Structural Realism as an Epistemology for Structuralism

1. Theno-miracleargument andthe pessimisticmeta-induction

2. Structuralrealism - thenotion ofstructuralcontinuity

3. Objections tostructural realism

4. Structuralismas a frameworkfor structuralrealism

5. A structuralrealistepistemology forstructuralism

6. Summary andoutlook

Bibliography

Structural Realism as an Epistemology forStructuralism

Workshop: "Perspectives on Structuralism"

Thomas MeierDoctoral Fellow

Munich Center for Mathematical Philosophy

Center for Advanced Studies, MunichFebruary 16th - 18th







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Main Thesis

Structuralism serves as an instrument toformulate and to strengthen structuralrealism.







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Content

1. The no-miracle argument and the pessimisticmeta-induction

2. Structural realism - the notion of structural continuity

3. Objections to structural realism

4. Structuralism as a framework for structural realism

5. A structural realist epistemology for structuralism

6. Summary and outlook

Bibliography







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1. The no-miracle argument and the pessimisticmeta-induction

In the discussion about scientific realism, the so-calledNo-Miracle-Argument (NMA) is known as a strong argumentfor standard scientific realism. This goes back to Smart(1963, 1979), Putnam (1975) and Boyd (1983). The NMAcan be formulated as follows:

(i) Our empirical theories are successful.

(ii) If our empirical theories are successful and ourempirical theories are false, then it is a miraclethat our empirical theories are successful.

(iii) It is not a miracle that our empirical theoriesare successful.

(iv) Therefore, our empirical theories are true.







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The pessimistic meta-induction:

I Laudan (1981) formulated an argument againstscientific realism, which is known as the PessimisticMeta-Induction (PMI).

I He refers to the history of science and argues that bylooking at the historical development of our scientifictheories, it is clearly recognizable that the empiricalsuccess of a theory does not entail its (approximate)truth.

I His argument can be stated as follows:







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(i) In the course of history, all our past empiricaltheories have turned out to be false. They havealways been abandoned and/or replaced bysuccessor theories.

(ii) If this has always been the case in the past, it isat least very likely that this will also be thecase for actual and future empirical theorieswhich we currently hold as being true/correct.

(iii) Therefore, it is very likely that our currentlyheld empirical theories are not true and thatour future empirical theories will turn out to befalse as well.







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2. Structural realism - the notion of structuralcontinuity

I Epistemic structural realism: All our knowledge isstructural. We remain ignorant with respect to theproperties of the entities that are part of thesestructures (Worrall 1989, et.al.).

I Ontic structural realism: All that exists is structure.Objects only fill places in structures and do not existindependently. The ontologically basic entities arestructures (Ladyman 1998, French and Ladyman 2003,et.al.).







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Worrall’s (1989) position:

I Although Fresnel was quite wrong about what oscillates,he was, from this later point of view, right, not justabout the optical phenomena, but right also that thesephenomena depend on the oscillations of something orother at right angles to light. Thus if we restrictourselves to the level of mathematical equations - notnotice the phenomenal level - there is in fact completecontinuity between Fresnel’s and Maxwell’s theories(ibid: 118-119).







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Worrall bases his position on a case study of opticaltheory, the theory change from Fresnel’s to Maxwell’stheory:

I Though the referents and names of the postulatedentities in our theories change, the mathematicalstructure is preserved through theory change.

I There is a continuity of mathematical structure(equations) when theories change. Some equationsreappear in successor theories after theoretical change.







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I Our empirical theories are not completely overthrownwhen they change, the structural parts are retained.

I We don’t have direct epistemic access to the referents ofthe (unobservable) entities which appear in our empiricaltheories. But we can have knowledge of themathematical structures (equations), in which theseentities appear.

I If it occurs that the same equations are part of radicallydifferent empirical theories, for the structural realist itseems reasonable to assume that what represents theworld as best possible are these equations.







