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When Empirical Success Implies Theoretical Reference: Structural Correspondence, Indirect Reference, and Partial Truth

Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination. When Empirical Success Implies Theoretical Reference: Structural Correspondence, Indirect Reference, and Partial Truth. Gerhard Schurz (University of Duesseldorf).

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When Empirical Success Implies Theoretical Reference: Structural Correspondence, Indirect Reference, and Partial Truth

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  1. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination When Empirical Success Implies Theoretical Reference:Structural Correspondence, Indirect Reference, and Partial Truth Gerhard Schurz (University of Duesseldorf)

  2. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 1. Introduction: Pessimistic Meta-Induction vs. Structural Correspondence  Putnam's no-miracles argument (NMA): The best explanation of the empirical success of contemporary scientific theories is the (approximate) truth (and hence: reference) of their theoretical part. Is NMA correct?  Laudan's pessimistic meta-induction: There is theoretical discontinuity in spite of cumulative empirical success. Many examples of outdated scientific theories, which were (even strongly) empirically successful, although they made 'wrong' theoretical assumptions.  Contemporary theories will share the fate of their predecessors.  Correspondence realism: are there at least relations of correspondence between successive theories which preserve part of theoretical content? Putnam, Boyd: yes. Laudan: no impossible because of incompatible ontologies. Worrall: yes, but what they preserve is purely structural. Papineau, Psillos: Content-structure distinction is problematic.

  3. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination Important question: are the discussed examples of inter-theoretic correspondence more than mere exceptions?  more than a result of the subjective constitution of our brain?  do they have a systematic reason in the cumulativity of (strong) empirical success?  if yes, would this yield an improved way of justifying scientific realism? I want to show: the answer to all four questions is yes. THESIS: If a theory T has been strongly successful in a domain of applications A, but was superseded later on by an empirically superior theory T* which was likewise successful in domain A but has an arbitrarily different theoretical superstructure (or 'ontology'), then under (natural) CONDITIONS T contains theoretical expressions which correspond (in A) to certain theoretical expressions of T*, and given T* is true, they refer indirectly to the entities denoted by these expressions of T*.  In Schurz (2008, submitted) I argue for this theses by way of  historical examples: phlogiston-oxygen  a logical correspondence theorem

  4. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination CONDITION 0: The theories (of the historical sequence) share a their non-theoretical vocabulary, but differ in theirtheoretical vocabulary. Phlogiston Theory (Stahl 1730, Cavendish 1766, Priestley 1782):Combustible substances contain phlogiston  the bearer of combustibility. When combustion or calcination (roasting) takes place, the burned or calcinated substance delivers its phlogiston (hot flame), and a dephlogisticated substance-specific residual remains. Oxygen theory ( Lavoisier 1780):Combustion and calcination consists in the oxidation of the substance being burned or calcinated  the formation of a chemical bond with oxygen molecules. The assumption of phlogiston became superfluous.Modern generalized oxidation theory: Oxidation of substance X consists in the formation of a polarized or ionic bond of X with a electronegative substance Y, in which X-atoms donate electrons to Y-atoms.  Y need not be oxygen(Lavoisier's error). Common pre-theoretical concepts and knowledge:Empirical classification of substances: metals, calx, water, acid, salt, etc.Empirically described reactions (input and output substances, reaction conditions).Common theoretical principles (substances as compounds; inversion of reactions) Distinct theoretical concepts and principles:Phlogiston vs. oxygen resp. some electronegative 'oxidans'

  5. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination  Different hypotheses ('glasses') on the unobservable components of substances involved in chemical reactions: Combustion of organic materials: Oxygen theory:Carbonium + Oxygen ® Carbonium+Oxide ↑ [+ Ash = residual] Phlogiston theory: Carbonium (= AshPhlog) ®Ash + PhlogAir↑ Calcination of metals: Oxygen theory:Metal + Oxygen ® Metal+Oxide [+ HotAir ↑] Phlogiston theory: Metal (= MetCalxPhlog) ®MetCalx + PhlogAir↑ Salt-formation of metals in acids: Oxygen theory: Metal + H+X (=Acid) ®Metal+X (=Salt) + Hydrogenium (H2)↑ Phlogiston theory: Metal + Acid ®MetCalxAcid (=Salt) + Phlog ('inflamm. air') ↑ Inversion of calcination  reduction with coal: Oxygen theory: Metal+Oxide + Coal ® Metal + Coal+Oxide↑ [+Ash] Phlogiston theory: MetCalx + Coal (=AshPhlog) ® Metal + Ash [+ PhlogAir]↑ Inversion of salt-formation (Priestley's novel prediction in 1782:) Oxygen theory: Metal+Oxide + Hydrogenium® Metal + Water (= Hydr+Oxide) Phlogiston theory: MetCalx + Phlog [+ Water-in-Air]) ® Metal [+ Water-in-Air]  Phlogiston theory had to face some problems (phlogiston = 'inflammable air' ?,problem of increased weight; ad-hoc explanations, e.g. Pierre J. Macquer 1779).  Also Lavoisier's oxygen theory had to face difficulties

