Langford - 2016 - Erkenntnis 81 (6):1195-1210.
    The cohabitation theory is a popular solution to the problem of personal fission. It affirms that all the people who result from fission were there cohabiting the pre-fission body all along. Adopting this solution is an uncontroversial move for four-dimensionalists, but is it open to three-dimensionalists too? Some have thought so, but Katherine Hawley, Mark Johnston, and Eric Olson have argued to the contrary. They claim three-dimensionalists simply cannot be cohabitation theorists. In this paper, I explain how they can.
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  25. Perdurantism, Fecklessness and the Veil of Ignorance.Michael Tze-Sung Longenecker - 2020 - Philosophical Studies 177 (9):2565-2576.
    There has been a growing charge that perdurantism—with its bloated ontology of very person-like objects that coincide persons—implies the repugnant conclusion that we are morally obliged to be feckless. I argue that this charge critically overlooks the epistemic situation—what I call the ‘veil of ignorance’—that perdurantists find themselves in. Though the veil of ignorance still requires an alteration of our commonsense understanding of the demands on action, I argue for two conclusions. The first is that the alteration that is required (...)
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  26. Classifying Processes: An Essay in Applied Ontology.Barry Smith - 2012 - Ratio 25 (4):463-488.
    We begin by describing recent developments in the burgeoning discipline of applied ontology, focusing especially on the ways ontologies are providing a means for the consistent representation of scientific data. We then introduce Basic Formal Ontology (BFO), a top-level ontology that is serving as domain-neutral framework for the development of lower level ontologies in many specialist disciplines, above all in biology and medicine. BFO is a bicategorial ontology, embracing both three-dimensionalist (continuant) and four-dimensionalist (occurrent) perspectives within a single framework. We (...)
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  27. Spatially-Rotated Paintings: A Reply to Markosian’s "Sideways Music".Shen-yi Liao - manuscript
    In “Sideways Music”, Ned Markosian uses aesthetic intuitions about temporally-rotated music to argue that the metaphysics of time is different from the metaphysics of space. In response, I use aesthetic intuitions about spatially-rotated paintings to pose a dilemma for Markosian’s argument: either he accepts the intuitions about spatially-rotated paintings, in which case he must give up on some assumptions in his argument, or he rejects intuitions about spatially-rotated paintings, in which case an analogous response can be given regarding intuitions about (...)
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  28. Fragmentalist Presentist Perdurantism.Samuele Iaquinto - 2019 - Philosophia 47 (3):693-703.
    Perdurantists think of continuants as mereological sums of stages from different times. This view of persistence would force us to drop the idea that there is genuine change in the world. By exploiting a presentist metaphysics, Brogaard proposed a theory, called presentist four-dimensionalism, that aims to reconcile perdurantism with the idea that things undergo real change. However, her proposal commits us to reject the idea that stages must exist in their entirety. Giving up the tenet that all the stages are (...)
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  29. Persistence of Simple Substances.Markku Keinänen & Jani Hakkarainen - 2010 - Metaphysica 11 (2):119-135.
    In this paper, we argue for a novel three-dimensionalist solution to the problem of persistence, i.e. cross-temporal identity. We restrict the discussion of persistence to simple substances, which do not have other substances as their parts. The account of simple substances employed in the paper is a trope-nominalist strong nuclear theory, which develops Peter Simons' trope nominalism. Regarding the distinction between three dimensionalism and four dimensionalism, we follow Michael Della Rocca's formulation, in which 3D explains persistence in virtue of same (...)
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  30. The Cornucopia of Formal-Ontological Relations.Barry Smith & Pierre Grenon - 2004 - Dialectica 58 (3):279–296.
    The paper presents a new method for generating typologies of formal-ontological relations. The guiding idea is that formal relations are those sorts of relations which hold between entities which are constituents of distinct ontologies. We provide examples of ontologies (in the spirit of Zemach’s classic “Four Ontologies” of 1970), and show how these can be used to give a rich typology of formal relations in a way which also throws light on the opposition between threeand four-dimensionalism.
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  31.  24
    Worm-Theoretic Persistence and Temporal Predication: A Reply to Johnston’s Personite Problem.Andrew Russo - forthcoming - Southwest Philosophy Review.
    Mark Johnston (2016, 2017) has raised concerns that a worm-theoretic account of persistence through time is incompatible with ethical singularity: that within the life of any actual person, there is only one morally considerable being, namely that person. To deny ethical singularity is to deny a core feature of our ordinary ethical and prudential thinking. The worm theory, Johnston concludes, proves to be “disastrous … for our ordinary moral outlook”. This paper defends the worm theory from Johnston’s argument. Though I (...)
