Policies, Technology and Markets: Legal Implications of Their Mathematical Infrastructures

  • Marcus Faro de CastroEmail author


The paper discusses legal implications of the expansion of practical uses of mathematics in social life. Taking as a starting point the omnipresence of mathematical infrastructures underlying policies, technology and markets, the paper proceeds by attending to relevant materials offered by general philosophy, legal philosophy, and the history and philosophy of mathematics. The paper suggests that the modern transformation of mathematics and its practical applications have spurred the emergence of multiple useful technologies and forms of social interaction but have impoverished access to meanings originating in the lifeworld. The paper also argues that, as part of devices of interest aggregation and expert networks, mathematical infrastructures can be scrutinized by a revised form of legal practice that subjects them to legal critique and reconstruction in order to overcome conditions that have eroded the moral self-awareness of individuals and communities and their existential meanings.


Indicators Jurisprudence Mathematics Philosophy 



  1. Adams, Marilyn McCord. 1982. Universals in the early fourteenth century. In The Cambridge history of later medieval philosophy: From the rediscovery of Aristotle to the disintegration of scholasticism, 1100–1600, ed. Norman Kretzmann, Anthony Kenny, and Jan Pinborg, 411–439. Cambridge; New York: Cambridge University Press.CrossRefGoogle Scholar
  2. Aertsen, Jan. 1996. Medieval philosophy and the transcendentals: The case of Thomas Aquinas. Leiden; New York: E.J. Brill.Google Scholar
  3. Amariles, David Restrepo. 2015. Legal indicators, global law and legal pluralism: An introduction. The Journal of Legal Pluralism and Unofficial Law 47(1): 9–21. Scholar
  4. Amariles, David Restrepo. 2017. Transnational legal indicators: The missing link in a new era of law and development. In Law and policy in Latin America: Transforming courts, institutions, and rights, ed. Pedro Fortes, Larissa Boratti, Andrés L. Lleras, and Tom Gerald Daly, 95–111. London: Palgrave Macmillan.CrossRefGoogle Scholar
  5. Arnoldi, Jakob. 2016. Computer algorithms, market manipulation and the institutionalization of high frequency trading. Theory, Culture & Society 33(1): 29–52. Scholar
  6. Berdahl, Robert M. 1988. The politics of the Prussian Nobility: The development of a conservative ideology, 1770–1848. Princeton: Princeton University Press.CrossRefGoogle Scholar
  7. Berkowitz, Roger. 2010. The gift of science: Leibniz and the modern legal tradition. New York: Fordham University Press.Google Scholar
  8. Berman, Harold Joseph. 1983. Law and revolution: The formation of the western legal tradition, vol. 8. Cambridge, MA: Harvard Univ. Press.Google Scholar
  9. Blackstone, William. 1893. Commentaries on the laws of England, vol. 2. Philadelphia: J.B. Lippincot Company. Accessed 7 December 2018.
