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  1. A Stochastic Model of Mathematics and Science.David H. Wolpert & David B. Kinney - 2024 - Foundations of Physics 54 (2):1-67.
    We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves stochastic mathematical systems (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a “calibration” relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an “oracle” SMS that can be interpreted as (...)
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  • Quantum Epistemology and Constructivism.Patrick Fraser, Nuriya Nurgalieva & Lídia del Rio - 2023 - Journal of Philosophical Logic 52 (6):1561-1574.
    Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If quantum theory correctly describes the structure of the physical world, and if quantum theoretic inferences about which measurement outcomes will be observed with unit probability count as knowledge, we demonstrate that constructivism cannot be upheld. Our derivation is compatible with both intuitionistic and quantum propositional logic. This result is implied by (...)
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  • Naturalized metaphysics or displacing metaphysicians to save metaphysics.Rasmus Jaksland - 2023 - Synthese 201 (6):1-25.
    Naturalized metaphysics aims to establish justified metaphysical claims, where metaphysics is meant to carry its usual significance, while avoiding the traditional methods of metaphysics—a priori reasoning, conceptual analysis, intuitions, and common sense—which naturalized metaphysics argues are not epistemically probative. After offering an explication of what it means to do metaphysics, this paper argues that naturalized metaphysics, at the outset, is hospitable to doing metaphysics. The underdetermination of metaphysics by science, however, changes the picture. Naturalized metaphysics has to break this underdetermination, (...)
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  • Resolving the Singularity by Looking at the Dot and Demonstrating the Undecidability of the Continuum Hypothesis.Abhishek Majhi - 2024 - Foundations of Science 29 (2):405-440.
    Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose. The _hypothesis_ that founds the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the Einstein’s equations is one of the assumptions that underlies the proof of the singularity theorem, therefore, the above (...)
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  • The Open Past in an Indeterministic Physics.Nicolas Gisin & Flavio Del Santo - 2022 - Foundations of Physics 53 (1):1-11.
    Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, while (...)
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  • Potentiality realism: a realistic and indeterministic physics based on propensities.Flavio Del Santo & Nicolas Gisin - 2023 - European Journal for Philosophy of Science 13 (4):1-16.
    We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain) as elements of reality, thereby complementing the actual properties taken by physical variables. This allows one to naturally reconcile realism and fundamental indeterminism in any theoretical framework. We discuss our specific interpretation of propensities, that require them to depart from being probabilities at the formal level, though (...)
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  • Relational Quantum Mechanics and Intuitionistic Mathematics.Charles B. Crane - 2024 - Foundations of Physics 54 (3):1-12.
    We propose a model of physics that blends Rovelli’s relational quantum mechanics (RQM) interpretation with the language of finite information quantities (FIQs), defined by Gisin and Del Santo in the spirit of intuitionistic mathematics. We discuss deficiencies of using real numbers to model physical systems in general, and particularly under the RQM interpretation. With this motivation for an alternative mathematical language, we propose the use of FIQs to model the world under the RQM interpretation, wherein we view the propensities that (...)
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