Re: Cantor Confusion

In article <1160145108.340148.16790@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> "Albrecht" <albstorz@xxxxxx> writes:
....
That's really untrue. I had read several books and papers of academics
(who do not post in this or the german math newsgroups) in which they
formulate (very cautious) criticism about ZF, axiomatic set theory or
especially the axiom of infinity.

Mathematicians? But pray, name a single book where that is done.

I understand, why they are cautious.
They fear the defamation they must be aware of if they would be very
concrete in criticism. I have experienced this defamation (not for me
but other persons).

You completely misunderstand. It is when people announce that the axiom
of infinity is self-contradictionary, without giving proper proof, that
they are severely criticised. If you look at all the proofs given in
this newsgroup upto now, you will find that in all cases a conclusion
is drawn that depends on the falsity of that axiom. That is not the
way to prove a contradiction.

Also when somebody writes a bold statement that the axiom of infinity
leads to nonsense, that is just opinion, and nothing more than that.
Everybody is free to develop mathematics without the axiom of infinity,
nobody will criticise somebody for doing that (unless it is done using
belittling statements about that axiom). But until such a form of
mathematics has been reasonable properly defined, you will not find many
followers.

So, if you come here, and simply state: "the axiom of infinity is false,
because no infinite sets do exist", that is just a bald statement of
opinion. And if you expect that every mathematician will immediately
see that you are justified, you are deluded. Mathematicians will not
take away one of the founding blocks of much of mathematics when there
is no adequate replacement. Or perhaps even not when there is adequate
replacement. Because, within mathematics, it is just a question of
opinion.
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