  10. Blaug, Mark. 2003. The formalist revolution of the 1950s. Journal of the History of Economic Thought 25(2): 145–156. Scholar
  11. Bloch, Ernst. 1986. Natural law and human dignity. Cambridge, MA: MIT Press.Google Scholar
  12. Boyer, Carl B. 1968. A history of mathematics. New York: Wiley.Google Scholar
  13. Broome, André, and Joel Quirk. 2015. Governing the world at a distance: The practice of global benchmarking. Review of International Studies 41(5): 819–841. Scholar
  14. Büthe, Tim, and Walter Mattli. 2013. The new global rulers: The privatization of regulation in the world economy. Princeton, NJ: Princeton University Press.Google Scholar
  15. Callon, Michel. 1998. An essay on framing and overflowing: Economic externalities revisited by sociology. In The laws of the markets, ed. Michel Callon, 244–269. Oxford; Malden, MA: Blackwell Publishers/Sociological Review.Google Scholar
  16. Callon, Michel, Pierre Lascoumes, and Yannick Barthe. 2009. Acting in an uncertain world: An essay on technical democracy. Cambridge, MA: MIT Press.Google Scholar
  17. Cassirer, Ernst. 1946. The myth of the state. New Haven: Yale University Press.Google Scholar
  18. Cassirer, Ernst. 1951. The philosophy of the enlightenment. Princeton: Princeton University Press.Google Scholar
  19. Cifoletti, Giovanna. 1995. La question de l’algèbre. Mathématiques et rhétorique des hommes de droit dans la France du XVIe siècle. Annales. Histoire, Sciences Sociales 50(6): 1385–1416. Scholar
  20. Cifoletti, Giovanna. 2006. From Valla to Viète: The rhetorical reform of logic and its use in early modern algebra. Early Science and Medicine 11(4): 390–423. Scholar
  21. Cohen, Edward S., and A.C. Cutler. 2013. Law, contestation, and power in the global political economy: An introduction. Oñati Socio-Legal Series 3(4): 611–621.Google Scholar
  22. Corry, Leo. 1997. The origins of eternal truth in modern mathematics: Hilbert to Bourbaki and beyond. Science in Context 10(2): 253–296. Scholar
  23. Corry, Leo. 2015. A brief history of numbers. Oxford; New York: Oxford University Press.Google Scholar
  24. Cutler, A.C. 2010. The legitimacy of private transnational governance: Experts and the transnational market for force. Socio-Economic Review 8(1): 157–185. Scholar
  25. Daston, Lorraine, and Michael Stolleis. 2008. Nature, law and natural law in early modern Europe. In Natural law and laws of nature in early modern Europe: Jurisprudence, theology, moral and natural philosophy, ed. Lorraine Daston and Michael Stolleis, 1–28. Farnham; Burlington, VT: Ashgate Pub. Company.Google Scholar
  26. Davis, Kevin E., Angelina Fisher, Benedict Kingsbury, and Sally Engle Merry (eds.). 2012. Governance by indicators: Global power through quantification and rankings. Oxford: Oxford University Press [in association with] Institute for International Law and Justice, New York University School of Law.Google Scholar
  27. Desrosières, Alain. 1990. How to make things which hold together: Social science, statistics and the state. In Discourses on society: The shaping of the social science disciplines, ed. Peter Wagner, Björn Wittrock, and Richard P. Whitley, 195–218. Dordrecht: Kluwer Academic Publishers.Google Scholar
  28. Desrosières, Alain. 2008. L’argument statistique I. Paris: Presses de l’École des Mines.Google Scholar
  29. Durand-Richard, Marie-José. 1996. L’École Algébrique Anglaise et les conditions conceptuelles et institutionelles d’un calcul symbolique comme fondement de la connaissance. In L’Europe mathématique: Histoires, mythes, identités. Librairie européenne des idées, ed. Catherine Goldstein, Jeremy Gray, and Jim Ritter, 447–477. Paris: Editions de la Maison des sciences de l’homme.Google Scholar
  30. Ferreirós, José, and Jeremy Gray. 2006. Introduction. In The architecture of modern mathematics: Essays in history and philosophy, ed. José Ferreirós Domínguez and Jeremy Gray, 1–43. Oxford; New York: Oxford University Press.Google Scholar
  31. Ferreirós Domínguez, José and Jeremy Gray (eds.). 2006. The architecture of modern mathematics: Essays in history and philosophy. Oxford; New York: Oxford University Press.Google Scholar
