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Logical Dependence of Physical Determinism on Set-theoretic Metatheory
Get PDFBaroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is deterministic—whether it fixes a unique future given the present—can depend on one's choice of set-theoretic axiom candidates over which there is intractable disagreement. This dependence is not confined to hypothetical examples. It reaches into mainstream, foundational, and frontier physics, including full discrete systems, the preferred basis problem in quantum mechanics, and the dynamics of Kerr-like black hole interiors. I argue that beyond the familiar analytic notion of well‑posedness, a theory’s determinism profile depends on a regularity layer, on whether the definable sets that carry our ensemble and canonicalization talk are measurable, have the Baire property, and admit measurable selectors. Competing axiom candidates extending ZFC—Gödel’s Axiom of Constructibility (V=L) and large cardinal (LC) assumptions strong enough to imply Projective Determinacy (PD)—diverge on these regularity facts. The divergence has three faces. First, coherence: weak formulations presuppose measurability of coefficients and under V=L one can arrange definable pathologies that collapse the statement of the weak problem, while under PD all projective sets are regular. Second, uniqueness: many determinism results are ensemble claims—“for almost all initial data there is a unique continuation”—whose sense depends on measurability or Baire category at projective complexity. PD secures this, while V=L may not. Third, identity: when multiple admissible continuations remain, physical practice demands a canonical, representation‑independent choice. That demand is a measurable uniformization problem. PD supports measurable, symmetry‑constrained selectors at the Π¹₂ level, while V=L guarantees at most Δ¹₂ (hence possibly non‑measurable) tie‑breaks. I develop a number of live cases, showing how the regularity properties toggle with the metatheory. The upshot is that which extension of standard ZFC we adopt changes what our best‑supported theories say. I close by sketching a research program, reverse physics, on analogy with Friedman’s and Simpson’s reverse mathematics, whose aim is to map a theory’s physical content against the foundational axioms that make its ensemble and canonical claims intelligible. I conclude that, given the entanglement of set-theoretic metatheory and physics, either physical theories must be relativized to set theories (in which case physics itself becomes relative), or, as Quine (1951, 1990) controversially argued, the search for new axioms to settle undecidables may admit of empirical input
How deep learning can justify pursuit, and why it matters
Get PDFWe are in the midst of a deep learning revolution in science – or so many scientific and philosophical commentators would suggest. This article addresses a relatively underexplored aspect of this putative revolution, concerning how deep learning models (DLMs) impact the decision to rationally pursue a scientific idea. First, we develop an economic model of pursuitworthiness and use this model to analyze two ways that DLMs can justify pursuit: (i) by increasing the expected epistemic value of pursuit, and (ii) by decreasing the expected practical cost of pursuit. Then, we put this analysis to work. We argue (i) that it clarifies the sense in which DLMs may be said to be revolutionizing science, by radically impacting the economics of scientific activity, and (ii) that it brings into sharper focus certain scientific risks – what we call ‘illusions of pursuitworthiness’ – incurred by the shift toward DLM-driven science
Externalism without Essentialism: Hilary Putnam on Natural Kind Terms
Get PDF“Amid all his famously changeable views, Hilary Putnam held a long-standing commitment to semantic externalism about natural kind terms. Early on, Putnam claimed an affinity between this view and Saul Kripke’s work on natural kind terms as ‘rigid designators’. This led to many authors referring to the ‘Kripke-Putnam’ view of natural kind terms. Subsequently though, Putnam sought to distance his view from that of Kripke, particularly with regard to Kripke’s commitment to metaphysical necessity and essentialism – a commitment I regard as untenable in the face of actual scientific classification. I want to argue that rejecting these commitments of Kripke’s should have also forced Putnam to revise some of his most strongly held views. First, I will argue that externalism without essentialism cannot support Putnam’s own intuition about his Twin Earth thought experiment. Second, I will argue that Putnam loses a sufficiently general and univocal notion of ‘substance identity’ that was necessary for supporting his reading of the Twin Earth case and also for guaranteeing the reference of scientific terms across theory changes.
