Metaphysical Underdetermination: Why Worry

1
Metaphysical Underdetermination Why Worry?

• Steven French
• Dept. of Philosophy
• University of Leeds
• s.r.d.french_at_leeds.ac.uk

2
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 Im about to say!)

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Van Fraassens 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)

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Kinds of Underdetermination

• Modal Underdetermination
• Jones Underdetermination
• Metaphysical Underdetermination

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Modal Underdetermination

• Underdetermination via possible alternative
  theories
  
• Weldons 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

6
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.

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Jones Underdetermination

• Consider undergraduate education in classical
  mechanics
  
• Different sets of world-furniture ? different
  ontological commitments
  
• E.g. Hamiltonian vs. Lagrangian formulations

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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

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Hamiltonian Mechanics

• Hamiltonian equations
• q. ?H/?p
• p. ?H/?q
• Obtained from Newtons equations
• Hamiltonian represents total energy of system and
  encodes dynamical content
  
• Underlying structure cotangent bundle

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Lagrangian

• Lagrangian equations
• d/dt (?L/?q.) ?L/?q
• Reduce to Newtons equations
• Underlying structure tangent bundle
• Applying Legendre transformation to Lagrangian,
  yields Hamiltonian

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(Brief) Comparison

• Content of Newtons 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.

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Pooleys 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

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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)

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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

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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)

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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)

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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.

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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 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)
  

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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.

20
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.

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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)

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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

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You Should Worry (if youre 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

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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

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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.)

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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. 571581

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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 (?)

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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.)