IDEAS home Printed from https://ideas.repec.org/p/trn/utwpas/1015.html
   My bibliography  Save this paper

Varieties of Mathematics in Economics- A Partial View

Author

Listed:
  • K. Vela Velupillai
  • Shu G. Wang

Abstract

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.

Suggested Citation

  • K. Vela Velupillai & Shu G. Wang, 2010. "Varieties of Mathematics in Economics- A Partial View," ASSRU Discussion Papers 1015, ASSRU - Algorithmic Social Science Research Unit.
    • Handle: RePEc:trn:utwpas:1015
    as

    Download full text from publisher

    File URL: http://www.assru.economia.unitn.it/files/DP15.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samuelson, P. A., 1974. "Remembrances of Frisch," European Economic Review, Elsevier, vol. 5(1), pages 7-23, June.
    2. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    2. John Cotrina & Javier Zúñiga, 2018. "Time-Dependent Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1054-1064, December.
    3. Förster, Manuel & Riedel, Frank, 2016. "Distorted Voronoi languages," Center for Mathematical Economics Working Papers 458, Center for Mathematical Economics, Bielefeld University.
    4. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    5. Gara Afonso & Ricardo Lagos, 2015. "The Over‐the‐Counter Theory of the Fed Funds Market: A Primer," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(S2), pages 127-154, June.
    6. Takeshi Nishimura, 2019. "Informed Principal Problems in Bilateral Trading," Papers 1906.10311, arXiv.org, revised Feb 2022.
    7. Bilancini, Ennio & Boncinelli, Leonardo, 2010. "Single-valuedness of the demand correspondence and strict convexity of preferences: An equivalence result," Economics Letters, Elsevier, vol. 108(3), pages 299-302, September.
    8. Said, Maher, 2012. "Auctions with dynamic populations: Efficiency and revenue maximization," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2419-2438.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    10. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    11. Vincent Anesi, 2009. "Moral hazard and free riding in collective action," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 197-219, February.
    12. Boháček, Radim & Kejak, Michal, 2018. "Optimal government policies in models with heterogeneous agents," Journal of Economic Theory, Elsevier, vol. 176(C), pages 834-858.
    13. Georg Nöldeke & Larry Samuelson, 2015. "Investment and Competitive Matching," Econometrica, Econometric Society, vol. 83(3), pages 835-896, May.
    14. Kets, W., 2008. "Beliefs in Network Games (Revised version of CentER DP 2007-46)," Other publications TiSEM a08e38fd-6b00-4233-94ce-3, Tilburg University, School of Economics and Management.
    15. Gersbach, Hans & Mamageishvili, Akaki & Tejada, Oriol, 2021. "The effect of handicaps on turnout for large electorates with an application to assessment voting," Journal of Economic Theory, Elsevier, vol. 195(C).
    16. JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised May 2023.
    17. K. Vela Velupillai, 2013. "Towards an Intuitionistic Constructive Mathematical Economics," ASSRU Discussion Papers 1304, ASSRU - Algorithmic Social Science Research Unit.
    18. Antonin Macé, 2017. "Voting with evaluations: characterizations of evaluative voting and range voting," Working Papers halshs-01222200, HAL.
    19. Kumaraswamy Velupillai, 2003. "Economics and the complexity vision: chimerical partners or elysian adventurers," Department of Economics Working Papers 0307, Department of Economics, University of Trento, Italia.
    20. Kets, W., 2007. "Beliefs in Network Games (Replaced by CentER DP 2008-05)," Other publications TiSEM 1c11352b-a9fb-4e2f-9bb0-d, Tilburg University, School of Economics and Management.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:trn:utwpas:1015. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: assru.tm@gmail.com (email available below). General contact details of provider: https://edirc.repec.org/data/detreit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.