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Department of History and Philosophy of Science


PhD researcher

College: Trinity
Supervisor: Jeremy Butterfield
Advisor: Hasok Chang
Thesis topic: Towards conceptual clarity about the use of functional realism to establish equivalence of theories

My main area of interest lies in solutions or dissolutions to theses of underdetermination by data. Such a thesis posits that there is a plurality of incompatible theories that fits the evidence. I am mostly concerned with the strongest version of such a thesis - strong underdetermination - that claims that multiple theories make exactly the same predictions in all empirical domains, while disagreeing about the unobservable domain. As such, there can be no experiment that highlights one theory over the other(s), not even in principle. This spells a problem for the monistic scientific realist, trying to establish one ontological picture of what the world is approximately like, in terms of a single explanation: the explanation given by the literal interpretation of the one (approximately) true theory.

I investigate a response to the thesis of strong underdetermination, mainly in physics and the philosophy of physics, that has picked up steam over the last twenty or so years: that these prima facie many possible incompatible claims about the  unobservable realm are in fact the same claim. No wonder, then, that they are empirically equivalent: they are theoretically equivalent. This can only be achieved if the theories are not interpreted literally or en bloc. Hence, one appeals to criteria that decreases the parts that of the formalism that we are epistemially committed to, of one or more of the putative underdetermined theories.

Such criteria are popularly (but not necessarily) of a structuralist or functionalist nature. The structuralist highlights the pattern of relations between unobservable entities - not the entities themselves - as an important part of the theory, which the structural realist will identify as the only part of the theory that we should ontologically commit to. The functionalist highlights those parts of the theory that do not signify internal constitution of something, but on the function or the role that something plays in a whole. For example, the linguistic role that is played by a computer that passes the Turing Test is the same role as the linguistic behaviour of a human being. I claim that this should be distinguished from the position of functional realism, where the functional role is taken to be ontologically sufficient: because the human and the computer that passes the Turing Test are functionally indistinguishable, they are also ontologically indistinguishable.

Apart from the general question of theory equivalence or inequivalence, I believe the claim of underdetermination is only truly believable (in the sense that it can be distinguished form wholesale Cartesian skepticism) if one is in fact presented with detailed examples, in the form of worked-out alternative hypotheses to reigning theories. I consider two of these as my main main case studies in physics:

  1. Electromagnetism: The Fields View and the Potentials View [my terms, see Mulder (2021) below]. The Fields View explains electrodynamic phenomena solely in terms of electric and magnetic fields, whereas the Potentials View maintains that in addition to the fields there lies physical salience in the electromagnetic potentials. Exciting about this example is that - even though these theories are strongly underdetermined - the Potentials View seems to be preferred over the Fields view, because it merges better when probed with quantum mechanical test particles. The reason to prefer the Potentials View is that it allows for an explanation of the Aharonov-Bohm effect, whereas the Fields View offers no explanation whatsoever. In Mulder (2021), I argue that if one takes this route, the realist runs the risk of speaking in terms of a rather vague ontology - in terms of quite broad equivalence classes of the potential; I suggest to narrow down this equivalence class by choosing the Lorenz gauge, such that one at least obtains an universally local explanation of electromagnetic phenomena.
  2. Relativistic Gravity: The putative empirical equivalence between General Relativity and Teleparallel Gravity. The latter theory was devised by Eli Cartan in the late twenties, and immediately pursued for years with great interest by (interestingly, historically) Einstein himself, who saw in it a hint to unify the forces of gravity and electromagnetism. Whereas it is clear from General Relativity that spacetime as an entity is curved, i.e. generally takes non-Euclidean form with non-vanishing Riemann components - the rival theory of Teleparallel Gravity uses torsion to explain the phenomena, without curvature being involved. The literal realist hence struggles to confirm or deny the proposition 'spacetime is curved'.



  • Ruward A. Mulder, Mônica  A. Caracanhas and Cristiane de Morais-Smith (2021), "Quantizing Lévy flights," Physical Review B 103: 174301. PDF.
  • Ruward A. Mulder (2021), "Gauge- underdetermination and shades of locality in the Aharonov-Bohm effect," Foundations of Physics 51: 48. PDF
  • Ruward A. Mulder, Yeshambel Melese and Niek Lopes Cardozo (2021), "Plant efficiency: a sensitivity analysis of the capacity factor for fusion power plants with high recirculated power," Nuclear Fusion 61: 046032. PDF
  • R. A. Mulder and D. G. B. J. Dieks (2017), "Determinism and Indeterminism on Closed Timelike Curves," in: General Relativity 1916-2016, edited by V. Petkov (Montreal: Minkowski Institute), pp. 93--114. PDF


Areas of Interest:

History and philosophy of science
Foundations of physics
Thought experiments
History of Medieval Islamic mathematics
Economic feasibility of nuclear fusion
Hellenistic philosophy
Time travel
Condensed matter physics
Ruward Mulder

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