Review of Mueckenheims book.

I reveived Wolfgam Mueckenheims book and agreed to make a review. Here
the basic part. The full review will be available at:
<http://www.cwi.nl/~***/english/mathematics/mueck>

Book:
Die Mathematik des Unendlichen
Wolfgang Mückenheim
Shaker Verlag, Aachen, Germany, 2006, ISBN 3-8322-5587-7.

The book contains two parts.

The first part are the initial eight chapters, the second part
contains the last two chapters. They are quite different in content, so
I do split the review in two parts (note that I have not yet completed
the second part, it takes a lot of time). The review of the first part
will be posted as a follow-up to this article, the review of the second
part will not be posted, but is available through the following link:
<http://www.cwi.nl/~***/english/mathematics/mueck/book2.html>
It will be updated while I read more.

My initial conclusion is that chapters 1 to 8 can serve quite well in
a course on the history of set theory. The historical context is set
out extremely well. Also the outlining of current set theory appears
to be adequate. The second part (at least what I have read until now)
is nonsense. It consists entirely of misunderstandings, bad logic,
ill-defined objects and whatever you can think. Moreover, I fail to
see why the authors needs over ten examples to show that actual infinity
leads to an inconsistency. Only one would be sufficient, if it were
valid. The lack of mathematical content in chapter 9 is shocking. And
I think it is even worse in chapter 10 (which appears to be more
philosophical than mathematical).
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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