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Metaphysical Underdetermination: Why Worry?

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Metaphysical Underdetermination: Why Worry?. Steven French Dept. of Philosophy University of Leeds [email protected] Acknowledgments. Thanks to members of the Structuralism Reading Group: Angelo Cei, Laura Crosilla, Kerry MacKenzie and Juha Saatsi - PowerPoint PPT Presentation
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  • Metaphysical Underdetermination: Why Worry?Steven FrenchDept. of PhilosophyUniversity of [email protected]

  • AcknowledgmentsThanks to members of the Structuralism Reading Group: Angelo Cei, Laura Crosilla, Kerry MacKenzie and Juha Saatsi(but of course, they are in no way to be held responsible for what Im about to say!)

  • Van Fraassens ChallengeThe phenomena underdetermine the theory. There are in principle alternative developments of science, branching off from ours at every point in history with equal adequacy as models of the phenomena. Only angels could know these alternative sciences, though sometimes we dimly perceive their possibility. The theory in turn underdetermines the interpretation. Each scientific theory, caught in the amber at one definite historical stage of development and formalization, admits many different tenable interpretations. What is the world depicted by science? That is exactly the question we answer with an interpretation and the answer is not unique. (B. Van Fraassen, Quantum Mechanics: An Empiricist View, OUP 1989)

  • Kinds of Underdetermination Modal Underdetermination

    Jones Underdetermination

    Metaphysical Underdetermination

  • Modal UnderdeterminationUnderdetermination via possible alternative theoriesWeldons non-Mendelian genetics G. Radick,, Other Histories, Other Biologies, Royal Institute of Philosophy Supplements, 80 pp. 3-4, 2005Problems: evidence & conceivabilityS. French, Genuine Possibilities in the Scientific Past and How to Spot Them, forthcoming in Isis, special issue.Problem of Unconceived AlternativesK. Stanford, Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives, OUP, 2006.Problems: discovery & heuristics

  • Jones UnderdeterminationRealism envisions mature science as populating the world with a clearly defined and described set of objects, properties, and processes, and progressing by steady refinement of the descriptions and consequent clarification of the referential taxonomy to a full-blown correspondence with the natural order. (p. 186)

    R. Jones, Realism About What?, Philosophy of Science 58 (1991) pp. 185-202.

  • Jones UnderdeterminationConsider undergraduate education in classical mechanicsDifferent sets of world-furniture different ontological commitmentsE.g.: Hamiltonian vs. Lagrangian formulations

  • Response: Appeal to Metaphysics physics has to look to metaphysics to help decide (fallibly, of course) between experimentally undecidable alternatives. (p. 696)A. Musgrave, Discussion: Realism About What?, Philosophy of Science 59 (1992) pp. 691-697physics is continuous with metaphysics (cf. Principle of Naturalistic Closure, J. Ladyman and D. Ross, Everything Must Go, OUP 2007)metaphysics mere philosophical whim and prejudice

  • Hamiltonian MechanicsHamiltonian equations:q. = H/p

    p. = H/q

    Obtained from Newtons equationsHamiltonian represents total energy of system and encodes dynamical contentUnderlying structure: cotangent bundle

  • LagrangianLagrangian equations:d/dt (L/q.) = L/qReduce to Newtons equationsUnderlying structure: tangent bundleApplying Legendre transformation to Lagrangian, yields Hamiltonian

  • (Brief) ComparisonContent of Newtons equations encoded in structures defined over certain spaces Hamiltonian: space = space of initial data for equations = space of possible instantaneous allowable statesLagrangian: space = space of solutions to equations = space of allowable possible worldsG. Belot, The Representation of Time and Change in Mechanics, in J. Butterfield and J. Earman (eds.), Handbook of Philosophy of Physics, North-Holland, 2006.

  • Pooleys ConcernsOn most straightforward characterisations of structure (e.g. set-theoretic) different formulations different structuresInter-relation between formulations not enoughsingle, unifying framework needed which can be interpreted as corresponding more faithfully to reality than alternativesUnderdetermination may be brokenvia heuristic fruitfulnessO. Pooley, Points, Particles and Structural Realism, in D. Rickles, S. French and J. Saatsi (eds.), Structural Foundations of Quantum Gravity, OUP 2006, pp. 83-120

  • ResponsesDistinguish between representation and characterisation of structure (see French, Banff & Paris talks)Single, unifying framework revealed by moving to underlying structure (see later)Is heuristic fruitfulness sufficient to break underdetermination?Now: promissory note (future breaking)Subsequently: different theory (retrospective breaking)

