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4 - The Naïve Conception

Published online by Cambridge University Press:  09 January 2020

Luca Incurvati
Affiliation:
Universiteit van Amsterdam
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Summary

The chapter discusses the naïve conception of set and criticizes attempts to rehabilitate it by modifying the logic of set theory. The focus is on the proposal that the Naïve Comprehension Schema – which formally captures the thesis that every condition determines a set – is to be saved by adopting a paraconsistent logic. Three strategies for doing so are distinguished: the material strategy, the relevant strategy and the model-theoretic strategy. It is shown that these strategies lead to set theories that are either too weak or ad hoc or give up on the idea that sets are genuinely extensional entities.

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Publisher: Cambridge University Press
Print publication year: 2020

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  • The Naïve Conception
  • Luca Incurvati, Universiteit van Amsterdam
  • Book: Conceptions of Set and the Foundations of Mathematics
  • Online publication: 09 January 2020
  • Chapter DOI: https://doi.org/10.1017/9781108596961.005
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  • The Naïve Conception
  • Luca Incurvati, Universiteit van Amsterdam
  • Book: Conceptions of Set and the Foundations of Mathematics
  • Online publication: 09 January 2020
  • Chapter DOI: https://doi.org/10.1017/9781108596961.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • The Naïve Conception
  • Luca Incurvati, Universiteit van Amsterdam
  • Book: Conceptions of Set and the Foundations of Mathematics
  • Online publication: 09 January 2020
  • Chapter DOI: https://doi.org/10.1017/9781108596961.005
Available formats
×