Re: Das Kalenderblatt 090628

Th. Skolem:

The author [A. A. Fraenkel] is well known for his research in set
theory as well as his published textbooks in this subject. He has
previously written the book "Einleitung in die Mengenlehre" which
appeared in three editions. The last edition which was published in
1928 was reprinted in New York in 1946. Whereas "Einleitung in die
Mengenlehre" contained an exposition of classical set theory as well
as a survey of modern theoretical research in the foundations of
mathematics, Fraenkel has now decided to write the present book as an
account of the classical theory only. The modern aspects of foundation
theory will be discussed in another book under the title "Foundations
of Set Theory" which is due to appear about 1955. Presumably, the
reason for this division of the contents of "Einleitung in die
Mengenlehre" into two different books is that the subject matter has
grown too large. The reviewer, however, is not enthusiastic about this
division since such a textbook as the present one will be read
primarily by students and they might form the impression that
classical set theory is securely founded just as other parts of
mathematics, e.g. arithmetic. Such an impression would, however, be
misleading. If it were not so, we could omit the entire modern
foundational research without real loss to mathematics. To the
reviewer it seems unfortunate that classical set theory is developed
in a separate book so that all scruples - or almost all of them - are
reserved for the second volume. This might have the effect that most
readers of this present volume will probably not become acquainted
with the criticisms at all. It is true that some hints to such
scruples are given, but most students might not think that they are
important. On the other hand, it must be conceded that the lack of
knowledge of the results of foundational research will not mean much
to mathematicians who are not especially interested in the logical
development of mathematics.

[Th. Skolem: "Review of: A. A. Fraenkel : Abstract Set Theory.
Amsterdam & Groningen, North-Holland Publishing Company, 1953. XII +
479 pp. " Mathematica Skandinavica 1 (1953) 313.]

Und SO ist es dann ja auch gekommen! :-)
Skolem war ein weitsichtiger Mann.


Herbert
.

Relevant Pages

  • Re: Das Kalenderblatt 090705
    ... die Materie, wuesste er, dass die weltweite Forschungsgemeinschaft der ... Schon diese Ansammlung von Themen ist merkwürdig. ... Und dann kommen die Axiome von ZFC, in einer Formulierung, die den Eindruck ... The Foundations of Mathematics, 2nd ed., p.365: ...
    (de.sci.mathematik)
  • Re: Das Kalenderblatt 090705
    ... die Materie, wuesste er, dass die weltweite Forschungsgemeinschaft der ... Schon diese Ansammlung von Themen ist merkwürdig. ... Und dann kommen die Axiome von ZFC, in einer Formulierung, die den Eindruck ... The Foundations of Mathematics, 2nd ed., p.365: ...
    (de.sci.mathematik)
  • JSH: filtered, decompressed quotable version
    ... "...I'm a crackpot and I've been babbling about surrogate factoring ... But they lie about the math to protect themselves. ... It's not like the mathematics changes. ... The human species can rot and die ...
    (sci.crypt)
  • Re: Dik T. Winter says: Definition: sum{i in N} i = 0
    ... we don't just sum up numbers when investigating sequences. ... This was an apt account of the mathematics you can do. ... Dauben is a distinguished expert concerning Cantor. ... Es gibt kein aktual Unendliches, das haben die Cantorianer ...
    (sci.math)
  • Re: Set Theory: Should You Believe
    ... Norman seems to be developing an interest in foundations, ... modern mathematics and set theory. ... Such an object would contain an 'infinite amount' of information, ... "Mathematics does not require 'Axioms'. ...
    (sci.logic)