  • Underdetermination Breaking1Lagrangian: configuration space with (Riemannian) metric structureHamiltonian: phase space has symplectic structureDistance measure vs. volume elementMore structure vs. lessSymplectic structure is sufficient

    J. North, The Structure of Physics: A Case Study, forthcoming in Philosophy of Science

  • The Structure of the World isI think modern physics suggests that realism about scientific theories is just structural realism: realism about structure. Modern geometric formulations of the physics suggest that there is such a thing as the fundamental stucture of the world, represented by the structure of its fundamental physics. There is an objective fact about what structure exists, there is a privileged carving of natures at its joints, along the lines of its fundamental physical structure. (North, pp. 27-28)

  • Phase space StructureTake the mathematical formulation of a given theory. Figure out what structure is required by that formulation. This will be given by the dynamical laws and their invariant quantities (and perhaps other geometric or topological constraints). Make sure there is no other formulation getting away with less structure. Infer that this is the fundamental structure of the theory. Go on to infer that this is the fundamental structure of the world, according to the theory. (North, p. 24)

  • or More Precisely, Symplectic StructureStructure of world = symplectic structuremomentum becomes fundamental propertyCrucial step: reject surplus, superfluous structureConcern: heuristic fruitfulness of surplus structureLagrangian and field theoriesD. Wallace, In Defence of Naivet: The Conceptual Status of Lagrangian Quantum Field Theory, Synthese 151, 2006, pp. 33-80.

  • CommonalitiesCommon structures:It is a fact of primary importance that for well behaved theories the space of initial data and the space of solutions share a common geometric structurethese spaces are isomorphic as symplectic manifolds. (Belot, p. 17)solutions mapped to initial data(actions of groups implementing time translation (Lag) and time evolution (Ham) intertwined)

  • The Structure of the World is Dynamical StructureExample: electronstructure given by Hamiltonian or Lagrangian formulation of electron theoryevidence for structure via historically stable propertiesJ. Bain, and J. D. Norton, 'What Should Philosophers of Science Learn from the History of the Electron?', in Buchwald, J. and A. Warwick (eds.), Histories of the Electron: The Birth of Microphysics, Cambridge: MIT Press, (2001), pp. 451-465.

  • Dynamical structure Group structureDynamical structure encoded not just in invariants of relevant groups, but also in spaces that carry representations of groupsExample: dynamics of Y-M theories encoded not just in invariants (twistors) but in geometric structures defined over projective carrying spaceContra French (boo!)J. Bain, Toward Structural Realism preprint.

  • Metaphysical UnderdeterminationImplications of quantum physics:Non-individual objects (described via quasi-set theory)Individual objects (subject to state accessibility constraints)Challenge to realism?Object-Oriented Realism (Psillos)

  • Why worry?Metaphysical underdetermination wrt everyday objectse.g. substance vs bundleRealist not expected to resolve thisA. Chakravartty, The Structuralist Conception of Objects, Philosophy of Science 70 (2003) pp. 867-878

  • You Should Worry (if youre a realist!)Metaphysical underdetermination in QM more problematiceveryday objects: non-structural access and distinguishability objecthood unproblematicquantum objects: structural access and indistinguishability objecthood problematiccf in bank vs. in pocket

  • Underdetermination breaking2Particle-as-individuals haecceity, primitive thisness Weak discernibility thin individualityRole of metaphysics againstructural identity; cf. NorthS. Saunders, Are quantum particles objects?, Analysis 66 (2006), pp. 52-63Particle-as-non-individuals meshes with QFTHeuristic fruitfulness again

  • Underdetermination breaking2 cont.Particle-as-individuals inaccessible statesSurplus structure againM. Redhead, and P. Teller, Particles, Particle Labels, and Quanta: the Toll of Unacknowledged Metaphysics, Foundations of Physics 21 (1991) pp. 43-62M. Redhead, and P. Teller,Particle Labels and the Theory of Indistinguishable Particles in Quantum Mechanics, British Journal for the Philosophy of Science 43 (1992) pp. 201-218Problem: heuristic fruitfulness of surplus structure (eg parastatistics, anyons etc.)

  • CommonalitiesRelevant structure = group-theoretical French, S. (1999). Models and mathematics in physics: The role of group theory. In J. Butterfield and C. Pagonis, eds., From Physics to Philosophy, pp. 187-207. Cambridge: Cambridge University Press.Object structures vs. dynamical structuresPresenting objects and representing structureK. Brading, and E. Landry, Scientific Structuralism: Presentation and Representation, Philosophy of Science 73 (2006), pp. 571581

  • ConclusionThe role of surplus structure in breaking or supporting underdeterminationproblematic as methodological princ

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