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The philosophically important underlying assumptions forstructural realism:

I It is reasonable to hold that what survives theory changeis what really latched on to the world. If we can identifywhich structures are retained through theory change, itmakes it reasonable to assert that the persistence ofthese structures "reflects" in every specific case aspecific part of the structure of the world.

I The persistence of certain structures makes reasonableto assume that at least the structural part of ourempirical theories represents the world correctly.







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3. Objections to structural realism

Psillos (1999: 147-161) developed several objections tostructural realism:

I The notion of structural continuity can be fully explainedby standard scientific realism. Mathematical equationshave been retained because they form an integral part ofthe (approximately) true theoretical content of theories.

I SR must be distanced in a clearer way frominstrumentalism. The feature of continuity on the levelof mathematical equations is compatible with bothrealism and instrumentalism.







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Furthermore:

I ... Worrall needs an argument to take him from the factthat mathematical equations are retained to theconclusion that this retention tells us something aboutthe structure of the world; in particular to the conclusionthat the retained mathematical equations represent realrelations between otherwise unknown, (or, worse,unknowable), physical entities (ibid:152).







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Concerning the SR-argument that the persistence ofmathematical structures through theory change reveals thelatching/connection to the world, Psillos argues:

I If the empirical success of a theory offers any groundsfor thinking that some parts of a theory have ’latched onto the world’, those parts cannot be just some(uninterpreted) mathematical equations of the theory,but must include some theoretical assertions concerningsome substantive properties as well as the law-likebehaviour of the entities and mechanisms posited by thetheory. These theoretical parts include, but are notexhausted by, mathematical equations (ibid: 154).







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I Another point made by Psillos (ibid.): The distinctionbetween structure and nature, as Worrall makes it, hasno justification. The nature of an entity and its structureform a continuum and are not clearly divisible. Scientistsnormally explain the nature of an entity by ascribingcertain basic properties and relations to it. The law-likebehavior of it is then described by a set of equations.

I Another open question for SR: What does thecorrespondence relation between old and new structureslook like? (Frigg and Votsis 2011).







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4. Structuralism as a framework for structuralrealism

I As it is well known, in structuralism, an empirical theoryconsists of its models, which are sequences of thefollowing form:

<D1, ..., Dm, R1, ..., Rn>

I The Di are so-called basic sets and the Rj are relationsconstructed on these sets. The Di contain what is takento be the ontology of the theory, i.e. they contain the"objects" assumed by the theory as "real" (but: these"objects" are part of a structure!)

I The Rj are usually functions. In scientific theories whichmake use of quantitative tools, they usually arefunctions mapping empirical objects into the realnumbers, or some other mathematical entities.







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I After a logical reconstruction of some theories underissue, we gain results about their relations to othertheories.

I In the intertheoretical relations, it is possible to identifystructures that might appear in both related theories.The respective potential models (i.e. their generalframeworks) of different theory-elements can be relatedthrough such relations.

I Such intertheoretical relations can count as one versionof structural continuity. In the Fresnel-Maxwell-case, thecontinuity would be that some differential equationsappear in both theories.







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Sneed (1983: 351) mentions the relation between scientificrealism and structuralism in the following way:

I It is important to understand that, on the structuralistview, empirical theories do make straightforward,descriptive, falsifiable claims about their subject matter.Structuralism is not just a new version ofinstrumentalism hiding behind a cloud of set theoreticnotation. On the other hand, structuralists see themathematical structures associated with a theory to bemuch more "essential" features of the theory than theclaims it makes. The claims may change with thehistorical development of the theory, but themathematical apparatus remains the same. Thusboth structuralist and realist would agree that empiricalscience makes descriptive claims but disagree about theextent to which empirical scientists, speakingprofessionally, "mean what they say".







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I We reconstruct our empirical theories logically and bydoing so we also aim to provide clarity about theontological commitments of the theories under issue.

I Structuralist reconstructions show the structure ofscientific theories. Theories are identified with structuresin the above mentioned formal sense.

