[dwheeler]

Strictly speaking that's true for any system that can handle arithmetic (as proved by Goedel). You can show an inconsistency, but you can't prove consistency. No one's found an inconsistency.

There are pros and cons for both systems.

[dmvdoug]

Yes, I was too loose with me words again. I was gesturing at relative consistency (especially, at least, when compared to the lack of serious doubt about ZF/C’s consistency), as well as the work of folks like RB Jensen and Randall Holmes.

The biggest problem NF has is, as usual, a social one: there just ain’t a lot of people working on, or interested in working on, NF compared to other set theories.