Abstract
The structural realist approach to spacetime theories, explored in Chap. 5, represents one of the more influential third-way spatial ontologies to have recently appeared on the scene, but there are various difficulties associated with this strategy that have the potential to undercut its viability. This chapter will examine what most likely constitutes the primary obstacle, namely, the numerous underdetermination problems that plague structuralist conceptions of spacetime theories, a significant and contentious development in the structuralist literature that, as will be argued, also demonstrates the advantages that the spacetime version of epistemic structural realism (ESR) holds over its ontic competitor (OSR). Recent non-realist structuralist accounts, by Friedman and van Fraassen, have touted the fact that different structures can accommodate the same evidence as a virtue vis-à-vis their realist counterparts; but, while problematic for OSR, and possibly ESR, these claims gain little traction against a properly constructed liberal version of epistemic structural realism (see Chap. 5 for an introduction to these structuralist concepts). Overall, a broad construal of spacetime theories along epistemic structural realist lines will be defended which draws upon both Friedman's earlier work and the convergence of approximate structure over theory change, but which also challenges various claims of the ontic structural realists.
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- 1.
Saatsi (2010) has argued that a scientific realism requires more than mere approximate continuity, but should also explain the success of the earlier theory from the vantage point of the succeeding theory. Yet, while correct as a final goal or heuristic of scientific realism, explanations of this sort would seem to require access to the ontologies underlying these theories (or, at least, the succeeding theory’s ontology). ESR-L denies that this requirement is necessary to establish the success of ESR-L relative to its non-realist rivals—the reason being that the non-realist alternatives have no grounds for claiming a future directed convergence of approximate continuity over the course of science (see, §8.4 and §8.5).
- 2.
See, e.g., French and Ladyman (2003), and Ladyman and Ross (2007) for more on the ontology of OSR. The characterization of this ontology as holistic, along with other descriptions, are outlined in Ladyman (2009). “World-Structure” is the term mentioned in Ladyman and Ross (2007, 158). French (2014, 183) mentions the “blobject” (see, Horgan and Potrc 2008) as a potential candidate for a monistic reading of the world’s structure.
- 3.
This is different from the “metaphysical underdetermination” mentioned in Ladyman (1998), which is generated by alternative realist interpretations of a single theory. Entity underdetermination, in contrast, is the thesis that different theories, with different ontologies, will likely replace our currently successful theories. In essence, entity underdetermination is the ontological consequence of the pessimistic meta-induction. However, metaphysical underdetermination is a major problem for a fictional nominalist construal of OSR, as will be discussed in §8.2.
- 4.
That is, given a QG ontology that posits a collection of discrete objects (quantum cellular automata) connected by information, the best QM analogue would seem to be the more traditional conception that relies on individual objects (electrons, etc.) and their interconnections (relations). Prospective QG theories of this sort may fail, of course, but the point is that they cannot be ruled out, hence OSR remains subject to the pessimistic meta-induction.
- 5.
Pooley (2006, 88) raises the formalism underdetermination issue, along with a number of metaphysical underdetermination objections (see also footnote 3). However, if OSR theorists fall back upon their world-structure ontology, it is not clear that these metaphysical underdetermination cases can gain much traction against OSR. For instance, Pooley raises the specter that different interpretations of the measurement problem (e.g., de Broglie-Bohm versus other interpretations) lead to the underdetermination of the exact nature of the realist ontology, despite the use of the same mathematical formalism by these different interpretations (of the collapse of the wave function). Yet, since the same mathematical formalism is utilized, both collapse interpretations uphold the same world-structure ontology, with the difference lying in the mere details of how that ontology functions in the collapse case—and this is a much less troubling underdetermination than the entity or formalism underdetermination problems raised above, which do call into question the world-structure ontology itself.
- 6.