  32. Foucault, Michel. 1980. Power/knowledge: Selected interviews and other writings, 19721977, ed. Colin Gordon. 1st American edn. New York: Pantheon Books.Google Scholar
  33. Fourcade, Marion. 2006. The construction of a global profession: The transnationalization of economics. American Journal of Sociology 112(1): 145–194. Scholar
  34. Frans, Joachim, and Laszlo Kosolosky. 2014. Revisiting the reliability of published mathematical proofs: Where do we go next? Theoria. An International Journal for Theory, History and Foundations of Science 29(3): 345–360. Scholar
  35. Frydman, Benoît. 2014. Prendre les standards et les indicatours au sérieux. In Gouverner par les standards et les indicateurs: de Hume aux rankings. Penser le droit, vol. 23, ed. Arnaud van Waeyenberge and Benoît Frydman, 5–65. Bruxelles: Bruylant.Google Scholar
  36. Glas, Eduard. 2002. Socially conditioned mathematical change: The case of the French Revolution. Studies in History and Philosophy of Science Part A 33(4): 709–728. Scholar
  37. Glas, Eduard. 2007. Mathematics as objective knowledge and as human practice. In Perspectives on mathematical practices: Bringing together philosophy of mathematics, sociology of mathematics, and mathematics education. Logic, Epistemology, and the Unity of Science, vol. 5, ed. Bart van Kerkhove and Jean Paul van Bendegem, 25–41. Dordrecht: Springer.CrossRefGoogle Scholar
  38. Goldstein, Catherine, Jeremy Gray, and Jim Ritter (eds.). 1996. L’Europe Mathématique: Histoires, mythes, identités. Librairie européenne des idées. Paris: Editions de la Maison des Sciences de l’Homme.Google Scholar
  39. Guicciardini, Niccolò. 2006. Method versus calculus in Newton’s criticisms of Descartes and Leibniz. In Proceedings of the International Congress of Mathematicians: Madrid, August 2230, 2006, ed. Marta Sanz-Solé, Javier Soria, Juan Luis Varona, and Joan Verdera, 1719–1742. Zürich: European Mathematical Society.Google Scholar
  40. Haakonssen, Knud. 1996. Natural law and moral philosophy: From Grotius to the Scottish Enlightenment. New York: Cambridge University Press.CrossRefGoogle Scholar
  41. Haakonssen, Knud. 2006. German natural law. In The Cambridge history of eighteenth-century philosophy, ed. Knud Haakonssen, 251–290. Cambridge; New York: Cambridge University Press.CrossRefGoogle Scholar
  42. Halliday, Terence C., and Gregory C. Shaffer. 2015. Transnational legal orders. In Transnational legal orders. Cambridge Studies in Law and Society, ed. Terence C. Halliday and Gregory C. Shaffer, 3–72. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
  43. Heidegger, Martin. 1990. The end of philosophy and the task of thinking. In Basic writings: From being and time (1927) to the task of thinking (1964), ed. David Farrell Krell, 371–392. San Francisco: Harper Collins.Google Scholar
  44. Huault, Isabelle, and Hélène Rainelli-Weiss. 2011. A market for weather risk? Conflicting metrics, attempts at compromise, and limits to commensuration. Organization Studies 32(10): 1395–1419. Scholar
  45. Kant, Immanuel. 2009. Critique of pure reason. In The Cambridge edition of the works of Immanuel Kant, ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.Google Scholar
  46. Katz, Victor J. 2009. A history of mathematics: An introduction. 3rd ed. Boston: Addison-Wesley.Google Scholar
  47. Katz, Victor J., and Karen Hunger Parshall. 2014. Taming the unknown: A history of algebra from antiquity to the early twentieth century. Princeton: Princeton University Press.Google Scholar
  48. Kaye, Jeffrey. 2017. Making pervasive computing technology pervasive for health & wellness in aging. Public Policy & Aging Report 27(2): 53–61. Scholar
  49. Kennedy, Duncan. 2006. Three globalizations of law and legal thought: 1850–2000. In The new law and economic development: A critical appraisal, ed. David M. Trubek and Alvaro Santos. Cambridge; New York: Cambridge University Press.Google Scholar
  50. Kennedy, David. 2011. Some caution about property rights as a recipe for economic development. Accounting, Economics, and Law 1(1): 1–64. Scholar
