Must
Evidence
Underdetermine
Theory?
John D. Norton
Center for Philosophy of Science and
Department of History and Philosophy of Science
University of Pittsburgh
1
The
Underdetermination
Thesis
2
The Underdetermination Thesis
No body of data or evidence or
observation can determine a scientific
theory or general hypothesis.
“Underdetermined”
means assured possibility
of rival theories equally
well supported by the
evidence.
A truism in science
studies and one of
philosophy of
science’s most
successful exports.
“Support”
means evidence bears on
theory by induction or
confirmation relations.
This sense essential to science.
Assured deductive compatibility of
many theories with any body of
evidence is trivial.
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The Gap Argument
1.
No body of data or evidence, no matter how extensive, can
determine the content of a scientific theory
(underdetermination thesis).
There is universal agreement on the content of mature
scientific theories.
Therefore, there is a gap: at least a portion of the agreement
cannot be explained by the import of evidence.
2.
My favorite social, cultural, political,
ideological or other factor is able to
account for what fills the gap.
Therefore, my favorite factor accounts
for a portion of the content of our
mature scientific theories.
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Philosophy of Science Gap
"…is at the very best a highly speculative,
unsubstantiated conjecture. Even if the
thesis can be expressed intelligibly in an
interesting form, there are no good reasons
for thinking that it is true.”
William Newton-Smith, "Underdetermination of Theory by Data," pp. 53236 in W. H. Newton-Smith, ed., A Companion to the Philosophy of Science.
Blackwell. p.553, emphasis in original.
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The Underdetermination Thesis
(Merely) de facto
underdetermination
is NOT…
Known evidence happens to
underdetermine some particular theory…
and in some cases it can be very hard to
procure requisite evidence.
(Merely) sporadic
underdetermination
Humean
underdetermination
Extreme or contrived cases of
theoretical content that transcends the
reach of all possible evidence.
No warrant to extrapolate any pattern.
Humean skepticism denies the viability of
induction itself.
Grue
Special case of artificial pearl (below).
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Justifications
1
2
3
Local
Global
Inductive
Duhemian adjustment of auxiliaries.
variant
adjusted
HYPOTHESIS and AUXILIARY entails EVIDENCE.
Metaphors of Quinean holism
"The totality of our so-called knowledge or beliefs, from the
most casual matters of geography and history to the
profoundest laws of atomic physics or even of pure
mathematics and logic, is a man-made fabric which
impinges on experience only at the edges…”
The resulting
underdetermination
extends to the
“abstract entities of
mathematics”!
We are to generalize from the display of a few
instances of observationally equivalent theories.
Natural
Cultured
Artificial
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No basis in
developed theories
of induction
8
1 and 2 depend on
Bare Hypothetico-Deductive Confirmation
If
and
then
theory T entails evidence E
theory T’ entails evidence E,
T and T’ are supported equally by E..
1 Local
EVIDENCE
supports
• HYPOTHESIS
(and AUXILIARY)
• variant HYPOTHESIS
(and variant AUXILIARY)
2
Global
Quine: "These observable
consequences of the hypotheses do not,
conversely, imply the hypotheses.
Surely there are alternative
hypothetical substructures that would
surface in the same observable ways."
equally.
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Most developed accounts of induction…
DO NOT admit any simple argument that assures
evidence must underdetermine theory.
DO NOT restrict evidence to deductive
consequences of hypotheses or theories.
DO NOT equally confirm hypotheses with same
observational consequences.
DO accord evidence local import and power to
discern between competing hypotheses.
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Three basic ideas
drive all accounts of inductive inference
1. Inductive
Generalization
2. Hypothetical
Induction
3. Probabilistic
Induction
An instance
confirms the
generalization
Ability to entail the
evidence is a mark of
truth
Degrees of belief
governed by a
calculus
Archetype
Enumerative
induction
Saving the
phenomena in
astronomy.
Probabilistic
analysis of games of
chance
Weakness
Limited reach of
evidence
Indiscriminate
confirmation
Applicable
to non-stochastic
systems?
