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Ethics and the Continuum Hypothesis

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Book cover Algorithms and Complexity in Mathematics, Epistemology, and Science

Part of the book series: Fields Institute Communications ((FIC,volume 82))

Abstract

Mathematics and ethics are surprisingly similar. To some extent this is obvious, since neither looks to laboratory experiments nor sensory experience of any kind as a source of evidence. Both are based on reason and something commonly call “intuition.” This is not all. Interestingly, mathematics and ethics both possess similar distinctions between pure and applied. I explore some of the similarities and draw methodological lessons from them. We can use these lessons to explore how and why Freiling’s refutation of the continuum hypothesis might be justified.

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Notes

  1. 1.

    There are a few notable exceptions, such as some of the authors in [12], and especially [2], [5], and [13]. These three take a different view from mine.

  2. 2.

    For more on this see [1].

  3. 3.

    See Borwein’s home page for his several books, articles, and various projects: https://www.carma.newcastle.edu.au/jon/.

  4. 4.

    For more detail, see [19], an early and influential source.

  5. 5.

    Rob Corless points out that with computers we can “zoom in” on a function and get a better look at the slope. So, (7) is arguably not so metaphorical, after all.

References

  1. Brown JR (2017) Proofs and guarantees. Math Intell 39(4):47–50. https://doi.org/10.1007/s00283-017-9730-1

    Article  MathSciNet  Google Scholar 

  2. Clark-Doane (2012) Morality and mathematics. Ethics 122:313–340

    Article  Google Scholar 

  3. Cohen P (1963) Set theory and the continuum hypothesis. W.A. Benjamin, New York

    Google Scholar 

  4. Foot P (1958) Moral arguments. Mind 67(268):502–513

    Article  Google Scholar 

  5. Franklin J (2004) On the parallel between mathematics and morals. Philosophy 79:97–119

    Article  Google Scholar 

  6. Freiling C (1986) Axioms of symmetry: throwing darts at the real number line. J Symb Log 51:190–200

    Article  MathSciNet  Google Scholar 

  7. Gödel K (1938) The consistency of the axiom of choice and the generalized continuum hypothesis. Proc Natl Acad Sci U S A 24:556–557

    Article  Google Scholar 

  8. Gödel K (1939) Consistency proof of the axiom of choice and the generalized continuum hypothesis. Proc Natl Acad Sci U S A 25:220–224

    Article  Google Scholar 

  9. Greene JD, Sommerville RB, Nystrom LE, Darley JM, Cohen JD (2001) An fMRI investigation of emotional engagement in moral judgment. Science 293:2105–2108

    Article  Google Scholar 

  10. Hardy H (1944) A mathematician’s apology. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  11. Kac M (1966) Can one hear the shape of a drum. Am Math Mon 73(4, part 2):1–23

    Article  MathSciNet  Google Scholar 

  12. Leibowitz UD, Sinclair N (eds) (2016) Explanation in ethics and mathematics: debunking and dispensability. Oxford University Press, Oxford

    MATH  Google Scholar 

  13. Leng M (2016) Naturalism and placement, or, what should a good Quinean say about mathematical and moral truth? Proc Aristot Soc cxvi, Part 3. https://doi.org/10.1093/arisoc/aow014

    Article  Google Scholar 

  14. Manin Y (2002) Georg Cantor and his heritage. arXiv:math.AG/0209244 v1

    Google Scholar 

  15. Mumford D (2000) Dawning of the age of stochasticity. In: Arnold V (ed) Mathematics: frontiers and perspectives. American Mathematical Society, New York

    Google Scholar 

  16. Spivak M (1994) Calculus. Publish or Perish

    Google Scholar 

  17. Thomson JJ (1971) A defense of abortion. Philos Public Aff 1(1):47–66

    Google Scholar 

  18. Thurston W (1994) On proof and progress in mathematics. Bull Am Math Soc 30(2):161–174

    Article  MathSciNet  Google Scholar 

  19. Williams B (1985) Ethics and the limits of philosophy. Harvard University Press, Cambridge

    Google Scholar 

Further Reading

  • Brown JR (1999/2008) Philosophy of mathematics: a contemporary introduction to the world of proofs and pictures, 2nd edn. Routledge, London/New York

    Book  Google Scholar 

  • Elstein DY, Hurka T (2009) From thick to thin: two moral reduction plans. Can J Philos 39(4):5-5-536

    Article  Google Scholar 

  • Gödel K (1951) Some basic theorems of the foundations of mathematics and their implications. Reprinted in Feferman, et al. Gödel: collected works, vol III, Oxford (1995)

    Google Scholar 

  • Gödel K (1964) What is Cantor’s continuum problem? Reprinted in Feferman et al. Gödel: collected works, vol II, Oxford (1995)

    Google Scholar 

  • Hurka T (2014) British ethical theorists from Sidgwick to Ewing. Oxford University Press, Oxford

    Google Scholar 

  • Jaffe A, Quinn F (1993) ‘Theoretical mathematics’: toward a cultural synthesis of mathematics and theoretical physics. Bull Am Math Soc 29(1):1–13

    Google Scholar 

  • Moore GE (1903) Principia ethica. Cambridge University Press, Cambridge

    Google Scholar 

  • Robinson JA (2000) Proof= Guarantee+ Explanation. In: Intellectics and computational logic (to Wolfgang Bibel on the occasion of his 60th birthday. Kluwer, Dordrecht, pp 277–294

    Google Scholar 

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Acknowledgements

Thanks to Paul Bartha, Philipp Berghofer, Mark Colyvan, Rob Corless, Nic Fillion, Chris Freiling, Tom Hurka, Tracy Issacs, Mary Leng, Kathleen Okruhlik, Debbie Roberts, Zvonimir Šikić, John Sipe, Alan Sokal, and Harald Wiltsche for discussions of various issues including information about ethical intuitions and the thin-thick distinction. Thanks also to an anonymous referee who provided several useful remarks. Finally, I am grateful to various audiences who heard versions of this material, especially at the ACMES conference at The University of Western Ontario, May 12–15, 2016.

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Authors and Affiliations

  1. Department of Philosophy, University of Toronto, Toronto, ON, Canada

    James Robert Brown

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  1. James Robert Brown
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Correspondence to James Robert Brown .

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Editors and Affiliations

  1. Department of Philosophy, Simon Fraser University Philosophy, Burnaby, BC, Canada

    Nicolas Fillion

  2. The Rotman Institute of Philosophy, The Ontario Research Center for Computer Algebra and The School of Mathematical and Statistical Sciences, The University of Western Ontario, London, ON, Canada

    Robert M. Corless

  3. Department of Physics & Computer Science, Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

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Brown, J.R. (2019). Ethics and the Continuum Hypothesis. In: Fillion, N., Corless, R., Kotsireas, I. (eds) Algorithms and Complexity in Mathematics, Epistemology, and Science. Fields Institute Communications, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9051-1_1

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