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MustEvidence

UnderdetermineTheory?

John D. NortonCenter for Philosophy of Science and

Department of History and Philosophy of Science

University of Pittsburgh

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The Underdetermination

Thesis

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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.

“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.

A truism in science studies and one of philosophy of science’s most successful exports.

The Gap Argument

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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.

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.

2.

Philosophy of Science Gap

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"…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. 532-36 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 is NOT…

(Merely) de facto underdetermination

Known evidence happens to underdetermine some particular theory… and in some cases it can be very hard to procure requisite evidence.

Extreme or contrived cases of theoretical content that transcends the reach of all possible evidence.

(Merely) sporadic underdetermination

Humean underdetermination

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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1 variant adjusted

Justifications

Local Duhemian adjustment of auxiliaries.

HYPOTHESIS and AUXILIARY entails EVIDENCE.

2Global 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”!

3Inductive 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

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1 and 2 depend on

Bare Hypothetico-Deductive Confirmation

If theory T entails evidence Eand theory T’ entails evidence E,then T and T’ are supported equally by E..

1 LocalEVIDENCE

supports• HYPOTHESIS (and AUXILIARY)

• variant HYPOTHESIS (and variant AUXILIARY)

equally.

2 GlobalQuine: "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."

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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 ideasdrive all accounts of inductive inference

Family 1. Inductive Generalization

2. Hypothetical Induction

3. Probabilistic Induction

Principle 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(the weakness of

the “bare” theory)

Applicable

to non-stochastic systems?

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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

Demonstrative induction converts:

H saves phenomena E

toE and auxiliaries

ENTAILH.

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.

…and more.

EVIDence refutes (HYPothesis and AUXiliary), but …

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HYP .045 AUX .045

HYP & AUX .01

EVID .09

P(HYP & AUX) = 0.01

P(HYP) = 0.045

P(AUX) = 0.045

P(HYP & AUX | EVID) = 0 HYP & AUXrefuted

P(HYP | EVID) = 0.5 HYP confirmed

P(AUX | EVID) = 0.5 AUX confirmed

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Observationally equivalent

theoriesare self-defeating

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Observationally equivalent theoriesclassified

Natural 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.

Cultured Poincaré's disk.

Reichenbach's universal forces.

Continua without reals.

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.

mimic natural cases

gratuitous impoverishment

or mutilation

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They are Self-Defeating

For natural and cultured pairs:

IF the observational equivalence can be demonstrated within a philosophy paper,

THEN we cannot preclude the possibility that they are notational variants of one another, perhaps with some superfluous structure.

I do NOT claim that they MUST be notational variants.

e.g. Lorentz’s ether theory and Einstein’s special relativity. The ether state of rest is dismissed by Einstein as superfluous.

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?

Our theories of inductive inference are too rudimentary to support a decision either way on a thesis of such strength.

The underdetermination thesis is a strong claim about the logic of inductive inference.

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.

The thesis has no basis in developed theories of induction.

Attempts to justify the thesis by displayingobservationally 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.

Claims:

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More on Pairs

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The Argument

The

observational consequences

must be compactly describable

…else the equivalence

cannot be proved.

When two theories are readily shown to have the same observational consequences:

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.

Anything not carried over in the transformation is

superfluous to the observational

consequences

…hence dismiss as superfluous structure.

Thus they are good candidates

for notational variants of one

theory.

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Illustration: Toy Ptolemaic and Copernican observational

astronomy.

Image from http://faculty.fullerton.edu/cmcconnell/Planets.html

Observations:the retrograde motion of Mars.

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Illustration: Toy Ptolemaic and Copernican observational

astronomy.

Animations from http://faculty.fullerton.edu/cmcconnell/Planets.html

Ptolemy’s construction Copernicus’ construction

are inter-translatable 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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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 confirman ancient

Earththan

Earth created on Wednesdaywith 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!

The equivalence involves only deductive compatibility of many spacetime models to one set of observations.… but Manchak has recently extended the equivalence to some inductive discriminations.

1Underdetermination of general facts about many possible worlds (=theory) by facts in this world.

Underdetermination of facts in this world by other facts in this world.

versus2

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?

NOT this. Only one theory at issue, general relativity. No observationally equivalent rival theories.

THIS. It is a form of indeterminism. Fixing past light cone fails to fix the rest.

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Underdetermination by

Grue

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Incompatible hypotheses

confirmsequally

Same evidence if emerald

observed prior to t.

Grue, again

A greenemerald

confirms All emeralds are green.

A grueemerald

confirms All emeralds are grue.

grue = green and examined before t

or blue

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What is NOT new

Patterns may not be projectible.

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…”

Enumerative induction is

troubled.

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.

Bleen = observed before t and blue or green.

Green = observed before t and grue or bleen.

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

Observationalevidence

Ordinary theory

Grue-ified version of ordinary theory

bears symmetrically in any inductive

logic on

Factually distinct butobservationally equivalent theories equally supported by the evidence...

To avoid this escape

grue-ify our total science. Grue is natural grue-kind.Green in not a natural grue-kind.

… but only if the logic of induction

cannot step outside the symmetry.

Natural kinds only are projectible.Green is a natural kind.Grue is not a natural 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.

…

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.…

The language of ordinary gemology text books.

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.