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Multiverse and the Society

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Handbook of the History and Philosophy of Mathematical Practice

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Abstract

This chapter follows the philosophical line of mathematical pluralism to make two points: that if there is a view that mathematics is a basis for sciences including social sciences and if there is a pluralism in mathematics, then this implies that the only way to model society is a pluralist one. Along the way to this conclusion, we argue why mathematical logic is a good part of mathematics to use in modeling and, in particular, explain the use of set theory in this context.

This research was supported by the European Union Horizon 2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement No. 1010232. The author would also like to thank the Institut d’Histoire et de Philosophie des Sciences et des Techniques CNRS-Université Paris 1 Panthéon-Sorbonne, Paris, where she is an Associate Member and the School of Mathematics at the University of East Anglia in Norwich, where she holds the title of a Visiting Professor.

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Notes

  1. 1.

    In fact, Gauss was not the only one. In 1733, Giovanni Girolamo Saccheri (1733) and in 1766 Jean-Henri Lambert, separately found counter-examples to the parallel postulate (see Kagan 1974). Saccheri’s also did not quite know how to treat this discovery and it only appears implicitly in his final work, while Lambert discretely added it to the second edition of his book (Lambert 1759).

  2. 2.

    In this text the noun human is used for members of any gender identity and the pronoun he is used as a generic human pronoun as well as the masculine pronoun.

  3. 3.

    Those who claim otherwise, waging equations and statistics in their own defense, need only to consider the remarkable lack of success that such a dogmatic approach has had in various concrete contemporary situations. Modelling is hard and nobody has a monopoly.

  4. 4.

    Note that the other connectives ∨, ⇒, and ⇔, as well as the quantifier 8, can be derived from the ones given above.

  5. 5.

    Of course, this example is somewhat subjective, which is why we emphasise that like in any model where large finite numbers are treated as infinite, there is an element of fine-tuning the model to the purpose. Usually, the rule followed in applied mathematics is that a quantity that is being treated as infinite is indeed infinite in some reasonably taken limit. In our case that limit would be the limit taken over the growing number of inhabitants of the planet.

  6. 6.

    One needs the axioms of Union and Pairing to verify that for any set x, the resulting set S(x) is a set.

  7. 7.

    The existence of the unique empty set \( \emptyset{0} \) used in the formulation of the Axiom is justifiable by the axioms above.

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Author information

Authors and Affiliations

  1. IRIF(CNRS & Université de Paris-Cité), Paris, France

    Mirna Džamonja

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  1. Mirna Džamonja
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Correspondence to Mirna Džamonja .

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Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. George Washington University, Washington, D.C., USA

    Michele Friend

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Džamonja, M. (2024). Multiverse and the Society. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-031-40846-5_29

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