  51. Kennedy, David. 2016. A world of struggle: How power, law, and expertise shape global political economy. Princeton: Princeton University Press.CrossRefGoogle Scholar
  52. Klein, Jacob. 1992. Greek mathematical thought and the origin of algebra. New York: Dover Publications.Google Scholar
  53. Koskenniemi, Martti. 2011. What use for sovereignty today? Asian Journal of International Law 1(1): 61–70. Scholar
  54. Krever, Tor. 2013. Quantifying law: Legal indicator projects and the reproduction of neoliberal common sense. Third World Quarterly 34(1): 131–150. Scholar
  55. Lang, Andrew T.F. 2013. The legal construction of economic rationalities? Journal of Law and Society 40(1): 155–171. Scholar
  56. Latour, Bruno. 2005. Reassembling the social: An introduction to actor-network-theory. Oxford; New York: Oxford University Press.Google Scholar
  57. Law, John. 2009. Actor network theory and material semiotics. In The new Blackwell companion to social theory, ed. Bryan S. Turner, 141–158. Chichester; Malden: Wiley-Blackwell.CrossRefGoogle Scholar
  58. MacKenzie, Donald A. 1993. Negotiating arithmetic, constructing proof: The sociology of mathematics and information technology. Social Studies of Science 23(1): 37–65. Scholar
  59. MacKenzie, Donald A. 2006. An engine, not a camera: How financial models shape markets. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  60. Maier, Charles. 1981. ‘Fictitious bonds… of wealth and law’: On the theory and practice of interest representation. In Organizing interests in Western Europe: Pluralism, corporatism, and the transformation of politics. Cambridge Studies in Modern Political Economies, ed. Suzanne Berger, 27–61. Cambridge; New York: Cambridge University Press.Google Scholar
  61. Malinovsky, Mikhail, Alexey Solntsev, Anastasia Juravleva, and Slavomir Makovski. 2017. Estimation method of nonresident vehicle fleet inflow influencing road traffic safety in Megalopolis. Transportation Research Procedia 20: 751–755. Scholar
  62. Mancosu, Paolo (ed.). 2008. The philosophy of mathematical practice. Oxford; New York: Oxford University Press.Google Scholar
  63. Merry, Sally Engle. 2011. Measuring the world: Indicators, human rights, and global governance. Current Anthropology 52(S3): S83–S95. Scholar
  64. Merry, Sally Engle, Kevin E. Davis, and Benedict Kingsbury (eds.). 2015. The quiet power of indicators: Measuring governance, corruption, and the rule of law. Cambridge Studies in Law and Society. New York, NY: Cambridge University Press.Google Scholar
  65. Millo, Yuval. 2007. Making things deliverable: The origins of index-based derivatives. The Sociological Review 55(2_suppl): 196–214. Scholar
  66. Mirowski, Philip. 2002. Machine dreams: Economics becomes a cyborg science. Cambridge; New York: Cambridge University Press.Google Scholar
  67. Mirowski, Philip. 2012. The unreasonable efficacy of mathematics in modern economics. In Philosophy of economics. Handbook of the Philosophy of Science, vol. 13, ed. Uskali Mäki, 159–197. Amsterdam: North Holland (an imprint of Elsevier).Google Scholar
  68. Morgan, Mary. 2003. Economics. In The Cambridge history of science: The modern social sciences, vol. 7, ed. Theodore M. Porter and Dorothy Ross, 275–305. Cambridge; New York: Cambridge University Press.CrossRefGoogle Scholar
  69. Muniesa, Fabian, Yuval Millo, and Michel Callon. 2007. An introduction to market devices. The Sociological Review 55(2_suppl): 1–12. Scholar
  70. Pasquale, Frank. 2015. The black box society: The secret algorithms that control money and information. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  71. Perry-Kessaris, Amanda. 2011. Prepare your indicators: Economics imperialism on the shores of law and development. International Journal of Law in Context 7(4): 401–421. Scholar
  72. Plato. 2000. The Republic. Trans. Tom Griffith. Cambridge; New York: Cambridge University Press.Google Scholar
  73. Porter, Theodore M. 1994. Probability, statistics and the social sciences. In Companion encyclopedia of the history and philosophy of the mathematical sciences, ed. Ivor Grattan-Guinness, 1341–1350. London: Routledge.Google Scholar