I The method of structuralist metatheory contributes to adevelopment of SR. It shows what structural connectionsbetween empirical theories look like set-theoretically.

I The somehow imprecise or insufficient approach ofWorrall, which is only about mathematical structure inthe sense of equations, is abandoned.







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Theory-specialization (see Architectonic) is one form ofstructural continuity:

If T =< Mp,Mpp,M,GC ,GL, I >

and

T ′ =< M ′p,M

′pp,M

′,GC ′,GL′, I ′ >

are theory-elements, then: T ′ is a specialization of T , iff:

M ′p = Mp and M ′

pp = Mpp

and

M ′ ⊆ M

GC ′ ⊆ GC

GL′ ⊆ GL

I ′ ⊆ I







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Theory-specialization:

I More specialized theory-elements reflect special featuresof a local system. Specialization can model structuralcontinuity, for certain structures of a more generalsystem are continuous with structures in a morerestricted system.

I That is, certain laws are applied with more restrictions.







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I Structuralism provides tools for a clarification of thenotion of structural continuity.

I In structuralism, empirical theories are taken to bestructural entities themselves. All general relationsbetween theory-elements or theory-nets are trivially ofstructural form.

I Some information about links, reductions orspecializations might be trivial and not reallyinformative. Anyhow, the structuralist frameworkprovides a strong tool for capturing all kinds ofstructural continuities, trivial and non-trivial.

I Concrete case studies help to distinguish between trivialand non-trivial structural continuities.







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5. A structural realist epistemology forstructuralism

I It can be the case that some equations re-appearthrough theory change, as Worrall states.

I This just by itself is a weak assertion, for it is alsocompatible with instrumentalism. It is not only theequations that can count for continuity of structure.

I For an enriching postulation of SR, it would bepromising to think about theories as structuresthemselves (as structuralism does) and to identify(structural) relations between them.







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I It is no longer required that a theory contains equations.We take scientific theories to have a certain structurewhich only comes out clearly after a logicalreconstruction.

I All kinds of empirical theories - strongly mathematizedor not - can be formalized and representedset-theoretically, as structuralist metatheory demands.

I What we can know, is the logical structure of ourscientific theories. These are taken to be our mostelaborated and sophisticated expressions of ourknowledge about the world. In this sense, through theknowledge of the logical structure of our theories, whichis "structural" knowledge, we have knowledge of theworld.







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In the Aufbau, Carnap traced how the distinction betweenstructure and nature (Carnap calls it the material) should beunderstood and argued for the plausibility of structuralknowledge:

I Carnap (1928): Every scientific statement can inprinciple be so transformed that it is only a structuralstatement. But this transformation is not only possible,but required. For science wants to speak about theobjective; however, everything that does not belong tothe structure but to the material, everything that isostended concretely, is in the end subjective. From thepoint of view of constitutional theory this state of affairsis to be expressed in the following way. The series ofexperiences is different for each subject. If we aim, inspite of this, at agreement in the names given for theobjects constituted on the basis of the experiences, thenthis cannot occur through reference to the completelydiverging material but only through the formal indicatorsof the object-structures.







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6. Summary and outlook

My PhD research-project:

I Outline and discuss the framework of structuralism andshow its applicability to structural realism.

I A structuralist logical reconstruction of linguistictheories. From Bloomfield’s structural linguistics toHarris’ and Chomksky’s early transformational grammar.

I Show the continuity of structure through theoreticalchange in these reconstructed linguistic theories.

I Discuss and answer the possibility of structural realismin linguistics.







