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url *mueckenh*
-4
votes
Cantor and infinities
Look here into Mückenheim's source book on transfinity for over 250 sceptical voices: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, chapter V. …
- 1
-1
votes
Why was the concept of empty domains introduced?
The empty domain or empty set was introduced for formal reasons only.
Georg Cantor mentioned the empty set with some reservations and only once in all his work: "Further it is useful to have a symbol …
- 1
0
votes
Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor ...
A multitude of examples is analyzed in Mueckenheim's comprehensive Source Book on Transfinity https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. …
- 1
0
votes
Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor ...
For an overview see chapter III of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. …
- 1
0
votes
How many numbers does it take to describe conscious reality?
uncountable set of "real numbers" requires to miss the fundamental mistake in the concept of countability or "finished infinity" (for closer information see chapters V and VI of https://www.hs-augsburg.de/~mueckenh …
- 1
0
votes
Accepted
Implications of a discovered mathematics
Some important paragraphs have been translated by Mückenheim into English: See Chapter IV of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. …
- 1
2
votes
Unexplained paradox
A paradox is a result that seems self-contradictory or logically unacceptable to the layman. Usually it can be explained by experts. A self-contradictory or logically unacceptable result that cannot b …
- 1
0
votes
Is there any philosophical significance to the arithmetization of infinity?
One of several proofs collected in https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf
is this: Scrooge Mc Duck earns daily 10 enumerated dollars and spends daily 1 $. …
- 1
0
votes
Which philosophers considered mathematics an experimental science?
Who is a philosopher? I think a mathematician who ponders about this topic is at least a philosopher of mathematics. Here are three:
Mathematics is a part of physics. Physics is an experimental scien …
- 1
-1
votes
Validity of mathematical induction
set theory differing from mathematics, but the refusal of mathematical induction and Cantor's own words prove this case: Cantor said (on more than one occasion, for more see https://www.hs-augsburg.de/~mueckenh …
- 1
-3
votes
Will McDuck go bankrupt?
Let me add another aspect which might deserve attention because it is not common knowledge but very important for set theory: In set theory we can count to ω. See the evidence collected in the footnot …
- 1
1
vote
Why do mathematical Axioms work so well in science?
For debunked examples see: "Applications" of set theory in https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 124ff. …
- 1
2
votes
Is it generally taken that the thesis of Kant's first antinomy fails?
By the way the formalism of limits in set theory can be found here:
https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 55f. …
- 1