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Multiversism and Concepts of Set : How Much Relativism Is Acceptable?

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2016

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https://doi.org/10.1007/978-3-319-31644-4_11
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BOCCUNI, Francesca, ed., Andrea SERENI, ed.. Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics. Cham: Springer, 2016, pp. 189-209. Boston Studies in the Philosophy and History of Science. 318. ISBN 978-3-319-31642-0. Available under: doi: 10.1007/978-3-319-31644-4_11

Zusammenfassung

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position.

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100 Philosophie

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Philosophy of mathematics, Set theory, Foundations of mathematics, Multiverse

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ISO 690BARTON, Neil, 2016. Multiversism and Concepts of Set : How Much Relativism Is Acceptable?. In: BOCCUNI, Francesca, ed., Andrea SERENI, ed.. Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics. Cham: Springer, 2016, pp. 189-209. Boston Studies in the Philosophy and History of Science. 318. ISBN 978-3-319-31642-0. Available under: doi: 10.1007/978-3-319-31644-4_11
BibTex
@incollection{Barton2016Multi-52679,
  year={2016},
  doi={10.1007/978-3-319-31644-4_11},
  title={Multiversism and Concepts of Set : How Much Relativism Is Acceptable?},
  number={318},
  isbn={978-3-319-31642-0},
  publisher={Springer},
  address={Cham},
  series={Boston Studies in the Philosophy and History of Science},
  booktitle={Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics},
  pages={189--209},
  editor={Boccuni, Francesca and Sereni, Andrea},
  author={Barton, Neil}
}
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