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  32. Three Arguments From Temporary Intrinsics.M. Eddon - 2010 - Philosophy and Phenomenological Research 81 (3):605-619.
    The Argument from Temporary Intrinsics is one of the canonical arguments against endurantism. I show that the two standard ways of presenting the argument have limited force. I then present a new version of the argument, which provides a more promising articulation of the underlying objection to endurantism. However, the premises of this argument conflict with the gauge theories of particle physics, and so this version of the argument is no more successful than its predecessors. I conclude that no version (...)
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  33. Naturalistic Theories of Life After Death.Eric Steinhart - 2015 - Philosophy Compass 10 (2):145-158.
    After rejecting substance dualism, some naturalists embrace patternism. It states that persons are bodies and that bodies are material machines running abstract person programs. Following Aristotle, these person programs are souls. Patternists adopt four-dimensionalist theories of persistence: Bodies are 3D stages of 4D lives. Patternism permits at least six types of life after death. It permits quantum immortality, teleportation, salvation through advanced technology, promotion out of a simulated reality, computational monadology, and the revision theory of resurrection.
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  34.  54
    Identity and Spatio-Temporal Continuity.B. N. Langtry - 1972 - Australasian Journal of Philosophy 50 (2):184-189.
    This article considers recent arguments against the proposition that one and the same object cannot go out of existence and then come into existence again (so that, e.g., teleportation would involve change of identity.). It argues that these arguments can be evaded by adopting a four-dimensional ontology, according to which human beings, trees, etc., have temporal as well as spatial parts.
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  35. 3,5-Dimensionalismus und Überleben: ein prozess-ontologischer Ansatz.Godehard Brüntrup - 2010 - In Godehard Brüntrup, Matthias Rugel & Maria Schwartz (eds.), Auferstehung des Leibes - Unsterblichkeit der Seele. pp. 245-268.
    Paper on personal identity and the possibility of survival within a framework of a process-oriented metaphysics that combines elements of four-dimensionalism and three-dimensionalism.
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  36. In Light of the Theory of Special Relativity is a Passage of Time and the Argument of the Presentist Untenable?Mekhi Dhesi - 2016 - Dissertation, University College London
    In light of the Special Theory of Relativity and the Minkowski creation of ‘spacetime’, the universe is taken to be a four-dimensional entity which postulates bodies as existing within a temporally extended reality. The Special Theory of Relativity’s implications liken the nature of the universe to a ‘block’ within which all events coexist equally in spacetime. Such a view strikes against the very essence of presentism, which holds that all that exists is the instantaneous state of objects in the present (...)
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  37. An Argument for Dualism From the Lived Experience of Time.Steven Merle Duncan - manuscript
    Temporal passage is an irrefragable and ineliminable feature of our lived experience of time. In this essay, I argue that, regardless of whether one adopts a three-dimensional, A theory of time or a four-dimensional, B theory of time, the subject of lived experience of time has to be conceived of as something that stands outside of the physical order in order for the experience of temporal passage to actually occur. This implies the truth of Dualism as the only account of (...)
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  38. A Case for Stage View Presentism.Jorgen Hansen - manuscript
    Until recently, perdurantism has been considered to be incompatible with the presentist ontology of time. However, discussions about presentist theories of perdurance are now surfacing, one of the most prominent arguments for which being Berit Brogaard’s essay: “Presentist Four-Dimensionalism”. In this paper, I examine Brogaard’s argument in contrast to Ted Sider’s arguments for (an Eternalist theory of) the “Stage View”. I then argue for another (and, I think, novel) view of presentist perdurantism, which avoids the problematic consequences that Brogaard’s view (...)
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  39. Jonathan Edwards's Monism.Antonia LoLordo - 2017 - Philosophers' Imprint 17.
    The 18th-century American philosopher Jonathan Edwards argues that nothing endures through time. I analyze his argument, paying particular attention to a central principle it relies on, namely that “nothing can exert itself, or operate, when and where it is not existing”. I also consider what I supposed to follow from the conclusion that nothing endures. Edwards is sometimes read as the first four-dimensionalist. I argue that this is wrong. Edwards does not conclude that things persist by having different temporal parts; (...)
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  40. Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s.Frederique Janssen-Lauret - 2018 - In Walter Carnielli, Frederique Janssen-Lauret & William Pickering (eds.), The Significance of the New Logic. Cambridge: Cambridge University Press.
    As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...)
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  41.  92
    Becoming a Statue.Justin Mooney - forthcoming - Australasian Journal of Philosophy.
