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arXiv:2601.14316

The burden of Fundamentality: Metaphysical ambiguities and the issue of Superdeterminism

Gabriele Cafiero, Luca Molinari, Jonte R. Hance

physics.hist-phquant-phSubmitted Jan 19, 2026• Announced Jan 20, 2026• 0 citations• Revised Aug 2, 2026 (v2)
v1 · Jan 19, 2026v2 · Aug 2, 2026
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Abstract

In this paper we approach the problem of superdeterminism from a novel point of view, highlighting its character as a more metaphysical than scientific proposition. First, we introduce a distinction between two types of superdeterministic theories, naïve (NSD) and metaphysical (MSD), and argue how NSD presents significant epistemic flaws. We show how NSD justifies itself through claims to fundamentality, thus connoting itself as a metaphysical theory rather than a scientific one. We finally illustrate that the most developed MSD model so far, Invariant Set Theory, implicitly proposes a confused form of priority monism. Our paper thus reinforces the thesis that theories should demonstrate rather than assume fundamentality and that it is methodologically flawed for a theory to assume its own fundamentality for the sole purpose of defending against criticisms.

Comments
24 pages, 2 figures. Accepted for publication in Philosophy of Science, matches accepted version

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Comment on "Analysis of the superdeterministic invariant-set theory in a hidden-variable setting"

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•Aug 18, 2021•1 citation
In this paper we approach the problem of superdeterminism from a novel point of view, highlighting its character as a more metaphysical than scientific proposition. First, we introduce a distinction between two types of superdeterministic theories, naïve (NSD) and metaphysical (MSD), and argue how NSD presents significant epistemic flaws. We show how NSD justifies itself through claims to fundamentality, thus connoting itself as a metaphysical theory rather than a scientific one. We finally illustrate that the most developed MSD model so far, Invariant Set Theory, implicitly proposes a confused form of priority monism. Our paper thus reinforces the thesis that theories should demonstrate rather than assume fundamentality and that it is methodologically flawed for a theory to assume its own fundamentality for the sole purpose of defending against criticisms.
Abstract This chapter discusses epistemic issues arising in superdeterministic accounts of quantum nonlocality. I argue that the specific kind of fine-tuning needed to make superdeterminism work undermines assumptions about the initial state of the universe which are needed to justify the use of memories and records in scientific practice, and thus at least the most naïve version of superdeterminism encounters serious epistemic problems. I then discuss naturalness and fine-tuning more generally, comparing the kind of fine-tuning involved with superdeterminism with other kinds of fine-tuning which have provoked debate in physics and philosophy.
A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However, a clear cut hidden-variable model has not been developed, which makes it difficult to assess the Proposal from a quantum foundational perspective. In this article, we first build a hidden-variable model based on the Proposal, and then critically analyse several aspects of the Proposal using the model. We show that several arguments related to counter-factual measurements, nonlocality, non-commutativity of quantum observables, measurement independence etcetera that appear to work in the Proposal fail when considered in our model. We further show that our model is not only superdeterministic but also nonlocal, with an ontic quantum state. We argue that the bit string defined in the model is a hidden variable and that it contains redundant information. Lastly, we apply the analysis developed in a previous work (Sen I, Valentini A, 2020 Proc. R. Soc. A , 476 , 20200214) to illustrate the issue of superdeterministic conspiracy in the model. Our results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.
In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor ψψψ-epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.
This essay aims to show that the recent development of quantum theory may provide us with an answer to one of the most compelling metaphysical problems, namely the problem of determinism.First, I sketch the conceptual background and draw the distinction between metaphysical and epistemological determinisms.Then, on the ground of the analysis of the problem of determinism in quantum mechanics, I argue that (1) metaphysical determinism is independent of quantum-mechanical formalism, and (2) that quantum nonlocality makes epistemological determinism impossible.I also try to show that metaphysical determinism should be regarded as a Kantian regulative idea which sets the horizon for scientific inquiry but which at the same time lacks what Kant calls "objective validity."The main conclusion is that metaphysical determinism should be regarded as an idealization -a formal, cognitive principle that we a priori assume and not something that we discover through scientific inquiry.
Superdeterminism has received recent attention as a possible path toward a locally causal explanation of the entanglement correlations that appear in experimental tests of Bell's theorem. While the term `superdeterminism' was coined by Bell to refer to restrictions on the free will of experimenters, it was not rigorously defined until recently. It has now been defined as a property of any physical theory that produces systematic violations of statistical independence. Here we focus on formalizing the requirements that being nonsuperdeterministic places on a physical theory, and setting a standard that must be met before we can conclude that a given theory is not superdeterministic. We begin by carefully examining how a physical theory determines what outcomes we observe when performing measurements in terms of ontic states and response functions, and how this differs between superdeterministic and nonsuperdeterministic theories, in terms of the behavior of the types of vetted random sampling procedures that we use in experiments. The core result is that individual samples and measurement outcomes must be representative of the observed distributions, which is explained in detail. This also has a bearing on how measurement settings are chosen by agents, whether freely or randomly, and we argue that this standard ultimately defines what freedom/independence actually mean. We then discuss contextuality, and show that in most cases, superdeterminism is contextual. Finally, we discuss how different physical theories, with different notions of ontic states and response functions, can give rise to the same empirical data, and how the same operational contextuality may appear in different forms.
In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor ψ\psiψ-epistemic. We here detail multiple problems with Sen's argument.