Is Structural Underdetermination Possible?
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Transcript of Is Structural Underdetermination Possible?
Is StructuralIs Structural
UnderdeterminationUnderdetermination
Possible?Possible?
Holger LyrePhilosophy DepartmentUniversity of Augsburg/Bonn
Theoretical Frameworks and Empirical Underdetermination
International Workshop, University of Düsseldorf,
April 10-12, 2008
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
OverviewOverview
1. The Thesis of Theory Underdetermination by Empirical Evidence (TUD)
2. Intermediate Structural Realism
3. Structural Underdetermination(and Mathematical Overdetermination)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Part 1:Part 1:
The Thesis of Theory UnderdeterminationThe Thesis of Theory Underdeterminationby Empirical Evidence (TUD)by Empirical Evidence (TUD)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
The TUD thesis and its „neighbors“The TUD thesis and its „neighbors“
Thesis of Theory Underdetermination (TUD)For any theory T and any body of observation O there exists another theory T‘, such that T and T‘ are empirically equivalent (but ontologically different).
main intuition behind TUD: „T>O“, theory exceeds observation
TUD-„neighbors“:Duhem-Quine holism (confirmational holism)Hume‘s problem of inductionConventionalism
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
TUD, Duhemian holism, inductionTUD, Duhemian holism, induction
Duhemian confirmational holism: no scientific hypothesis can be tested in isolation it is possible to adhere to a thesis (in the face of adverse
observations) by revising other theses theories can only be confirmed as a whole small gap to TUD: generate rivaling theories by readjusting
the total system of hypotheses BUT: even the total system is underdetermined by all
possible observationsInduction problem as „Humean underdetermination“: underdetermination of theory by past evidence BUT: underdetermination even in the case of all possible
(past and future) observations
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
TUD and the problem of missing examplesTUD and the problem of missing examples
Earman (1993): „Are there interesting cases of empirically indistinguishable theories?... Here I find the philosophical literature disappointing... [but] I claim ... That what we have is a shortcoming of the philosophical literature and not a failure of the underdetermination thesis.“
Is Earman right? Given the generality of the TUD thesis, the fact that there doesn‘t exist (many) „interesting“ examples is indeed a pressing problem for TUD!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Classes of TUD examplesClasses of TUD examples
Pathological cases
Cases of „epistemic TUD“
Conventionalism-borderline cases
History of science cases
Examples from factual, mature science...!?
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Pathological cases of TUDPathological cases of TUD
Consider a law G(X;t) = 0 versus G(X;t) + g(t) = 0,where g(t) = go(t) (t - t1) (t - t2) ...with arbitrary go(t) and measuring times ti.
„The world has been created ... just 5 minutes ago / ... in 7 days“ (creationism vs. evolution)
always possible, but not really `thrilling‘...
take notice of simplicity, economy, coherence...
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
„„Epistemic TUD“Epistemic TUD“
1. General boundaries of technical feasability in experiments (e.g. string energies?)
2. Glymour (1977) and Malament (1977) consider cosmologies where even idealized observers (who live forever) cannot decide about certain global topological features
BUT: As an anti-realistic argument we should be interested in „ontological TUD“
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Conventionalism-borderline casesConventionalism-borderline cases
Poincaré: space as infinite versus space as finite with suitably shrinking measuring rods
„Hollow earth“: inversion at
the sphere:r' = R2/r
with earth radius R
nice example for Duhemian holism: avert possibility to attack the theory by a `journey to the center of the earth‘ by introducing an additional „wrap around“-hypothesis
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Conventionalism-borderline cases (II)Conventionalism-borderline cases (II) rather a reconstrual of predicates:
convex picture concave picturestraight line circlepoint at infinite distance centercenter of earth point at infinite distance
Quine (1975): „[The] case ... due to Poincaré ... is less simple than the mere switch of ‚electron‘ and ‚molecule‘, but it presents no serious challenge. The two formulations are formulations, again, of a single theory.“
BUT: Poincaré and „hollow earth“ assume distinguished points
(center of earth and point of infinity)violation of the „Principle of Homogeneity of Space“Quine (1990): „...drastically unlike theory formulations“sufficient for „ontological difference“?
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
History of science examples of TUDHistory of science examples of TUD
1. TN: Newtonian mechanics and gravityH(v): hypothesis of absolute space
with center of mass velocity vTN+ H(v): infinitely many theories for v R
2. Lorentz‘ ether theory vs. Einstein‘s Special Relativity
BUT: in retrospect historic cases appear mainly as artefacts of incomplete scientific knowledge!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Examples from actual, mature science...?!Examples from actual, mature science...?!
Gauge Theories
Quantum Mechanics (part 3, briefly)
General Relativity (part 3)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Ontology of gauge theories (I)Ontology of gauge theories (I)
Explanation of gauge theoretic holonomy effects (e.g. Aharonov-
Bohm) by different entities and different locality assumptions:
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Locality assumptionsLocality assumptions
Point-like interactionInteracting entities can be defined within arbitrarily small spacetime regions (usually idealized as spacetime points), couple to each other in that regions and are non-zero in overlapping regions.
