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Against Pointillisme about Geometry

In Friedrich Stadler & Michael Stöltzner (eds.), Time and History: Proceedings of the 28. International Ludwig Wittgenstein Symposium, Kirchberg Am Wechsel, Austria 2005. Frankfurt, Germany: De Gruyter. pp. 181-222 (2006)

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  1. (1 other version)Gunk, Topology and Measure.Frank Arntzenius - 2008 - Oxford Studies in Metaphysics 4.
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  • On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
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  • Falling cats, parallel parking, and polarized light.Robert W. Batterman - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (4):527-557.
    This paper addresses issues surrounding the concept of geometric phase or "anholonomy". Certain physical phenomena apparently require for their explanation and understanding, reference to toplogocial/geometric features of some abstract space of parameters. These issues are related to the question of how gauge structures are to be interpreted and whether or not the debate over their "reality" is really going to be fruitful.
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  • On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
    This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.
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  • (2 other versions)Philosophical Papers, Volume II.David Lewis - 1986 - New York, US: Oxford University Press.
    A collection of 13 papers by David Lewis, written on a variety of topics including causation, counterfactuals and indicative conditionals, the direction of time, subjective and objective probability, explanation, perception, free will, and rational decision. The conclusions reached include the claim that time travel is possible, that counterfactual dependence is asymmetrical, that events are properties of spatiotemporal regions, that the Prisoners’ Dilemma is a Newcomb problem, and that causation can be analyzed in terms of counterfactual dependence between events. These papers (...)
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  • Humean Supervenience Debugged.David Lewis - 1994 - Mind 103 (412):473--490.
    Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...)
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  • On the emergence of time in quantum gravity.Jeremy Butterfield & Chris Isham - 1999 - In The Arguments of Time. New York: Oup/British Academy. pp. 111--168.
    We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...)
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  • Spacetime and the philosophical challenge of quantum gravity.Jeremy Butterfield & Chris Isham - 2001 - In Jeremy Butterfield & Chris Isham (eds.), Physics Meets Philosophy at the Panck Scale. Cambridge University Press.
    We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...)
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  • Extrinsic properties.David Lewis - 1983 - Philosophical Studies 44 (2):197-200.
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  • Against pointillisme about mechanics.Jeremy Butterfield - 2006 - British Journal for the Philosophy of Science 57 (4):709-753.
    This paper forms part of a wider campaign: to deny pointillisme, the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. (...)
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  • On natural properties in metaphysics.Barry Taylor - 1993 - Mind 102 (405):81-100.
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  • Four Dimensionalism.Theodore Sider - 1997 - Philosophical Review 106 (2):197-231.
    Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...)
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  • Matter, motion, and Humean supervenience.Denis Robinson - 1989 - Australasian Journal of Philosophy 67 (4):394 – 409.
    This paper examines a doctrine which David Lewis has called 'Humean Supervenience' (hereafter 'HS'), and a problem which certain imaginary cases seem to generate for HS. They include rotating perfect spheres or discs, and flowing rivers, imagined as composed of matter which is perfectly homogeneous right down to the individual points. Before considering these examples, I shall introduce the doctrine they seem to challenge.
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  • Against quidditism.Robert Black - 2000 - Australasian Journal of Philosophy 78 (1):87 – 104.
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  • (1 other version)New work for a theory of universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
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  • (1 other version)New Work For a Theory of Universals.David Lewis - 1997 - In David Hugh Mellor & Alex Oliver (eds.), Properties. New York: Oxford University Press.
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  • A Primer of Infinitesimal Analysis.John Lane Bell - 1998 - Cambridge University Press.
    This is the first elementary book to employ the concept of infinitesimals.
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  • "Humean" Supervenience?G. Oppy - 2000 - Philosophical Studies 101 (1):77-105.
    As with many aspects of David Lewis’s work, it is hard to provide a better summary of his views than he provided himself. So the following introduction to what the Humean Supervenience view is will follow the opening pages of Lewis (1994a) extremely closely. But for those readers who haven’t read that paper, here’s the nickel version.
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  • Philosophy of mathematics and mathematical practice in the seventeenth century.Paolo Mancosu (ed.) - 1996 - New York: Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
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  • (1 other version)Gunk, Topology and Measure.Frank Arntzenius - 2008 - In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press UK.
    I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.
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  • (1 other version)Intrinsic properties defined.Peter Vallentyne - 1997 - Philosophical Studies 88 (2): 209-219.
    Intuitively, a property is intrinsic just in case a thing’s having it (at a time) depends only on what that thing is like (at that time), and not on what any wholly distinct contingent object (or wholly distinct time) is like. A property is extrinsic just in case it is non-intrinsic. Redness and squareness are intrinsic properties. Being next to a red object is extrinsic.
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  • (1 other version)Intrinsic vs. extrinsic properties.Dan Marshall & Brian Weatherson - 2013 - Stanford Encyclopedia of Philosophy.
    We have some of our properties purely in virtue of the way we are. (Our mass is an example.) We have other properties in virtue of the way we interact with the world. (Our weight is an example.) The former are the intrinsic properties, the latter are the extrinsic properties. This seems to be an intuitive enough distinction to grasp, and hence the intuitive distinction has made its way into many discussions in philosophy, including discussions in ethics, philosophy of mind, (...)
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  • Quantum mechanics does not require the continuity of space.E. B. Davies - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (2):319-328.
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  • Leibniz.Richard Arthur - 2014 - Malden, MA, USA: Polity.
    Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...)
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  • (1 other version)Against Pointillisme: a call to arms.Jeremy Butterfield - 2011 - In Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation. Springer. pp. 347--365.