Family
Principle
(the weakness of
the “bare” theory)
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Families develop to remedy weaknesses
Inductive Generalization
Hypothetical Induction
Probabilistic Induction
Enumerative Induction
Hempel's Satisfaction
Criterion
Mill's Methods
Glymour's Bootstrap
Demonstrative induction
Exclusionary accounts
(error statistics, common
cause)
Inference to the simplest
Inference to the best
explanation
Reliabilism
Probabilistic accounts
(especially Bayesian)
Interval valued beliefs
Non-probabilistic calculi
Controlled studies:
Only treatment can account
for difference in test and
control group.
Very fine grained
distribution of weight of
evidence.
Limit theorems specify
determination of theory.
Demonstrative induction
converts:
H saves phenomena E
to
E and auxiliaries
ENTAIL
H.
…and more.
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EVIDence refutes (HYPothesis and AUXiliary), but …
HYP & AUX .01
AUX .045
HYP .045
EVID .09
P(HYP & AUX | EVID) = 0
HYP & AUX
refuted
P(HYP) = 0.045
P(HYP | EVID) = 0.5
HYP confirmed
P(AUX) = 0.045
P(AUX | EVID) = 0.5
AUX confirmed
P(HYP & AUX) = 0.01
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Observationally
equivalent
theories
are self-defeating
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Observationally equivalent theories
classified
Natural
Cultured
mimic
natural
cases
Artificial
gratuitous
impoverishment
or mutilation
Newtonian mechanics with different states of rest.
Special relativity and Lorentz ether theories.
Flat and curved spacetime forms of Newtonian
gravitation theory.
Matrix and wave mechanics.
Standard and Bohmian mechanics.
Poincaré's disk.
Reichenbach's universal forces.
Continua without reals.
Deceiving demons.
Recently created worlds with memories, fossil
records.
Variant T' of theory T with same observables as T but
negation of T's theoretical claims.
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They are Self-Defeating
For natural and cultured pairs:
IF the observational
THEN
equivalence can be
demonstrated within
a philosophy paper,
we cannot preclude the possibility
that they are notational variants of
one another, perhaps with some
superfluous structure.
e.g. Lorentz’s ether theory and Einstein’s special
relativity. The ether state of rest is dismissed by
Einstein as superfluous.
I do NOT claim that
they MUST be
notational variants.
I DO claim the possibility
makes them inadmissible as
the inductive base for the
underdetermination thesis.
Should not ask
evidence to
separate theories
that may not be
factually distinct.
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Conclusion
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Must evidence underdetermine theory?
The underdetermination thesis is a strong claim about the
logic of inductive inference.
Our theories of inductive inference are too rudimentary to
support a decision either way on a thesis of such strength.
The thesis survives largely through a mix of wishful thinking and
inattention to theories of inductive inference.
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Appendices
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This Talk
The underdetermination thesis and the arguments
for it are reviewed.
Claims:
The thesis has no basis in developed theories of
induction.
Attempts to justify the thesis by displaying
observationally equivalent theories are self-defeating.
Underdetermination by grue fails to add novelty
for the same reason.
"Must Evidence Underdetermine Theory?"
in The Challenge of the Social and the Pressure of
Practice: Science and Values Revisited, M. Carrier,
D. Howard and J. Kourany, eds., Pittsburgh:
University of Pittsburgh Press, 2008, pp. 17-44.
"The Formal Equivalence of Grue and
Green and How It Undoes the New
Riddle of Induction." Synthese, (2006)
150: 185-207.
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More on Pairs
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The Argument
Thus they are
good candidates
for notational
When two theories are readily shown to have
the same observational consequences:
variants of one
The
observational
consequences
must be
compactly
describable
…else the
equivalence
cannot be proved.
Compact description
must be given in
terms of the
theories’
structures
… else both theories
are most likely
superfluous.
The two theories
structures must be
easily
intertranslatable
… else observational
equivalence cannot be
shown.
theory.
Anything not
carried over in the
transformation is
superfluous to
the observational
consequences
…hence dismiss as
superfluous
structure.
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Illustration: Toy Ptolemaic and Copernican observational
astronomy.
Observations:
the retrograde motion of Mars.