Bain (2009) strives to address the formalism underdetermination discussed in Pooley (2006) (dubbed, “Jones underdetermination” by both authors). Bain’s very promising analysis employs a category-theoretic approach in order to model a theory’s dynamical structure (say, solutions of the field equations in GR) via the symplectic manifold that encodes the phase space of dynamically possible states. This conception may blunt the worries associated with formalism underdetermination, but it depends on a category theory framework which some may find problematic (Bain 2009, 17). More importantly, the many different constructions of GR occupy different symplectic manifolds (e.g., twistor models are different from tensor models with/without boundary conditions; 19), and so neither the entity nor the metaphysical underdetermination problems, as we have called them, have been diminished (see footnote 3). The OSR theorist can, of course, always claim that future empirical data may favor some of these competing models, given their different dynamical structure—but the ESR-L theorist will interpret this state of affairs as supporting their more cautious brand of SR, since the evidence may forever fail to decide among these alternatives.
- 7.
The type of underdeterminism raised by Bueno would seem to be of the “metaphysical underdeterminism” variety (see footnote 3), since the same physical theory is open to many different ontological interpretations.
- 8.
On Diek’s analysis, which rejects substantivalism for a property theory or a sophisticated relationist proposal, “one should take the Hilbert space formalism as basic. All features which are traditionally associated with attributes of space should be distilled from this Hilbert space description. Obviously, Hilbert space is here not seen as something substantial, replacing absolute space, but rather as a mathematical device with the aid of which we give a systematical account of physical properties and their evolution” (2001b, 235). See, also, Chaps. 5 and 7.
- 9.
Lam and Esfeld, in fact, cite the Everett interpretation of QM in their analysis (2013, 289–290). But, one might reasonably ask: Is a branching universe (or spacetime) really more ontologically palatable than a fundamental ontology that lacks the metrical and topological properties of spacetime? Many would, I suspect, demur.
- 10.
There is, of course, a great deal of subjective license involved in attempting to translate early twentieth century neo-Kantian theories into the modern OSR/ESR dichotomy, but their collective approach would seem to fall clearly on the epistemological side of that dichotomy, and not the ontological. That is, given the predominant emphasis on conceptual categories and their like in shaping our experience of the world, drawing purely ontological lessons, apart from these epistemic components, seems quite problematic. Friedman’s discussion of the goals of Cassirer’s Substance and Function makes this point clear: “[I]n accordance with the ‘critical’ theory of knowledge,…convergence, on this view, does not take place towards a mind- or theory-independent ‘reality’ of ultimate substantial ‘things’....‘Reality’, on this view, is simply the purely ideal limit or endpoint towards which the sequence of [theoretical] structures is mathematically converging—or, to put it another way, it is simply the series itself, taken as a whole” (Friedman 2005, 75).
- 11.
More problematically, some of these fragmented local theories may violate the laws and data of other local theories: e.g., a theory confined to just biology could undermine the conservation of mass-energy, the latter constituting just another local theory. Now, a number of objections might be raised in response. First, the neo-Kantian might claim that a mathematical invariant can always be found that will link the totality of empirical data, thus rejecting the possibility just noted (although, as a counter-reply, this would be difficult to prove). Second, the anti-realist may insist that empirical adequacy dictates that all empirical data must be subsumed under more general theories (since empirical adequacy would be sacrificed if they failed to be subsumed in that manner). However, as argued previously, this demand would render anti-realism practically indistinguishable from ESR-L, since it basically admits that scientific theories must converge, and it hard to imagine an anti-realist embracing that position.
- 12.
Can Friedman’s neo-Kantian claim, as does the realist, that the world provides the needed constraints to rule out the egalitarian option? While the world’s ontology obviously plays a major role in scientific theorizing for Friedman (i.e., given his admission of empirical realism), to claim that it explains convergence would clash with his insistence that his view is consistent with anti-realism. As explained previously, van Fraassen’s anti-realism holds that convergence is contingent; so, if Friedman really accepts that his view is consistent with anti-realism, then he would need to add that convergence may also be a mere accident. Given Friedman’s past history of supporting realism, along with his demand for convergence (explored above), it appears unlikely that he would regard convergence as merely a contingent accident.
- 13.