Quantum Interference and the Limits of Separability
Get PDFQuantum theory implies, and empirical evidence confirms, that while particles can exhibit wave-like behavior in interferometric experiments, this behavior is so limited as not to allow for third- and higher-order interference. The article at hand shows that this possibility-impossibility structure suggests the universal validity of a principle that regulates statistical correlations between spatiotemporally localized events, independently of the nature of the objects that may or may not partake in these events. Roughly, and up to some qualifications, the said principle mandates that any joint influence of m mutually spacelike separated events on another event, be such, that it can be separated by at least m/2 mediating events, and in some cases, by no more than m/2 mediating events. The structure of quantum interference thus teaches us that events can influence each other in a non-separable fashion, but that this non-separability has a certain exactly quantifiable limit
Mapping the communication of science
Get PDFScience communication is a broad field and involves very diverse activities. This paper aims to illuminate and partly systematise the diversity of science communication. We focus on three important dimensions: size of the audience, frequency of interaction, and decision-making relevance. Based on them, we introduce a three-dimensional space of science communication wherein particular scenarios can be located. We argue that relevant challenges for science communication are particularly associated with certain areas of this space. Based on the proposed framework, we also address potential strategies and developments in science communication
Blindspots of Empiricism in the Discovery of Chaos Theory
Get PDFChaos theory is a branch of classical physics, founded in the 1960s-70s, that studies systems whose solutions are sensitively dependent on their initial conditions. For many, it is surprising that chaos theory arrived so late. However, through the work of Henri Poincaré, we know that much of the math of chaos was understood by some 70 years prior. Furthermore, through the writings of Poincaré's colleagues - Jacques Hadamard and Pierre Duhem - we also see a detailed understanding of the chaos found in his work. They also have explicit reasons of why the math of chaos was to be ignored. It was a strict form of empiricism - positivism - causing them to label chaos as "useless" and "meaningless" mathematics because it was thought to be ungrounded in experience. In this paper, I describe how the empiricist tenets of positivism exiled chaos from physics following Poincaré
Laws, Initial Conditions and Physical Modality: Lessons from Cosmology
Get PDFCertain considerations from cosmology (Ellis 2006, 2014) and other areas of physics (Sklar, 1990; Frisch, 2004) pose challenges to the traditional distinction between laws and initial conditions, indicating the need for a more nuanced understanding of physical modality. A solution to these challenges is provided by presenting a conceptual framework according to which laws and fundamental lawlike assumptions within a theory’s nomic structure determine what is physically necessary and what is physically contingent from a physical theory’s point of view. Initial conditions are defined within this framework in terms of the possible configurations of a physical system allowed by the laws and other lawlike assumptions of a theory. The proposed deflationary framework of physical modality offers an alternative way of understanding the distinction between laws and initial conditions and allows the question of the modal status of the initial conditions of the Universe to be asked in a meaningful way
Limiting Reduction and Modified Gravity
Get PDFModified Newtonian Dynamics (MOND) is a framework of theories that adjust Newton's laws of gravity to explain effects such as galactic rotation anomalies, offering an alternative to dark matter. This essay examines the justification of MOND by assessing its inter-theoretical relationship to established theories across relevant scales, in particular its connection to Newtonian gravitation. We argue that MOND fails a key condition for a theory's justification--what we call `reduction-wise justification'--since it does not adequately reduce to Newtonian gravity in a fully non-arbitrary way. More precisely, despite satisfying the standard formal criteria for successful limiting reduction, MOND does not properly reduce to Newtonian gravitation because of (i) the absence of a fundamental theoretical framework to justify the interpolating function introduced in MOND and (ii) the lack of a unified mathematical structure working across all scales, independent of Newtonian theory. Hence, the case study of MOND provides crucial results for the general debate on inter-theoretic reduction in science: MOND’s failure as a case of reduction highlights important limitations in standard accounts of limiting reduction. We respond by proposing a more refined framework for limiting reduction that introduces two additional criteria to better distinguish successful from pathological reductions. More broadly, this case illustrates how analysing reduction-wise justification can serve as a powerful tool for evaluating the validity of novel theories that are not yet empirically established
Three Problems for Predictive Policy Advice
Get PDFScientific policy advice has become a key input for rational decision making. In this article, we address three fundamental challenges predictive policy advice is faced with and that are inextricably linked to each other. The first challenge revolves around the question of which disciplines should – and indeed can – be drawn upon in providing input for predictive policy advice. We will explore field-specific differences in (actual and attributed) predictive capabilities, unearthing practical and normative challenges for science-informed policy. The second problem concerns navigating inherent, but often implicit, value influences in predictive policy advice. We will address issues of value transparency and legitimacy and highlight shortcomings in current practice. Finally, we will discuss the issue of model performativity as a deep problem for predictive policy advice. We will focus in particular on the question of how performative models ought to be evaluated and drawn upon for predictive policy advice. In the concluding part of the article, we will highlight connections among these challenges and suggest ways forwar