Local actionAll causes of an event propagate via some continuous physical processes.
SeparabilityGiven a physical system S and its exhaustive, disjoint decomposition into spatiotemporally divided subsystems, it is possible to retrieve the properties of S from the properties of these subsystems.
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Ontology of gauge theories (II)Ontology of gauge theories (II)
Interference shift of AB effect by Stokes formula:
Potentials Field strengths Holonomies
Point-like int. yes no no
Local action yes no yes
Separability no yes no
Measurability no yes yes
Good example of TUD in mature science? Perhaps… …BUT: Holonomy view is presumably the most coherent one with
the biggest potential for further developments...
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Conclusion part 1: lots of problems with TUDConclusion part 1: lots of problems with TUD
it’s quite doubtful that the problem of missing TUD examples is a mere „... shortcoming of the philosophical literature“ (Earman) – it rather strongly undermines the plausibility of TUD itself!
The rare TUD cases in the actual practice of science may rather be considered artefacts of incomplete knowledge! as such they could be used as an indication of open
scientific problems! The TUD thesis is at best a highly speculative thesis with a
pressing problem of missing examples!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Part 2: Intermediate Structural RealismPart 2: Intermediate Structural Realism
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
What is a “structure”?What is a “structure”?“Define a system to be a collection of objects with certain
relations among them. [...] Define a pattern or structure to be the abstract form of the system, highlighting the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.”
Shapiro (2000)
Working definition: structures as domains (= sets of objects) with sets of relations imposed on them:
set a = {a1, a2, ...an} of n objects ai and arbitrary k-ary
relations R(a), then structure ∑ = a,R(a) Structural realism (SR): roughly the view that we should be
committed in the structural rather than object-like content of our mature scientific theories
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
SR-views about structureSR-views about structure
Epistemic SR:There are relations and (maybe) relata, but we have epistemic access to relations only
Ontic SR:non-eliminative (moderate) OSR:
There are relations and relata, but there is nothing more to the relata than the relations in which they stand
eliminative OSR:There are only relations and no relata
Note: The widely debated question whether the slogan „structures is all there is“ leads to the problem of “relations without relata” doesn’t depend on the ESR/OSR distinction
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
An example: Michael Esfeld’s Moderate SR (2004)An example: Michael Esfeld’s Moderate SR (2004)
“Quantum entanglement shows that there are [cor-] relations among physical systems … [which] … amount to the whole having intrinsic properties that do not supervene on intrinsic properties of the parts.”
this in turn suggests “replacing a metaphysics of intrinsic properties with a metaphysics of relations”
From the metaphysics of relations to Moderate SR:things exist, but “the relations in which they stand are all there is to the things at the basic level”
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Problems of Moderate SRProblems of Moderate SR
taken literally, the idea to individuate theories by means of their pure structural content is far too weak
problem of “unintended domains”! physical examples of “structural equivalents”:
Classical electrodynamics vs. hydrodynamics(continuity equation, currents, theorems of Gauss and Stokes…)
SU(2) of strong or weak isospinU(1) as temporal or gauge groupand many more…
The examples already show: the structural content of modern physics theories is mostly given by their symmetry structure
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Symmetries in physicsSymmetries in physics
Symmetry of a domain D: set of one-to-one mappings of D onto itself (symmetry transformations), such that the structure of D is preserved
Symmetry transformations form a group and exemplify equivalence relations (partitioning of D into equivalence classes)
Note the distinction between symmetries with real instantiations (e.g. space-time transformations) as opposed to symmetries without real instantiations:scale transformationscoordinate transformationsgauge transformations!
only invariants allow for a realistic interpretation!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Gauge transformations: no real instantiations!Gauge transformations: no real instantiations!
Well-known for global gauge transformations:
AA
iA e
expectation value
of some observable does not change under
y y
y ycy y
=
®
Less well-known for local gauge transformations: x x
{ }
i (x) ˆx e x U x
wavefunction in position representation
with spanning an abstract Hilbert space
local gauge transformations are changes in the
position representation
Hilbert space op
ˆ ˆˆ ˆO ' UOU
ˆ ˆ ˆp p ' p (x)
erators transform as ,
in particular
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
SR and gauge symmetriesSR and gauge symmetries
Gauge theories are the most important case of symmetry structure in modern physics
BUT: Gauge symmetries do not posses real instantiations
only invariants allow for a realistic interpretation! eigenvalues of Casimir operators m, s, q ...