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Chomsky already mentions the Aufbau and traces an analogybetween structural realism and linguistics:

I Chomsky (1951) 1-2: Thus Carnap in the Aufbau, forexample, begins with a primitive relation between slicesof experience and attempts to construct, by a series ofdefinitions, the concepts of quality class, quality,sensation, etc., i.e., he tries to construct concepts forthe most general description of experience. Similarly, itcan be shown that the theoretical part of descriptivelinguistics, beginning with three 2-place predicates ofindividuals, and restricting its individuals to a tinydomain of experience (i.e. speech sounds) can constructconcepts such as ’phoneme’, ’morpheme’, etc., whichare available for a general description of that part ofexperience called linguistic phenomena.







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I A full-blown version of scientific realism has been refutedby the PMI. But full-blown instrumentalism has beenrefuted by the NMA. An extenuated version of realism,structural realism, has been reintroduced by Worrall.

I Structuralism is an adequate tool for making precisesense of epistemic structural realism. The core-notion ofstructural continuity finds several possible explanationsin the structuralist framework.

I The notion of structural continuity can be understood asa theory specialization. Theory-nets give us a clearexample of how structural continuity can be understoodin the framework of structuralism.

I Psillos’ objections can be addressed in a clear way if weincorporate the structuralist approach to the debate onstructural realism.







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I If a theory-element is reducible to another one, or ifcertain intertheoretical links obtain, they can also beseen as forms of structural continuity. Concrete casestudies are needed.

I By adapting the structuralist framework, it is possible tomodel structural continuity in a precise sense.Structuralism provides a sophisticated framework forepistemic structural realism.

I The notion of structural continuity is no longerrestricted to equations. In a more general sense: whydoes the notion of structural continuity have to berestricted to equations, as Worrall originally proposed?

I What we can know, is what the world is like accordingto the structures of our best empirical theories.







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Thank you!







Bibliography

BibliographyBalzer, W. / Moulines, C.U. / Sneed, J. (1987) AnArchitectonic for Science. Reidel, Dordrecht.

Boyd, R. (1983) "On the Current Status of the Issue ofScientific Realism", Erkenntnis 19: 45-90.

Carnap, R. (1928) Der logische Aufbau der Welt. FelixMeiner, Hamburg, 1998.

Chomsky, N. (1951) Morphophonemics of ModernHebrew. Unpublished masters Thesis catalogued as378.748 PoA/1951. 60 (RBC) in the Rare book andManuscript Library in the van Pelt Library at theUniversity of Pennsylvania.

Diez, J. / Moulines, C.U. (1997) Fundamentos defilosofia de la ciencia. Ariel. Barcelona.

French, S. / Ladyman, J. (2003) "Remodeling StructuralRealism: Quantum Physics and the Metaphysics ofStructure", Synthese 36, 31-66.







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Frigg, R. / Votsis, I. (2011) "Everything you AlwaysWanted to Know about Structural Realism but WereAfraid to Ask", European Journal for Philosophy ofScience, 2011, No. 1(2): 227-276.

Ladyman, J. (1998) "What is Structural Realism?",Studies in History and Philosophy of Science 29,409-424.

Laudan, L. (1981) "A Confutation of ConvergentRealism", Philosophy of Science 48, Nr.1.

Moulines, C.U. (1991) Pluralidad y Recursion. Estudiosepistemologicos. Alianza Editorial. Madrid.

Psillos, S. (1999) Scientific Realism: How Science TracksTruth. Routledge. London.

Putnam, H. (1975) "Philosophical Papers", Vol. 1:Mathematics, Matter and Method. Cambridge.Cambridge University Press.







Bibliography

Smart, J.J.C. (1963) Philosophy and Scientific Realism.Routledge. London.

Smart, J.J.C. (1979) "Difficulties for Realism in thePhilosophy of Science", in L.J. Cohen et.al. (eds.) Logic,Methodology and the Philosophy of Science VI.North-Holland Publishing Company. Amsterdam.

Sneed, J. (1983) "Structuralism and Scientific Realism".Erkenntnis 19 345-370.

Worrall, J. (1989) "Structural Realism": The Best ofBoth Worlds?". Dialectica 43, 99-124.

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Structural Realism as an Epistemology for Structuralism

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