Which Mathematical Objects are Referred to by the Enhanced Indispensability Argument?

Discussion
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Abstract

This discussion note points to some verbal imprecisions in the formulation of the Enhanced Indispensability Argument (EIA). The examination of the plausibility of alternative interpretations reveals that the argument’s minor premise should be understood as a particular, not a universal, statement. Interpretations of the major premise and the conclusion oscillate between de re and de dicto readings. The attempt to find an appropriate interpretation for the EIA leads to undesirable results. If assumed to be valid and sound, the argument warrants the rationality of the belief in an unusual variant of Platonism (partial and mutable domain admitting gaps and gluts). On the other hand, if taken as it stands, the argument is either invalid or is unsound or does not support the mathematical Platonism. Thus, the EIA in its present form cannot serve as a useful device for the Platonist.

Keywords

Platonism Enhanced Indispensability Argument Mathematical explanation de re and de dicto statements 

Notes

Acknowledgements

Even though it is not common for an author to express gratitude to the co-author, it is however necessary to do so under present circumstances. Namely, Berislav Žarnić, professor at the University of Split, passed away on 25th May 2017, at the time when our joint paper was being under review of the Journal for General Philosophy of Science. Being his co-author, colleague and an old friend, I owe him a profound gratitude for the effort he invested in this work, feeling no less profound regret for the fact that he did not see it published.

References

  1. Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114, 223–238.CrossRefGoogle Scholar
  2. Baker, A. (2009). Mathematical explanation in science. The British Journal for the Philosophy of Science, 60, 611–633.CrossRefGoogle Scholar
  3. Baker, A. (2012). Science-driven mathematical explanation. Mind, 121, 243–267.CrossRefGoogle Scholar
  4. Colyvan, M. (2001). The indispensability of mathematics. Oxford: Oxford University Press.CrossRefGoogle Scholar
  5. Molinini, D. (2016). Evidence, explanation and enhanced indispensability. Synthese, 193, 403–422.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Philosophy, Faculty of PhilosophyUniversity of MontenegroNikšićMontenegro
  2. 2.Research Center for Logic, Epistemology and Philosophy of Science, Faculty of Humanities and Social SciencesUniversity of SplitSplitCroatia
  3. 3.Filozofski fakultetSplitCroatia

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