Metaphysical Underdetermination: Why Worry?

Metaphysical Underdetermination: Why Worry? Steven French Dept. of Philosophy University of Leeds s.r.d.french@leeds.ac.uk

Acknowledgments Thanks 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 I’m about to say!)

Van Fraassen’s Challenge • ‘The 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 Underdetermination • Underdetermination via possible alternative theories • Weldon’s non-Mendelian genetics • G. Radick,, “Other Histories, Other Biologies”, Royal Institute of Philosophy Supplements, 80 pp. 3-4, 2005 • Problems: evidence & conceivability • S. French, ‘Genuine Possibilities in the Scientific Past and How to Spot Them’, forthcoming in Isis, special issue. • ‘Problem of Unconceived Alternatives’ • K. Stanford, Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives, OUP, 2006. • Problems: discovery & heuristics

‘Jones’ Underdetermination • Realism ‘… 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’ Underdetermination • Consider undergraduate education in classical mechanics • Different sets of world-furniture  different ontological commitments • E.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. 691-697 • physics 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 Mechanics • Hamiltonian equations: q. = ∂H/∂p p. = ∂H/∂q • Obtained from Newton’s equations • Hamiltonian represents total energy of system and encodes dynamical content • Underlying structure: cotangent bundle

Lagrangian • Lagrangian equations: d/dt (∂L/∂q.) = ∂L/∂q • Reduce to Newton’s equations • Underlying structure: tangent bundle • Applying Legendre transformation to Lagrangian, yields Hamiltonian

(Brief) Comparison • Content of Newton’s equations encoded in structures defined over certain spaces • Hamiltonian: space = space of initial data for equations = space of possible instantaneous allowable states • Lagrangian: space = space of solutions to equations = space of allowable possible worlds G. Belot, ‘The Representation of Time and Change in Mechanics’, in J. Butterfield and J. Earman (eds.), Handbook of Philosophy of Physics, North-Holland, 2006.

Pooley’s Concerns • On ‘most straightforward characterisations of structure’ (e.g. set-theoretic) different formulations  different structures • Inter-relation between formulations not enough • ‘single, unifying framework’ needed which can be interpreted as corresponding more faithfully to reality than alternatives • Underdetermination may be broken • via heuristic fruitfulness O. 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

Responses • Distinguish 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 Breaking1 • Lagrangian: configuration space with (Riemannian) metric structure • Hamiltonian: phase space has symplectic structure • Distance measure vs. volume element • More structure vs. less • Symplectic structure is sufficient J. North, ‘The “Structure” of Physics: A Case Study’, forthcoming in Philosophy of Science

The Structure of the World is… • ‘I 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 Structure • ‘Take 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 Structure • Structure of world = symplectic structure • momentum becomes fundamental property • Crucial step: reject surplus, ‘superfluous’ structure • Concern: heuristic fruitfulness of surplus structure • Lagrangian and field theories D. Wallace, ‘In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory’, Synthese 151, 2006, pp. 33-80.

Commonalities • Common 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 structure—these 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 Structure • Example: electron • structure given by Hamiltonian or Lagrangian formulation of electron theory • evidence for structure via ‘historically stable properties’ J. 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 structure • Dynamical structure encoded not just in invariants of relevant groups, but also in spaces that carry representations of groups • Example: dynamics of Y-M theories encoded not just in invariants (twistors) but in geometric structures defined over projective carrying space • Contra French (boo!) J. Bain, ‘Toward Structural Realism’ preprint.

Metaphysical Underdetermination • Implications 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 objects • e.g. substance vs bundle • Realist not expected to resolve this A. Chakravartty, ‘The Structuralist Conception of Objects’, Philosophy of Science 70 (2003) pp. 867-878

You Should Worry (if you’re a realist!) • Metaphysical underdetermination in QM more problematic • everyday objects: non-structural access and distinguishability  objecthood unproblematic • quantum ‘objects’: structural access and indistinguishability  objecthood problematic • cf £ in bank vs. £ in pocket

Underdetermination breaking2 • Particle-as-individuals  haecceity, primitive thisness … • Weak discernibility  ‘thin’ individuality • Role of metaphysics again • structural identity; cf. North S. Saunders, ‘Are quantum particles objects?’, Analysis 66 (2006), pp. 52-63 • Particle-as-non-individuals meshes with QFT • Heuristic fruitfulness again

Underdetermination breaking2 cont. • Particle-as-individuals  inaccessible states • Surplus structure again M. Redhead, and P. Teller, ‘Particles, Particle Labels, and Quanta: the Toll of Unacknowledged Metaphysics’, Foundations of Physics 21 (1991) pp. 43-62 M. 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. 201-218 • Problem: heuristic fruitfulness of surplus structure (eg parastatistics, anyons etc.)

Commonalities • Relevant 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 structures • Presenting objects and representing structure K. Brading, and E. Landry, ‘Scientific Structuralism: Presentation and Representation’, Philosophy of Science 73 (2006), pp. 571–581

Conclusion • The role of surplus structure in breaking or supporting underdetermination • problematic as methodological principle • The role of heuristic fruitfulness in breaking or supporting underdetermination • problematic as guide to truth • The role of metaphysics in breaking or supporting underdetermination • problematic for realist (?)

Structuralist Lessons • Underdetermination  focus on ‘essential structure’ • Essential structure = object structures + dynamical structures {state space, dynamics, symmetries} (Bain, p. 24; motivated by Ruetsche, L. (2002), 'Interpreting Quantum Theories', in P. Machamer and M. Silberstein (eds.), The Blackwell Guide to the Philosophy of Science, Malden: Blackwell, pp. 199-226.)

Metaphysical Underdetermination: Why Worry?