1. 1 Must Evidence Underdetermine Theory? John D. Norton Center for Philosophy of Science and Department of History and Philosophy of Science University of Pittsburgh

2. 2 The Underdetermination Thesis

3. 3 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.

4. The Gap Argument 4 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.

5. Philosophy of Science Gap 5 "…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.

6. 6 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).

7. 7 1 variant adjusted Justifications Local Duhemian adjustment of auxiliaries. HYPOTHESIS and AUXILIARY entails EVIDENCE. 2 Global 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”! 3 Inductive We are to generalize from the display of a few instances of observationally equivalent theories. Natural Cultured Artificial

8. 8 No basis in developed theories of induction

9. 9 1 and 2 depend on Bare Hypothetico-Deductive Confirmation Iftheory T entails evidence E andtheory T’ entails evidence E, thenT and T’ are supported equally by E.. 1 Local EVIDENCE supports HYPOTHESIS (and AUXILIARY) variant HYPOTHESIS (and variant AUXILIARY) equally. 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."

10. 10 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.

11. 11 Three basic ideas drive 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?

12. 12 Families develop to remedy weaknesses Inductive GeneralizationHypothetical InductionProbabilistic 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 to E and auxiliaries ENTAIL H. 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.

13. EVIDence refutes (HYPothesis and AUXiliary), but … 13 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 & AUX refuted P(HYP | EVID) = 0.5 HYP confirmed P(AUX | EVID) = 0.5 AUX confirmed

14. 14 Observationally equivalent theories are self-defeating

15. 15 Observationally equivalent theories classified 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

16. 16 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.

17. 17 Conclusion

18. 18 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.

19. 19

20. 20 Appendices

21. 21 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 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. Claims:

22. 22 More on Pairs

23. 23 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.

24. 24 Illustration: Toy Ptolemaic and Copernican observational astronomy. Image from http://faculty.fullerton.edu/cmcconnell/Planets.html Observations: the retrograde motion of Mars.

25. 25 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.

26. 26 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.

27. 27 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. 1 Underdetermination 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. versus 2 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.

28. 28 Underdetermination by Grue

29. 29 Incompatible hypotheses confirms equally Same evidence if emerald observed prior to t. Grue, again A green emerald confirms All emeralds are green. A grue emerald confirms All emeralds are grue. grue = green and examined before t or blue

30. 30 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.”

31. 31 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.

32. 32 The symmetry suggest a more general inductive result Observational evidence Ordinary theory Grue-ified version of ordinary theory bears symmetrically in any inductive logic on Factually distinct but observationally 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.

33. 33 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.