  6. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination CONDITION 1 (for T): T entails strong success in the sense of novel predictions, and this strong success is yielded by T-theoretical expression(s) j which can beempirically indicated or measured by several bilateral 'reduction sentences'. BRi(j): ("x,t) Ai(x,t) ® (j(x) « Ri(x,t)) (system x, time t) in words: in empirical circumstances (domain of application) Ai, the presence of j is indicated by an empirical phenomenon or process Ri. Note: BR's are understood in a 'modernized' non-reductionistic sense: synthetic consequences of T. They cover also quantitative measurement laws. Causal interpretation: the theoretical entity j figures as the common cause of the (strictly) correlated dispositions "if Ai then Ri".  Many such BRi(j)'s entail strong empirical success of T: A1® (j(x) « R1) (Potentially) novel predictions: A2® (j(x) ® R2) (i) (A1ÙR1) ® (A2®R2), (ii) (A1ÙØR1) ® (A2®Ø R2) etc. etc. In words: one infers from what has happened in one domain of application about what will happen in another domain.

  7. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination Definition: A strong (potential) empirical success of theory T w.r.t. partitioned domain A = A1An is a set of conditionals {AiÙRi® (Aj®Rj) : 1 ij n} entailed by T. Such a strong (potential) empirical success is yielded by j of T iff T entails this success by means of entailing BR(T) = {Ai® (j(x) « Ri) : 1in}. In phlogiston theory:j was not 'phlogiston' (this was empirically underdetermined). The theoretical expressions (j) which yielded success and were not empirically underdetermined were the composite expressions of dephlogistication = release of phlogiston, and phlogistication = assimilation of phlogiston. BR for dephlogistication: If an input substance x of kind Xi (e.g., a metal) is exposed to the influence of an input substance y of type Yi (e.g. hydrochloric acid), then x gets dephlogisticated iff the chemical reaction produces output substances z of type Zi (e.g., the metal dissolves and inflammable air evaporates). Examples for novel predictions of phlogiston theory:From inverse-calcination and salt-formation: every new and unexplored kind of metal, extracted from some calx by phlogistication (AiÙRi), will form a salt with an acid (Aj®Rj). From inversion of salt-formation, Priestley 1782 (Carrier): by adding pure phlogiston ('inflammable 'air') to metal calx one should regain the pure metal.

  8. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination CONDITION 2 (for T*): the entailment of T's strong empirical succcess by T* depends on T*'s theoretical part. Motivation: from empirical descriptions of what goes on in a system (e.g. chemical substance) x in circumstances Ai nothing can be inferred by empirical induction alone about what happens with x in a qualitatively different domain Aj. For example, from observing reactions of metals in hydrochloric acid nothing can inductively be inferred about the behaviour of metals in oxygen or water. Definition: A strong (potential) empirical success entailed by T* is T*-dependent iff for every conditional of the form (AiÙRi) ® (Aj®Rj) following from T*, there exists a mediating T*-theoretical description ti*(x) of the underlying system x, i.e.: (AiÙRi®ti*(x)) and ti*(x) ® (Aj®Rj) follow from T*. CONDITION 3 (for T and T*): T and T* are causally normal. Definiton: T is causally normal w.r.t. A = A1An iff (i) T's non-theoretical vocabulary divides into a set of independent and a set of dependent parameters (predicates), (ii) the 'Ai(x)' are formulated solely in terms of independent parameters, and (iii) no non-trivial claim about the state of independent parameter can be derived within T from a purely T-theoretical (consistent) description of x. Motivation: For example, from the intrinsic (theoretical) nature of a certain substance nothing can be concluded about what humans will do with it (expose it to hydrochloric acid or to heat or whatever). Etc.

  9. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination Correspondence theorem: Let T be a consistent theory which is causally normal w.r.t. a partitioned domain A = A1An and which contains a T-theoretical expression j which yields a strong potential empirical success of T w.r.t. partitioned domain A. Let T* be a consistent successor theory of T which is likewise causally normal w.r.t. A and which entails T's strong potential empirical success w.r.t. A in a T*-dependent way. Then: T* contains a theoretical expression t* such that T and T* together imply a correspondence relation of the form (C): A ® (j(x)«t*(x)) in words: whenever a system x is in the circumstances of one of the subdomains of A, then x satisfies the T-theoretical description j iff x satisfies the T*-theoretical description t* which implies that j refers indirectly to the theoretical state of affairs described by t*, provided T* is true. Corollary 1: (C) follows already from the union of BR(T) and T* which is consistent. Corollary 2:t* is unique modulo T*-equivalence.

  10. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination Example: In the domain of calcination and saltification (and inverse reactions): Dephlogistication of X corresponds (and hence indirectly refers) to the donation of electrons of X-atoms to the bonding partner in the formation of a polarized or ionic chemical bond. Phlogistication of X corresponds (and hence implicitly refers) to the acceptance of electrons from the bonding partner by positively charged X-ions in the breaking of a polarized or ionic chemical bond.  This correspondence explains the strong empirical success of phlogiston theory.  This correspondence does not preserve all of the meaning of 'phlogistication'. It is not analytically true. Further historical examples of correspondences (sketch):Between the caloric theory and modern physical chemistry:The amount of caloric particles in a substance X = the mean kinetic energy of X's molecules. The Fresnel-Maxwell-correspondence:Velocity of the ether molecules corresponds to the oscillation strength of the electromagnetic field.

