Limitative results are not appalling, but they do mean your theory has hit a barrier, and you have to ask:  Why?  

The answer to why can be interesting.  

The Fates are kind.

Also, of course, I said, echoing Bronowski, that it CAN lead to killing people. The point remains that demanding absolute knowledge, based in indubitable foundations is misguided, and those who go on working within science without worrying too much about problems in basic theory are quite sensible. There was no need for apostasy - a term from religion of course where absolute knowledge is claimed and people also kill each other over rival claims to it.

Maybe it's because I'm a Londoner - that I moved to Nice.