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Romanian Studies in Philosophy of Science pp 167–179Cite as

Quantum Mechanics: Knocking at the Gates of Mathematical Foundations

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 313))

Abstract

Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics.

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Notes

  1. 1.

    I’m grateful to Prof. I. Pârvu for bringing to my attention Mac Lane’s article (Mac Lane, 1981) which shares a similar view of mathematical concepts.

  2. 2.

    Kochen’s distinction between intrinsic and extrinsic properties is different from the more well-known one discussed in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/intrinsic-extrinsic/.

  3. 3.

    Due to the finite experimental precision, the outcome of a measurement is always a rational number. However, it is generally assumed that the underlying physical property is continuous and takes values in a subset of \(\mathbb{R}\).

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Acknowledgements

I am grateful to Ilie Pârvu, Cristi Stoica and Iulian Toader for discussions and critical comments of the manuscript.

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Authors and Affiliations

  1. Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, 077125, Bucharest–Măgurele, Romania

    Radu Ionicioiu

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  1. Radu Ionicioiu
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Correspondence to Radu Ionicioiu .

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Editors and Affiliations

  1. Department of Theoretical Philosophy, University of Bucharest, Bucharest, Romania

    Ilie Pȃrvu

  2. Department of Philosophy, History, Culture and Art Studies, University of Helsinki, Helsinki, Finland

    Gabriel Sandu

  3. Department of Theoretical Philosophy, University of Bucharest, Bucharest, Romania

    Iulian D. Toader

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Ionicioiu, R. (2015). Quantum Mechanics: Knocking at the Gates of Mathematical Foundations. In: Pȃrvu, I., Sandu, G., Toader, I. (eds) Romanian Studies in Philosophy of Science. Boston Studies in the Philosophy and History of Science, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-319-16655-1_11

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