IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-57072-3_116.html
   My bibliography  Save this book chapter

Space and Time in the Foundations of Mathematics, or Some Challenges in the Interactions with Other Sciences

In: Handbook of the Mathematics of the Arts and Sciences

Author

Listed:
  • Giuseppe Longo

    (CNRS and Ecole Normale Supérieure, Centre Cavaillès
    Tufts University, School of Medicine)

Abstract

Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded “geometric judgments” from certainty and contributed, by this, to isolate the foundation of Mathematics from other disciplines. After the success of the logical approach, it is time to broaden our foundational tools and reconstruct, also in that respect, the interactions with other sciences. The way space (and time) organize knowledge is a cross-disciplinary issue that will be briefly examined in Mathematical Physics, Computer Science, and Biology. This programmatic paper focuses on an epistemological approach to foundations, at the core of which is the analysis of the “knowledge process,” as a constitutive path from cognitive experiences to mathematical concepts and structures. When first presented, in 2001, it opened to way to the idea that phylogenetic trajectories, in biology, co-construct the space of possibilities, in contrast to physical theories which assume a pregiven phase space of all possible dynamics.

Suggested Citation

  • Giuseppe Longo, 2021. "Space and Time in the Foundations of Mathematics, or Some Challenges in the Interactions with Other Sciences," Springer Books, in: Bharath Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, chapter 93, pages 2459-2486, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-57072-3_116
    DOI: 10.1007/978-3-319-57072-3_116
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-319-57072-3_116. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.