A famous counter-argument against structural realism, originally introduced by M. Newman against Russell, should be briefly addressed at this point, although we will only explore a version of the argument adapted for the semantic view of theories: if a mathematical structure represents the world by standing in an isomorphic relationship with the world’s structure, then one can undermine the uniqueness of this representation by introducing another world domain of the same cardinality and carving out a structure that is also isomorphic to the mathematical structure in this new domain. As argued by French and Saatsi (2006), however, this problem can be surmounted by including interpretations of the mathematical structure’s theoretical variables, so that they refer to a particular group of properties and relations. This reply to the Newman problem would seem to parallel Poincaré’s insight, namely, that structures are always linked to the world via coordinating principles—and hence our G + P approach to structure naturally includes French and Saatsi’s defense. Friedman himself regards the Newman argument as quite problematic for structuralism; see, Demopoulos and Friedman (1985).
- 14.
To be precise, Friedman tends to identify relationism with our eliminativist and super-eliminativist brands of relationism first defined in Chap. 1 (see, e.g., Friedman 1983, 217). He does entertain the proposal, a la Sklar, that absolute acceleration is a “primitive quantity”, and which he classifies as relationist, but he rejects it on the grounds that it lacks the unifying power of absolute space: since the domain of absolutist spacetime is the entire manifold, M, whereas the domain of the “primitive quantity” relationist is just the spacetime points occupied by physical events, p, Friedman argues that this Sklar-type relationism still suffers from a lack of unifying power in comparison with the absolutist due to the limitations of p’s domain (257). Yet, if one embraces the type of modality implicit in Teller (1991), where a single object can give rise to the inertial structure of the entire manifold, then Friedman’s argument is no longer applicable. For example, Teller concludes that his “liberalized relationist” is “committed to the same inertial structure to which the substantivalists feel committed”, but that “coordinate systems are now taken to describe actual and possible relations to actually existing objects, instead of objectively existing space-time points” (1991, 381; emphasis added). In all fairness, Friedman does seem to acknowledge that the relationist could appeal to a “primitive law” (1983, 257) to capture the unifying power enjoyed by the absolutist (and thus bring M and p into congruence, albeit indirectly through the primitive law), but he elsewhere deems this general strategy (of appealing to primitive quantities) as ad hoc (248), a description that foreshadows Earman’s later “instrumentalist rip-off” allegation (see Chap. 5).
- 15.
Friedman (1983, 297–299). That is, the force F i now explains why the particles that comprise an expanding or shrinking body, due to h′, deviate from straight-line trajectories as the body moves, apparently inertially, through various regions of space. Here, the °Γi jk are the flat components of °D, and the Γi jk are the non-flat components of D, such that, F i = (Γi jk − °Γi jk ) (dx j /dt)(dx k /dt).
- 16.
An anti-realist or OSR realist may object, at this point, that the multiple routes form of ESR-L is tantamount to an equivalence of structure at the empirical level only, and thus it is simply insufficient to qualify as a realist theory. This objection, nevertheless, fails to take into account the fact that ESR-L is, indeed, a very liberal brand of realism. Given the two requirements of the ESR-L theory advocated above—nonuniqueness, and that each nonunique G + P combination must be an invariant feature across all of the other nonunique combinations, G′ + P′—the “realism” in this theory is manifest in two important ways: (1) via predictions on future theoretical constructions (which runs counter to anti-realism, or at least is quite difficult for the anti-realist to explain), namely, that theories will converge; and (2) that there will exist constraints on the theoretical constructions (thus eliminating the egalitarian option along with its relativist implications for epistemology and ontology). Finally, it should be noted that a famous species of underdetermination concerning spacetime theories is consistent with this Poincaré-inspired exegesis, as well as with ESR-L; namely, the topological underdetermination manifest by observationally indistinguishable spacetime theories, as explored by Malament (1977) and Glymour (1977).
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Slowik, E. (2016). The Multiple Paths Towards an Epistemic Structural Realist Spatial Ontology. In: The Deep Metaphysics of Space. European Studies in Philosophy of Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44868-8_8
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