  11. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 3. Ontological interpretation of the correspondence theorem 3.1 Reference shift, indirect reference and indirect truth The correspondence relation (C) expresses the possibility of aj-t*-reference-shift: instead of the reference assigned to j in T's intended model (phlogiston leaves the substance), we can assign to j the reference of t* in T*'s intended model (electrons move to the bonding partner), under preservation of BR(T) and T's strong empirical success. That j refers indirectly to t*'s interpretation within T* means by definition that the j-t*-reference shift makes BR(T) indirectly true, i.e. true under the shifted interpretation true within the ontology of T*. ( model-theoretic proof of j's indirect reference and BR(T)'s indirect truth)

  12. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 3.2 On the inner and outer structure of j:  whenever j of T corresponds to t* of T*, but the ontology of T concerning the entities involved in j is incompatible with the ontology of T*, then j will not be a primitive but a complex expression, and T will make some assumptions about j's inner structure (composition) which from T*'s viewpoint are false ® for example, that 'dephlogistication' is a process in which a special substance-component called 'phlogiston' leaves the combusted substance.  T has got a right model about j's outer structure (j's causal relations to the empirical phenomena, and maybe to other T-theoretical expressions), but T has got a wrong model about j's inner structure.  This situation may be given even for most advanced contemporary theories. Example: Protons consisting of three quarks. The outer and inner structure ofa complex expression j reflects Worrall's distinction between 'structure' and 'content' in an ontologically harmless way: the preserved 'structure' is j's outer structure; the non-preserved 'content' is j's inner structure.

  13. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 3.3 Indirect realism and the realistically interpreted Ramsey-sentence: Indirect truth is an important kind of partial truth. However, the indirectly true and preserved content part of T is not a conjunctive part of T's axioms but 'structural' in nature. It can be explicated as a Ramsey-type existential quantification in which one quantifies over a complex T-expression j as a whole: if BR(T) = S(j)where j = f(y) (e.g. release-of-phlogiston) then what is preserved is not $XS(f(X)) but the logically weaker $XS(X). I would defend Ramsey-sentences from my epistemological position of partial & indirect realism:we have direct access only to introspective experiences; what we experience as 'direct reality' is our brain's construction of it.From this viewpoint, the emergence of reference-shifts (from intended to unintended referents) is something natural and expected.

  14. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 3.4 Objection: How can a correspondence theorem hold for arbitrary theories, even for 'witchcraft theories', provided that they have got some empirical predictions right? Reply: The genuine restriction on the outdated theory is condition 1. Schurz ("Patterns of Abduction", Synthese 2007): the common cause property distinguishes scientific abductions from speculative abductions. While typical speculations postulate for each new phenomenon a new kind of theoretical cause, science introduces new theoretical entities only if they figure as common causes of several intercorrelated phenomena (unification).  If j were characterized by only one BR-sentence A1® (j(x) « R1), the derivation of the correspondence principle would be impossible. Aristotelian physics is a case in point: condition 1 do not apply; correspondence between Aristotelean and Newtonian dynamics cannot be established.

  15. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 4. Consequences for scientific realism and comparison with other positions. 4.1. Comparison with standard versions of scientific realism: They base their arguments on some version of the (unrestricted) NMA.  I share with constructive empiricism the skeptical attitude concerning the unrestricted NMA. My major objection: If T doesn't satisfy condition 1 (common cause condition for T-terms), there is no way to infer from its empirical success something about the truth-status of its theoretical part. My account does in no place presuppose the NMA (or some other form of IBE). It is based on an analytic theorem. It establishes independent from the NMA why a specifically restricted version of the NMA can be defended.

  16. Duesseldorf-Workshop 2008: Theoretical Frameworks and Empirical Underdetermination 4.2 From minimal realism and correspondence to scientific realism The correspondence theorem alone justifies only a conditional realism:if one assumes the (approximate) realistic truth of the presently accepted theory T*, then  But minimal realism (MR) and correspondence theorem taken together entail a weak version of scientific realism: (MR) The observed phenomena are caused by an external reality whose structure can possibly be (approximately) represented by an ideal theory T+ (which satisfies conditions 2 and 3), whose language is in reach of humans' cognitive resources (which does not imply that humans will ever find T+). 4.3 In conclusion:Thescientific realism which results from my account is weaker that standard realism, insofar the indirect truth of BR(T) preserves only the outer not the inner structure of the T-theoretical expression(s) j, hence my account is compatible with a certain amount of empirical underdetermination, even in our most advanced theories. This weakness of my account is the price of two advantages: 1) It does not presuppose the reliability of NMA or IBE (but, rather, provides a kind of 2nd order justification for it), and 2) the (structural) content-part of T can be specified in advance (independent from T*) and with precision.

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