Originally Posted by Musashi
Bollocks. While there were some rapier models which did not include a sharpened edge, this was a very rare thing, and the majority of rapiers were quite capable cutting instruments. Of course they were much better for a thrust, but you could quite definitely kill an opponent with a slash to the throat.
The thing to keep in mind about the rapier is that it's a duelist's weapon, and developed for use against an unarmored opponent, a situation in which you don't need great weight to achieve an effective cut.