On Wednesday, 30 April 2014 17:05:37 UTC+2, FredJeffries wrote: > On Monday, April 28, 2014 11:50:51 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > Couldn't just the seemingly so fruitful hypothesis of the infinite >
> So you do agree that the "hypothesis of the infinite" is fruitful, > or at least seems to be so.
It is not me and it is not so simple. Let me explain,
In German we distinguish "anscheinend" and "scheinbar". Both is not easily distinguished in English. "anscheinend" means: The picture appears to the observer as if he could reliably draw his conclusions. I translate it with "apparently". Example: The USA apparently kill many innocent people by their robot plane attacks. "scheinbar" however, means that the observer should not draw the conclusions from the picture that he sees, but should expect that he is cheated. I translate this with "seemingly". Example: The USA are seemingly observing the human rights.
The original German text by Zermelo contains this phrase: "diese scheinbar so fruchtbare Hypothese des Unendlichen". That means Zermelo says that set theory is not really fruitful but seems only to be fruitful while in fact it is not.
However, even many Germans do not know their language well enough to know these subtle differences. I am convinced Zermelo did not know or at least did not use this distinction. Of course he wanted to express that set theory is apparently fruitful, but what he really said is: set theory seems to be fruitful but is not. And that is the truth in fact.