IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0346-0405-5_11.html

Concepts and contrasts: Hermann Grassmann and Bernard Bolzano

In: From Past to Future: Graßmann's Work in Context

Author

Listed:
  • Steve Russ

    (University of Warwick, Department of Computer Science)

Abstract

Both Bolzano and Grassmann worked intensively for much of their lives on mathematical concepts – both technical concepts within mathematics such as line, number, function, continuity, extension, and broader concepts about mathematics such as its nature and classification, and what should be understood by a “proof”. In this paper we shall compare some of the ways in which they worked with concepts because, while strikingly different, both scholars were led, through their analysis and development of concepts, often in a philosophical context, into fruitful new mathematics which was decades ahead of its time. The case is all the more interesting because of the close contextual parallels between the men which throws their differing treatment of concepts into greater relief. Furthermore, for Grassmann one of the major driving metaconcepts of his thinking about, and within,mathematics appears to have been the very concept of contrast, or of opposition (Gegensatz).

Suggested Citation

  • Steve Russ, 2011. "Concepts and contrasts: Hermann Grassmann and Bernard Bolzano," Springer Books, in: Hans-Joachim Petsche & Albert C. Lewis & Jörg Liesen & Steve Russ (ed.), From Past to Future: Graßmann's Work in Context, pages 117-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0346-0405-5_11
    DOI: 10.1007/978-3-0346-0405-5_11
    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:978-3-0346-0405-5_11. 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.