    This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: (...)
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  • Gunk and Continuous Variation.Frank Arntzenius & John Hawthorne - 2005 - The Monist 88 (4):441-465.
    Let us say that a thing is gunky just in case every part of that thing has proper parts. The idea that all physical objects are gunky seems sufficiently sweeping, interesting, and plausible that it is worth examining. However, there is a difficulty. The features of an extended object can surely vary continuously. If an object is gunky then it cannot have point-sized parts which have no further parts. But how can one conceive of a continuous variation in features other (...)
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  • On the persistence of homogeneous matter.Jeremy Butterfield - unknown
    Some recent philosophical debate about persistence has focussed on an argument against perdurantism that discusses rotating perfectly homogeneous discs. The argument has been mostly discussed by metaphysicians, though it appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. After introducing the argument and emphasizing the relevance of physics, I review some metaphysicians' replies to the argument, especially those by Callender, Lewis, Robinson and Sider. Thereafter, I argue (...)
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  • Energy Conservation in GTR.Carl Hoefer - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (2):187-199.
    The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither (...)
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  • Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
    Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...)
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  • The rotating discs argument defeated.Jeremy Butterfield - 2006 - British Journal for the Philosophy of Science 57 (1):1-45.
    The rotating discs argument against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ‘imagine away’ the dynamical effects of rotation. The second is that in general relativity, (...)
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  • Temporal parts and supervenient causation: The incompatibility of two Humean doctrines.Dean W. Zimmerman - 1998 - Australasian Journal of Philosophy 76 (2):265 – 288.
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  • Understanding electromagnetism.Gordon Belot - 1998 - British Journal for the Philosophy of Science 49 (4):531-555.
    It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.
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  • Grit or Gunk.Peter Forrest - 2004 - The Monist 87 (3):351-370.
    This paper concerns the structure of any spatially extended things, including regions of space or spacetime. I shall use intuitions about the quantity of extended things to argue for a dichotomy: either a given finite extended thing is point-free gunk, that is, it has no points as parts, or it is made of grit, that is there are only finitely many points.
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  • Contact with the Nomic.John T. Roberts - 2005 - Philosophy and Phenomenological Research 71 (1):1-22.
    This is the first part of a two-part article in which we defend the thesis of Humean Supervenience about Laws of Nature (HS). According to this thesis, two possible worlds cannot differ on what is a law of nature unless they also differ on the Humean base. The Humean base is easy to characterize intuitively, but there is no consensus on how, precisely, it should be defined. Here in Part I, we present and motivate a characteriza- tion of the Humean (...)
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  • The Fabric of Space: Intrinsic vs. Extrinsic Distance Relations.Phillip Bricker - 1993 - Midwest Studies in Philosophy 18 (1):271-294.
    In this chapter, I evaluate various conceptions of distance. Of the two most prominent, one takes distance relations to be intrinsic, the other extrinsic. I recommend pluralism: different conceptions can peacefully coexist as long as each holds sway over a distinct region of logical space. But when one asks which conception holds sway at the actual world, one conception stands out. It is the conception of distance embodied in differential geometry, what I call the Gaussian conception. On this conception, all (...)
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  • Defining sets as sets of points of spaces.Colin McLarty - 1988 - Journal of Philosophical Logic 17 (1):75 - 90.
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  • Nonclassical Mereology and Its Application to Sets.Peter Forrest - 2002 - Notre Dame Journal of Formal Logic 43 (2):79-94.
    Part One of this paper is a case against classical mereology and for Heyting mereology. This case proceeds by first undermining the appeal of classical mereology and then showing how it fails to cohere with our intuitions about a measure of quantity. Part Two shows how Heyting mereology provides an account of sets and classes without resort to any nonmereological primitive.
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  • Region-based topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
    A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...)
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  • Logical Atoms and Combinatorial Possibility.Brian Skyrms - 1993 - Journal of Philosophy 90 (5):219-232.
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  • On the Persistence of Particles.Jeremy Butterfield - 2004 - Foundations of Physics 35 (2):233-269.
    This paper is about the metaphysical debate whether objects persist over time by the selfsame object existing at different times (nowadays called “endurance” by metaphysicians), or by different temporal parts, or stages, existing at different times (called “perdurance”). I aim to illuminate the debate by using some elementary kinematics and real analysis: resources which metaphysicians have, surprisingly, not availed themselves of. There are two main results, which are of interest to both endurantists and perdurantists. (1) I describe a precise formal (...)
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  • Zimmerman and the spinning sphere.David Lewis - 1999 - Australasian Journal of Philosophy 77 (2):209 – 212.
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  • (2 other versions)Contact with the nomic: A challenge for deniers of Humean supervenience about laws of nature.John Roberts - manuscript
    This is the first part of a two-part article in which we defend the thesis of Humean Supervenience about Laws of Nature (HS). According to this thesis, two possible worlds cannot differ on what is a law of nature unless they also differ on the Humean base. The Humean base is easily to characterize intuitively, but there is no consensus on how, precisely, it should be defined. Here in Part I, we present and motivate a characterization of the Humean base (...)
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  • (1 other version)Philosophical Papers, Volume II.Frank Jackson - 1989 - Journal of Philosophy 86 (8):433-437.
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  • (1 other version)Against Pointillisme: a Call to Arms.Jeremy Butterfield - unknown
    This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: (...)
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  • Quantity in Lewisian Metaphysics.John Hawthorne - 2006 - In Metaphysical essays. New York: Clarendon Press. pp. 229-237.
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