  74. Porter, Theodore M. 1995. Trust in numbers: The pursuit of objectivity in science and public life. Princeton, N.J: Princeton University Press.Google Scholar
  75. Quack, Sigrid. 2010. Law, expertise and legitimacy in transnational economic governance: An introduction. Socio-Economic Review 8(1): 3–16. Scholar
  76. Rahman, K. Sabeel. 2018. The new utilities: Private power, social infrastructure, and the revival of the public utility concept. Cardozo Law Review 39: 1621–1689.Google Scholar
  77. Robson, Eleanor, and Jacqueline A. Stedall (eds.). 2009. The Oxford handbook of the history of mathematics. Oxford Handbooks. Oxford; New York: Oxford University Press.Google Scholar
  78. Sandmo, Agnar. 2011. Economics evolving: A history of economic thought. Princeton, NJ: Princeton University Press.Google Scholar
  79. Santos, Alvaro. 2006. The World Bank’s uses of the ‘Rule of Law’ promise in economic development. In The new law and economic development: A critical appraisal, ed. David M. Trubek and Alvaro Santos, 253–300. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  80. Scattola, Merio. 1991. Models in history of natural law. Ius Commune, Zeitschrift für Europäische Rechtsgeschichte XXVIII: 91–159.Google Scholar
  81. Schubring, Gert. 1996. Changing cultural and epistemological views on mathematics and different institutional contexts in nineteenth-century Europe. In L’Europe mathématique: Histoires, mythes, identités, ed. Catherine Goldstein, Jeremy Gray, and Jim Ritter, 363–388. Paris: Editions de la Maison des Sciences de l’Homme. Librairie européenne des idées.Google Scholar
  82. Serfati, Michel. 2010. Symbolic revolution, scientific revolution: Mathematical and philosophical aspects. In Philosophical aspects of symbolic reasoning in early modern mathematics. Studies in Logic, vol. 26, ed. Albrecht Heeffer and Maarten Van Dyck, 103–122. London: College Publications.Google Scholar
  83. Snapper, Ernst. 1979. The three crises in mathematics: Logicism, intuitionism and formalism. Mathematics Magazine 52(4): 207–216.CrossRefGoogle Scholar
  84. Stedall, Jacqueline A. 2012. The history of mathematics: A very short introduction. Very Short Introductions, vol. 305. Oxford; New York: Oxford University Press.CrossRefGoogle Scholar
  85. Stukalin, Dmitriy, and Werner H. Schmidt. 2011. Some applications of optimal control in sustainable fishing in the Baltic Sea. Applied Mathematics 2(7): 854–865. Scholar
  86. Sullivan, C., and J. Meigh. 2003. Access to water as a dimension of poverty: The need to develop a water poverty index as a tool for poverty reduction. In Water development and poverty reduction, ed. İ.H. Olcay Ünver, Rajiv K. Gupta, and Ayşegül Kibaroğlu, 31–52. New York: Springer.CrossRefGoogle Scholar
  87. Supiot, Alain. 2012. The spirit of Philadelphia: Social justice vs. the total market. London, New York: Springer.Google Scholar
  88. Supiot, Alain. 2017. Governance by numbers: The making of a legal model of allegiance. Hart Studies in Comparative Public Law, vol. 20. Oxford, Portland, Oregon: Hart Publishing.Google Scholar
  89. Tierney, Brian. 2004. The idea of natural rights—Origins and persistence. Northwestern Journal of International Human Rights 2(1): 2–12.Google Scholar
  90. Vamvacas, Constantine J. 2009. The founders of Western thought—The Presocratics: A diachronic parallelism. New York, Philadelphia: Springer Science & Business Media.CrossRefGoogle Scholar
  91. Van Kerkhove, Bart and Jean Paul van Bendegem (eds.). 2007. Perspectives on mathematical practices: Bringing together philosophy of mathematics, sociology of mathematics, and mathematics education. Logic, Epistemology, and the Unity of Science, vol. 5. Dordrecht: Springer.Google Scholar
  92. Wieacker, Franz. 1995. A history of private law in Europe with particular reference to Germany. Trans. Tony Weir. Oxford; New York: Clarendon Press; Oxford University Press.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of LawUniversity of Brasília (Universidade de Brasília)BrasíliaBrazil

Personalised recommendations