Papers

Please email me for a copy of any of the papers below in case you don’t have access to the respective journal.

Papers in peer-reviewed journals


Sophistry about symmetries?, Martens, N.C.M., & Read, J., forthcoming in Synthese 

  • Published version (SharedIt | Open Access)
  • Postprint
  • Editorial
  • Abstract

    A common adage runs that, given a theory manifesting symmetries, the syntax of that theory should be modified in order to construct a new theory, from which symmetry-variant structure of the original theory has been excised. Call this strategy for explicating the underlying ontology of symmetry-related models reduction. Recently, Dewar has proposed an alternative to reduction as a means of articulating the ontology of symmetry-related models—what he calls (external) sophistication, in which the semantics of the original theory is modified, and symmetry-related models of that theory are treated as if they are isomorphic. In this paper, we undertake a critical evaluation of sophistication about symmetries—we find the programme underdeveloped in a number of regards. In addition, we clarify the interplay between sophistication about symmetries, and a separate debate to which Dewar has contributed—viz., that between interpretational versus motivational approaches to symmetry transformations.

Machian Comparativism about Mass, Martens, N.C.M., forthcoming in The British Journal for the Philosophy of Science 

  • Published version (Free Access)
  • Postprint
  • Abstract

    Absolutism about mass within Newtonian Gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This paper develops a Machian form of comparativism about mass in Newtonian Gravity, obtained by replacing Newton’s constant in the law of Universal Gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically equivalent to the absolutist version of Newtonian Gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism (and especially its Machian form) are highly questionable.

The (Un)detectability of Absolute Newtonian Masses, Martens, N.C.M. (2021), Synthese 198(3):2511-2550

  • Published version (Free; Read Only | Paywall)
  • Postprint
  • Abstract

    Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta (2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is detectable (in some weak sense). Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is?

Cartography of the space of theories: an interpretational chart for fields that are both (dark) matter and spacetime, Martens, N.C.M., & Lehmkuhl, D. (2020b), Studies in History and Philosophy of Modern Physics 72:217-236

  • Published version (Open Access)
  • Postprint (arXivPhilSci-Archive)
  • It is advisable to first read the prequel paper: Dark Matter = Modified Gravity?
  • Erratum: p.10: “in the relative sense” should be “in the relevant sense”
  • Video
  • Abstract

    This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modied gravity/spacetime (MG) and dark matter (DM). A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury‘s ‘superfluid dark matter theory’ is as much (dark) matter as anything could possibly be, but also—below the critical temperature for superfluidity—as much (of a modification of) spacetime as anything could possibly be. Here we introduce and critically evaluate three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that Φ is both (dark) matter and a modication of spacetime, analogously to the sense in which Jesus (according to catholicism) is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether Φ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetime–matter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively.

Dark Matter = Modified Gravity? Scrutinising the spacetime–matter distinction through the modified gravity/ dark matter lens, Martens, N.C.M., & Lehmkuhl, D. (2020a), Studies in History and Philosophy of Modern Physics 72:237-250

  • Published version (Open Access)
  • Postprint (arXivPhilSci-Archive)
  • Video
  • Abstract

    This paper scrutinises the tenability of a strict conceptual distinction between space(time) and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury‘s novel ‘superfluid dark matter theory‘ (SFDM) as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much (dark) matter as anything could possibly be, but also—below the critical temperature for superfluidity—as much (of a modification of) spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of (the importance of) the modified gravity/ dark matter distinction and the broader spacetime–matter distinction.

The Metaphysics of Emergent Spacetime Theories, Martens, N.C.M. (2019), Philosophy Compass 14(7) e12596

  • Published version (Paywall)
  • Finalist, Philosophy of Cosmology Essay Competition (Templeton Project)
  • Abstract

    The debate concerning the ontological status of spacetime is standardly construed as a dilemma between substantivalism and relationalism. I argue that a trilemma is more appropriate, emergent spacetime theories being the third category. Traditional philosophical arguments do not distinguish between emergent spacetime and substantivalism. It is arguments from physics that suggest giving up substantivalism in favour of emergent spacetime theories. The remaining new dilemma is between emergent spacetime and relationalism. I provide a list of questions which one should consider when discussing emergent spacetime theories and apply them to a quantum superfluid toy model of emergent spacetime.

Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities, Martens, N.C.M. (2018), Foundations of Physics, 48(5):591-609

  • Published Version (Free; Read OnlyPaywall)
  • Postprint
  • Abstract

    Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace’s problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space (i.e. substantivalism) or merely relative to other material bodies (i.e. relationalism) and between absolute masses (i.e. absolutism) or merely mass ratios (i.e. comparativism). This paper extends these discussions of Laplace’s problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity.

Regularity Comparativism about Mass in Newtonian Gravity, Martens, N.C.M. (2017), Philosophy of Science 84(5): 1226-1238

  • Published Version
  • Postprint
  • Abstract

    Comparativism—the view that mass ratios are not grounded in absolute masses—faces a challenge by Baker which suggests that absolute masses are empirically meaningful. Regularity comparativism uses a liberalised version of the Mill-Ramsey-Lewis Best Systems Account to have both the Laws of Newtonian Gravity and the absolute mass scale supervene on a comparativist Humean mosaic as a package deal. I discuss three objections to this view, and conclude that it is untenable. The most severe problem is that once we have reduced away the absolute masses, there is nothing that stops us from also reducing the mass ratios.

Edited Volumes


Dark Matter Realism, Martens, N.C.M., forthcoming in C. Smeenk & J.O. Weatherall (eds.) New Directions in Philosophy of Cosmology

  • Winner of Philosophy of Cosmology Essay Award, New Directions in Philosophy of Cosmology Project
  • Abstract

    According to the standard model of cosmology, ΛCDM, the mass-energy budget of the current stage of the universe is not dominated by the luminous matter that we are familiar with, but instead by dark matter (and dark energy). It is thus tempting to adopt scientific realism about dark matter. However, there is barely any constraint on the myriad of possible properties of this entity—it is not even certain that it is a form of matter. In light of this underdetermination I advocate caution: we should not (yet) be dark matter realists. The type of anti-realism I have in mind is different from that of Hacking (1989), in that it is semantic rather than epistemological. It also differs from the semantic anti-realism of logical empiricism, in that it is naturalistic, such that it may only be temporary and does not automatically apply to all other unobservables (or even just to all other astronomical unobservables, as with Hacking’s anti-realism). The argument is illustrated by using as analogy the much longer history of the concept of a gene, as the current state of the concept of dark matter resembles in some relevant ways that of the early concept of genes.

Special issues (Editor)


Special Issue: Dark Matter & Modified Gravity, Martens, N.C.M., Carretero Sahuquillo, M.Á., Scholz, E., Lehmkuhl, D. & Krämer, M. (eds.) (in progress)

  • Editorial: Integrating Dark Matter, Modified Gravity, and the HumanitiesStudies in History and Philosophy of Science
  • Contributed papers, distributed across Studies in History and Philosophy of Modern Physics and Studies in History and Philosophy of Science

Conference proceedings (peer-reviewed)


Parity violation and the reality of space, Martens, N.C.M. (2012), In: Proceedings of the Student Research Conference, Utrecht, the Netherlands, 21 November 2012, p.221-224.

Conference reports


Simplicity in the Sciences and Humanities: Report on the Bonn “Simplicities and Complexities” Conference, Chall, C. & Martens, N.C.M. (2020), Journal for General Philosophy of Science, 51(3):491-497

Work in progress


  • The Aharonov-Bohm Effect as a Case Study for Motivational Realism
  • Explanatory power of Dark Matter vs Modified Gravity (w Martin King)
  • The Trading Zone between Dark Matter and Modified Gravity
  • Reduction vs sophistication (w James Read)
  • Metaphysics without the final theory of physics (w Niels Linnemann)
  • Supersymmetry, unification & reduction (w Tushar Menon)
  • Semantic realism

Theses