Hoyningen-Huene (Synthese, 2009/2011) formalized transient underdetermination measure-theoretically and proved, via a mathematical curve-fitting example, that on that supposition the use-novelty version of the Miracle Argument for scientific realism is unsound. The paper leaves open empirical questions: whether the measure-theoretic condition holds of actual historical theory-spaces, whether the unsoundness result survives alternative modelling choices, and whether transient underdetermination is in fact prevalent in scientific practice; it also sets aside the question whether structural realism evades the critique. The measure-theoretic condition has not been tested against actual historical theory-spaces, and the problem remains open.

Background

Scientific realism is the view that our best scientific theories are approximately true, including their claims about unobservable entities such as electrons or fields. Its most influential positive argument is the Miracle Argument (also called the no-miracles argument, or the 'ultimate argument for scientific realism'): the empirical success of mature scientific theories would be a miracle unless those theories were at least approximately true, so only realism renders that success non-miraculous. A particularly persuasive version rests on use-novel predictions — predictions of evidence that played no role in constructing the theory, so that success cannot be explained as mere accommodation of already-known data. Realists argue that only approximate truth explains recurrent use-novel predictive success.

The classic antirealist counter is underdetermination of theory by evidence: the available evidence fails to single out one theory as uniquely warranted. Permanent underdetermination claims that for any theory there are empirically equivalent rivals matching all possible evidence; transient underdetermination, a notion going back to Larry Sklar and developed historically by Kyle Stanford, makes the weaker claim that at any given time there are rivals consistent with all evidence available then, rivals that scientists simply fail to conceive yet which are later discovered and often supplant the accepted theory. Stanford's 'problem of unconceived alternatives' (2006) argues from the history of science that such recurrent failures to conceive of serious alternatives are a deep, continuing feature of scientific inquiry and undermine realist confidence in current theories; his catch-all-hypothesis paper (2009) presses the same worry about testing fundamental theories against all serious alternatives.

Hoyningen-Huene (2009/2011) gave transient underdetermination a measure-theoretic form. Measure theory is the branch of mathematics that assigns sizes (generalized lengths, areas, volumes) to sets, and it allows one to say that one set of hypotheses is negligible or vast relative to another. In his idealization the space of possible theories is modelled as a bounded, high-dimensional parametric family of hypothesis curves equipped with a Euclidean-type measure, and transient underdetermination is expressed as a measure inequality between sets of candidate theories; the exact formulation is the one defined in the paper itself, whose definition is canonical for this problem. Against a formalized use-novelty Miracle Argument he then proved, by a mathematical curve-fitting example, that if this form of transient underdetermination holds, the Miracle Argument is unsound: a whole family of false hypotheses can deliver multiple use-novel predictions, so use-novel success is no indicator of truth. The paper closes by setting aside, among other things, whether structural realism — the selective realist view that preserves realism about the mathematical or causal structure of successful theories rather than about their unobservable entities — could evade the critique.

What the proof establishes is conditional: unsoundness follows only if the measure-theoretic supposition holds of real science. Whether it does — as an empirical, historical claim about actual theory-spaces, and as a robust claim about modelling choices rather than an artifact of one idealized example — is the unresolved question this task addresses.

Problem Statement

Determine whether the supposition on which Hoyningen-Huene's formal refutation of the Miracle Argument rests actually holds of real science, thereby settling the epistemic standing of the use-novelty Miracle Argument under transient underdetermination as a claim about actual scientific practice and not merely about an idealized model. The measure-theoretic condition to be tested is the condition of transient underdetermination as defined in Hoyningen-Huene (2011), Synthese 180:173-187 (doi:10.1007/s11229-009-9600-2); the paper's own definition is canonical. The central question is empirical-historical: does that measure-theoretic condition of transient underdetermination hold recurrently of actual theory-spaces in the history of science, across domains and episodes, rather than being an artifact of the idealized bounded parametric model space used in the paper's mathematical example? The empirical-historical claim is that the condition holds recurrently of actual theory-spaces across more than one domain or episode, not merely that it can be instanced once; whether real theory-spaces can instantiate the condition at all is an open part of the question. The question has two parts: whether the measure-theoretic condition holds of actual theory-spaces, and whether the conclusion that the use-novelty Miracle Argument is unsound is sensitive to modelling choices — different parameterizations of theory space, different measures, or broader or different classes of hypothesis families — or specific to the idealized curve-fitting family presented. The question is whether the paper's conditional proof has empirical purchase for actual scientific practice, or whether the formal refutation depends on idealizations that actual scientific practice does not satisfy.

References

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