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.)