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The Mereological Foundation of Megethology

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Abstract

In Mathematics is megethology (Lewis (1993). Philosophia Mathematica, 1(1), 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification.

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Notes

  1. For an analysis of the power of mereology and plural quantification see also Geoffrey Hellman’s [8] and [10].

  2. For a general survey of mereology see [19].

  3. A general introduction to plural quantification is in [16].

  4. Hellman [7] and Feferman & Hellman [5] also incorporated primitive pairing in their systems.

  5. The situation is very similar to Zermelo’s quasi-categoricity. See on that [9].

References

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Acknowledgments

We would like to thank the referee of the JPL for the helpful comments and suggestions.

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Authors and Affiliations

  1. FISPPA Department, University of Padua, P.zza Capitaniato 3, 35139, Padova, Italy

    Massimiliano Carrara & Enrico Martino

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  1. Massimiliano Carrara
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  2. Enrico Martino
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Correspondence to Massimiliano Carrara.

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Carrara, M., Martino, E. The Mereological Foundation of Megethology. J Philos Logic 45, 227–235 (2016). https://doi.org/10.1007/s10992-015-9373-7

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  • DOI: https://doi.org/10.1007/s10992-015-9373-7

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