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Image from http://faculty.fullerton.edu/cmcconnell/Planets.html
Illustration: Toy Ptolemaic and Copernican observational
astronomy.
Ptolemy’s construction
Copernicus’ construction
are intertranslatable by
switching
Mars’ deferent
(Ptolemy) with
Earth’s orbit
(Copernicus)
Which of Earth or Sun is truly at rest is superfluous to saving the
astronomical observations.
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Animations from http://faculty.fullerton.edu/cmcconnell/Planets.html
Artificial pairs require a different response
Artificial
Deceiving demons.
Recently created worlds with memories, fossil records.
Variant T' of theory T with same observables as T but
negation of T's theoretical claims.
Artificial pairs are NOT equally confirmed by the observations.
Observations of
the fossil record
better confirm
an ancient
Earth
than
Earth created on
Wednesday
with spurious
fossil record.
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Glymour, Malament, Geroch, Manchak
Observationally indistinguishable spacetimes
This is a hard case that
has bothered me a lot!
1
The equivalence involves only deductive compatibility of many
spacetime models to one set of observations.
2
Underdetermination of general
facts about many possible worlds
(=theory) by facts in this world.
… but Manchak has recently extended the equivalence to some inductive
discriminations.
NOT this. Only one theory at
issue, general relativity. No
observationally equivalent rival
theories.
versus
Underdetermination of
facts in this world by
other facts in this world.
THIS. It is a form of
indeterminism. Fixing past
light cone fails to fix the rest.
Is past light cone determinism better suited to relativity? We cannot
observe a complete time slice. Is time slice determinism an artifact
of classical physics? Or of a metaphysics of presentism that does
not belong in relativity?
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Underdetermination by
Grue
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Grue, again
A green
emerald
confirms
A grue
emerald
confirms
Same
evidence
confirms
equally
All emeralds
are green.
All emeralds
are grue.
grue = green and
examined before t
or blue
Incompatible
hypotheses
if emerald
observed prior to t.
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What is NOT new
Patterns
may not be
projectible.
Enumerative
induction is
troubled.
Hume (18thc.) That fire has always burned
and bread always nourished gives us no
assurance they will continue to do so.
Jevons (19thc.) Multiple continuation of
any numeric sequence. “An apparent law
never once failing up to a certain point
many then suddenly break down…”
Denounced since antiquity
Francis Bacon (17th c.) “The induction
which proceeds by simple enumeration is
puerile, leads to uncertain conclusions,
and is exposed to danger from one
contradictory instance, deciding generally
from too small a number of facts, and
those only the most obvious.”
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What IS new: Symmetry of grue/green
Grue = observed
before t and green or
blue.
Green = observed
before t and grue or
bleen.
Bleen = observed
before t and blue or
green.
Blue = observed
before t and bleen or
grue.
…hence cannot dismiss “grue” as derived or contrived.
Take “grue” as fundamental and declare “green” derived.
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The symmetry suggest a more general inductive result
Ordinary
theory
Observational
evidence
bears symmetrically
in any inductive
logic on
Factually distinct but
observationally equivalent theories
Grue-ified
version of
ordinary theory
equally supported by the evidence...
… but only if the logic of induction
cannot step outside the symmetry.
To avoid this escape
grue-ify our total science.
Natural kinds only are projectible.
Green is a natural kind.
Grue is not a natural kind.
Grue is natural grue-kind.
Green in not a natural grue-kind.
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Isomorphism of ordinary and grue-ified total science
Ordinary science
This emerald is green.
All emeralds are green
All emeralds have the same color.
Green is a natural kind.
…
The language of ordinary
gemology text books.
Grue-ified total science
This emerald is grue.
All emeralds are grue.
All emeralds have the same g-color.
Green is a natural g-kind.
…
Gemology text books would convey the
same information if every ordinary term
were replaced by its grue-fied counterpart.
We would have created a notational
variant of ordinary gemology.
That the two are not notational variants is inexpressible in science!!
Ordinary science is the
real science.
Grue-ified science is the
g-real science.
More: analog in the problem of the nocturnal expansion.
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