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Metaphysical Pseudo-underdetermination

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Abstract

At the heart of the realist epistemology of science lies the belief that empirically successful theories deliver truth. This belief is challenged by the underdetermination of theory by evidence, which arises when rival theories that are contradictory in their unobservable constituents entail observationally indistinguishable consequences. Hence, the scientific realist is elicited to withdraw their ontological commitment to the unobservable aspects of reality. Earlier counterarguments aiming at weakening the thesis of underdetermination have been largely formulated in conceptual and extra-empirical terms. In this essay, I showcase the strength of a pragmatic route to dispel certain occurrences of empirical underdetermination. To that end, I critically examine an intriguing argument, originally advanced by William Newton-Smith, seeking to underdetermine Newton’s theory in classical mechanics by constructing a rival theory termed Notwen’s theory. Notwen’s theory mirrors the core relationships of the parent theory but operates on discrete, instead of continuous, time and space. Newton’s theory and Notwen’s theory are posited to be empirically equivalent yet ontologically divergent. Here, I argue that the competition between Newton’s theory and Notwen’s theory does not constitute a genuine case of empirical underdetermination. Instead, I denote this occurrence as pseudo-underdetermination, as the empirical evidence necessary to resolve the tie between competing theories has consistently been available. First, I dissolve the empirical equivalence by providing a set of counterfactual scenarios that leverage the differentiation constraint inherent to Newton’s theory but lacking in Notwen’s theory. Second, I show that the ontological commitment of the sophisticated scientific realist is resilient to these rival theories owing to the parasitic nature of Notwen’s theory. Overall, this analysis underscores the effectiveness of an operative approach in resolving instances of empirical underdetermination emerging from ad hoc-generated rival theories.

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Notes

  1. In the context of standard scientific realism, truth is customarily understood according to the correspondence theory, that is, a theory is true (false) if it is (not) corresponding to the actual state of affairs in the world.

  2. A now-classic argument casting doubt on the connection between empirical success and approximate truth is Larry Laudan’s ‘pessimistic meta-induction’ (Laudan 1981). The argument, in essence, states that (i) the history of science is replete with instances of empirically successful theories that have subsequently been proven false, with their theoretical terms failing to refer according to our current best theories; (ii) our current best theories are fundamentally no different from the abandoned theories of the past; (iii) consequently, we have no ground to assume that our current best theories will not ultimately be abandoned. According to Laudan, the list of empirically successful theories that have been rejected includes, e.g., the crystalline sphere theory in astronomy, the humoral theory in medicine, or the phlogiston theory in chemistry. Several counterarguments have been put forth to defuse the pessimistic-meta induction. For example, Stathis Psillos (Psillos 1999) noted that many of the theories mentioned by Laudan should not be regarded as mature and therefore should not be taken into consideration. As a result, by shrinking the pool of instances from which induction is inferred, the argument loses its probative force. Pertinent to the present discussion is a set of counterarguments seeking to show that the theoretical entities (Psillos 1999) and mathematical structures (Worrall 1989) responsible for the empirical success of past theories have been, to some extent, retained in subsequent theories.

  3. In the most acute cases, empirical underdetermination can even extend to the observable aspects of reality. A representative example concerns spin measurements (Stern-Gerlach experiment) and the conflicting descriptions offered by the standard quantum theory and de Broglie-Bohm theory (Bell 1982).

  4. In the following, I consider a charitable reading of Newton-Smith’s argument by assuming that the resolution of any experimental measurement aiming at distinguishing Newton’s theory and Notwen’s theory is much coarser than h. If not, the underdetermination originating from these two rival theories does not arise and the argument loses its philosophical relevance.

  5. There are two technical aspects that are not addressed by Newton-Smith (Newton-Smith and Lukes 1978) in the elaboration of the argument. First, it is not sufficient for space and time to be merely dense (i.e., h to be small) to induce empirical equivalence between Newton’s theory and Notwen’s theory, but it also necessary to be evenly spaced (i.e., h to be constant). Second, if the aim is to underdetermine a differential equation, it remains unclear why the forward finite-difference expression given in Equation (2) is preferred to a more accurate central finite-difference expression. Specifically, the former is accurate to order O(h) whereas the latter is accurate up to . For the sake of clarity of the presentation, I ignore these technical details.

  6. The computer code implementing Newton’s and Notwen’s theories is provided in the Supplementary Information as a Jupiter Notebook.

  7. Kukla (Kukla 2001) labels a putative theory as bizarre if it fails to secure acceptance among the majority of scientists, thus meeting the criterion of scientific disregard (Kukla 1996) for theoreticity. Note that Notwen’s theory, although classified as a quasitheory, it is not a bizarre theory as it is widely deployed in science as a computer implementation of Newton’s dynamics where discrete grids are required.

  8. Whether or not the various interpretations of quantum mechanics hitherto developed lead to empirical underdetermination is a long-standing debate in which David Wallace advocates for the superiority of the many-world theory of Everett. Here, I do not take sides in this debate. Rather, I point out that Wallace’s argument if accepted relies on a pragmatic approach to the problem of underdetermination that is methodologically analogous to the one advanced in this essay.

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Author information

Authors and Affiliations

  1. Department of Physics, University of Bath, Bath, BA2 7AY, United Kingdom

    Michele Pizzochero

  2. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, United States

    Michele Pizzochero

Corresponding author

Correspondence to Michele Pizzochero.

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Pizzochero, M. Metaphysical Pseudo-underdetermination. J Gen Philos Sci (2025). https://doi.org/10.1007/s10838-024-09705-5

  • Accepted
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  • DOI https://doi.org/10.1007/s10838-024-09705-5

Keywords

  • Underdetermination
  • Scientific realism
  • Entity realism
  • Structural realism
  • Newton’s theory
  • Notwen’s theory

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