Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Matheology § 175
Replies: 3   Last Post: Dec 10, 2012 1:54 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
mueckenh@rz.fh-augsburg.de

Posts: 14,648
Registered: 1/29/05
Matheology § 175
Posted: Dec 9, 2012 5:06 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Matheology § 175

Until then, no one envisioned the possibility that infinities come in
different sizes, and moreover, mathematicians had no use for ?actual
infinity.? The arguments using infinity, including the Differential
Calculus of Newton and Leibniz, do not require the use of infinite
sets.
T. Jech: "Set Theory", Stanford Encyclopedia of Philosophy (2002)
http://plato.stanford.edu/entries/set-theory/

There are only countably many names.
An uncountable set of names cannot be well-ordered - because it does
not exist.
A set of numbers cannot be well-ordered unless all the numbers have
names.
This seems to contradict Cantor's diagonal argument - but only if
infinite set are complete.

Conclusion: Infinities do not come come in different sizes. In fact
mathematicians have never had use for actual infinity because they
could not. All they could is to believe that they had use for actual
infinity, i. e., for numbers that have no names and cannot be used.
That's called mathelogy.

Regards, WM



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.