    One simple but relatively neglected solution to the notorious coincidence puzzle of the statue and the piece of clay claims that the property being a statue is a phase sortal property that the piece of clay instantiates temporarily. I defend this view against some standard objections by reinforcing it with a novel counterpart-theoretic account of identity under a sortal. This proposal does not require colocation, four-dimensionalism, eliminativism, deflationism, or unorthodox theses about classical identity.
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  42. Foreword to ''Temporal Parts''.Achille C. Varzi - 2000 - The Monist 83 (3):319-320.
    A brief introductory note to the Monist issue on "Temporal Parts", setting the background for the eight papers included in the rest of the issue (by Y. Balashov, B. Brogaard, K. Fine, M. Heller, R. LePoidevin, J. Parsons, P. M. Simons, and P. van Inwagen).
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  43. Two-Dimensionalism: A Neo-Fregean Interpretation.Manuel García-Carpintero - 2006 - In Manuel García-Carpintero & Josep Macià (eds.), Two-Dimensional Semantics. Oxford: Clarendon Press.
    The truth of a statement depends on the world in two ways: what the statement says is true if the world is as the statement says it is; on the other hand, what the expressions in the statement mean depends on what the world is like (for instance, on what conventions are in place). Each of these two kinds of dependence of truth on the world corresponds to one of the dimensions on the two-dimensional semantic framework, developed in the 1970’ (...)
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  44. Two-Dimensionalism and the Social Character of Meaning.Derek Ball - 2014 - Erkenntnis 79 (S3):567-595.
    This paper develops and critiques the two-dimensionalist account of mental content developed by David Chalmers. I first explain Chalmers's account and show that it resists some popular criticisms. I then argue that the main interest of two-dimensionalism lies in its accounts of cognitive significance and of the connection between conceivability and possibility. These accounts hinge on the claim that some thoughts have a primary intension that is necessarily true. In this respect, they are Carnapian, and subject to broadly Quinean attack. (...)
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  45. Extended Modal Dimensionalism.Martin Vacek - 2017 - Acta Analytica 32 (1):13-28.
    Modal dimensionalism is realism about spaces, times and worlds—metaphysical indices that make objects spatial, temporal and modal, respectively, and that play the role of alethic relativizers, i.e. items to which matters of truth are relativized. This paper examines several arguments against MD and shows that MD offers a feasible way to understand modal discourse.
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  46. Two-Dimensionalism and the Metaphysical Possibility of Zombies.Daniel Cohnitz - 2003 - In B. Löwe, W. Malzkorn & T. Räsch (eds.), Foundations of The Formal Sciences II. Applications of Mathematical Logic in Philosophy and Linguistics [Trends in Logic]. Kluwer Academic Publishers. pp. 55--62.
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  47. Four Questions of Iterated Grounding.David Mark Kovacs - 2020 - Philosophy and Phenomenological Research 101 (2):341-364.
    The Question of Iterated Grounding (QIG) asks what grounds the grounding facts. Although the question received a lot of attention in the past few years, it is usually discussed independently of another important issue: the connection between metaphysical explanation and the relation or relations that supposedly “back” it. I will show that once we get clear on the distinction between metaphysical explanation and the relation(s) backing it, we can distinguish no fewer than four questions lumped under QIG. I will also (...)
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  48. Four Pillars of Statisticalism.Denis M. Walsh, André Ariew & Mohan Matthen - 2017 - Philosophy, Theory, and Practice in Biology 9 (1):1-18.
    Over the past fifteen years there has been a considerable amount of debate concerning what theoretical population dynamic models tell us about the nature of natural selection and drift. On the causal interpretation, these models describe the causes of population change. On the statistical interpretation, the models of population dynamics models specify statistical parameters that explain, predict, and quantify changes in population structure, without identifying the causes of those changes. Selection and drift are part of a statistical description of population (...)
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  49. Four Meta-Methods for the Study of Qualia.Lok-Chi Chan & Andrew James Latham - 2019 - Erkenntnis 84 (1):145-167.
    In this paper, we describe four broad ‘meta-methods’ employed in scientific and philosophical research of qualia. These are the theory-centred metamethod, the property-centred meta-method, the argument-centred meta-method, and the event-centred meta-method. Broadly speaking, the theory-centred meta-method is interested in the role of qualia as some theoretical entities picked out by our folk psychological theories; the property-centred meta-method is interested in some metaphysical properties of qualia that we immediately observe through introspection ; the argument-centred meta-method is interested in the role of (...)
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  50. Four Tails Problems for Dynamical Collapse Theories.Kelvin J. McQueen - 2015 - Studies in the History and Philosophy of Modern Physics 49:10-18.
    The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...)
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