IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-0967-6_31.html
   My bibliography  Save this book chapter

Quantification Theory in a Nutshell

In: PAUL HALMOS Celebrating 50 Years of Mathematics

Author

Listed:
  • Raymond M. Smullyan

    (Indiana University, Department of Philosophy)

Abstract

I first knew Professor Halmos when I was a student at the University of Chicago. I recall sitting in on a course he gave on axiomatic set theory and that towards the beginning he announced that he was about to prove the existence of the empty set. I, brash student that I was, interrupted him and said: “But that’s obvious! If there wasn’t an empty set, then the set of all empty sets would be empty and we would have a contradiction! ”I was very proud of myself, until Halmos wisely answered: “That’s a bad pun! ”I then realized that my fallacy consisted in the unwarranted assumption that there was such a thing as the set of all empty sets. [Incidentally, if one took this assumption as an axiom, instead of the weaker axiom that there exists a set, then the existence of the empty set would follow (by the very argument I gave) without use of the separation axiom (aussunderungsaxiom) necessary for the usual proof.

Suggested Citation

  • Raymond M. Smullyan, 1991. "Quantification Theory in a Nutshell," Springer Books, in: John H. Ewing & F. W. Gehring (ed.), PAUL HALMOS Celebrating 50 Years of Mathematics, pages 297-304, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0967-6_31
    DOI: 10.1007/978-1-4612-0967-6_31
    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

    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:978-1-4612-0967-6_31. 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.