General feature of a “symmetry-based” physics Mass, spin, charge as paradigmatic cases of …
… intrinsic properties(“A thing has its intrinsic properties in virtue of the way that thing itself, and nothing else, is.“ - D. Lewis)
… but “structurally derived”: do not suppose objects independently of structure!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
„„Structurally derived intrinsic properties…“Structurally derived intrinsic properties…“
Note: group invariants lead to object classes only! Such „structurally derived intrinsic properties“ do not
individuate objects, but may nevertheless apply to lone objects
Hence, variants of SR including structurally derived intrinsic properties don‘t collapse into entity realism
Possible solution to the problem of unintended domains:Theory models are individuated via structurally derived intrinsic properties connected with those particular phenomena which make up our data models
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Conclusion Part 2Conclusion Part 2: “Intermediate SR”: “Intermediate SR”
ESR: There are relations and (maybe) relata, but we have epistemic access to relations only
OSRnon-eliminative variants:
„Moderate“ SR:Only relational, but no intrinsic properties exist
Intermediate SR (ISR):Relational and structurally derived intrinsic properties exist (as invariants of structures)
eliminative variant („relations without relata“)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Part 3:Part 3:Structural UnderdeterminationStructural Underdetermination(and Mathematical Overdetermination)(and Mathematical Overdetermination)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
SR as an antidote against TUD?SR as an antidote against TUD?
SR is sometimes considered an antidote against the anti-realistic threat of TUD
TUD undermines entity content (only) SR seems to avoid the threat of TUD by not
committing us to entities BUT:
Can we make sure that the structural content of theories is not underdetermined either?
Are there cases of structural TUD?
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Is structure unique? – The case of QMIs structure unique? – The case of QM
QM not only provides a case for TUD (with its different interpretations), but perhaps for “structural TUD”
Different interpretations, but perhaps not different mathematical structure
BUT YES: QM in Hilbert space, phase space, operator algebras, lattices…
BUT NO: only a certain structural core is connected with the empirical evidence of QM e.g. non-commutative algebra as structural core
(Stone-von Neumann-theorem: uniqueness of the
Heisenberg CCR’s) SR should focus on the relevant structural core…
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Is structure unique? – The case of GR…Is structure unique? – The case of GR…
“... there is no unique “gauge theory of gravitation.” ... this is due to the fact that gravitation is a “rich” theory from the geometrical point of view: it contains several invariants which may be used to build the kinetic part of the gravitational Lagrangian.”
Andrzej Trautman (1980)
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Four versions of General RelativityFour versions of General Relativity
Consider the following four formulations of General Relativity:
• GR in Riemannian spacetime entities: g, R
• GR in flat Minkowskian spacetime entities: g = + h
• GR as Lorentz gauge theory / gauge group SO(1,3) entities: tetrads
, curvature tensor R
• GR as translational gauge theory / gauge group G = R1,3
entities: tetrads , torsion tensor F
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Gronwald and Hehl (1996): On the Gauge Aspects of Gravity, gr-qc9602013
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Remarks on the translational gauge theoryRemarks on the translational gauge theory
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Is structure unique? – The case of GRIs structure unique? – The case of GR
Reconsider the ontology of the AB effectRivaling interpretations, but the U(1)-gauge group structure
is invariantSR should focus on this core structure only (or rather on the
gauge group invariants)SR seems to provide a solution to this TUD scenario
In GR, however: there is even dispute about the gauge group itself!No structural core between the four rivaling variants of GR!Apparently not only a case for entity, but for structural TUD!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
Interim: mathematical overdeterminationInterim: mathematical overdetermination
Erhard Scheibe: “mathematical overdetermination” (MOD) of modern physical theories T:
“M>P”, the mathematical exceeds the physical (parts of T)
Michael Redhead: “surplus structure” General problem: Is there a non-circular way to distinguish
between relevant physical and surplus structure?
SR needs an account of distinguishing M and P, otherwise the position transforms into Platonism(SR proponents commit themselves to physical in re-structure in the world only)
to focus on “relevant” structure is a special task for SR!
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
SR options in the face of structural TUD in GRSR options in the face of structural TUD in GR
There are basically two options for SR in order to deal with the case to structural TUD in GR:
1. Dismiss structural differences as mere cases of mathematical overdetermination and identify the relevant structural core
2. Declare the case of GR as a less interesting case since GR is not expected to be fundamental (TUD scenarios of GR can be dismissed as artifacts of incomplete knowledge)
Both options can of course never guarantee the impossibility of any structural TUD, but would help to undermine the power of an anti-SR argument based on it
Theoretical Frameworks and Empirical Underdetermination, Düsseldorf, 10-12 April 2008
General ConclusionGeneral Conclusion Gauge or, more generally, surplus structure from mathematical
overdetermination is a problem for SR SR needs an account of “relevant” as opposed to surplus structure SR should take relational and structurally derived intrinsic
properties (as invariants of structures) into account TUD is a speculative thesis with a pressing problem of missing
examples (from factual, mature science) “Practical TUD” rather an indicator for incomplete knowledge Two of three supposedly still existing interesting cases (QM and
U1-gauge theory) can be circumvented by adopting SR (by focusing on the structural core)
The third case, GR, seems to provide a case of structural TUD and, hence, a serious threat to SR!
Two options have been indicated to circumvent this threat