In the first episode, when Kirito was showing Klein the ropes of combat, the conversation goes

> Kirito: However, there is no magic.

>Klein: An RPG without magic? That is a bold decision.

However later on in the show, Kirito visits Lizbeth's shop in *Temperature of the Heart.*. Kirito is in shop for another sword, and shows Lizbeth his *Elucidator*. 

Lizbeth responds with:

>An Elucidator! This is the gnarliest **magic** sword a person can get from a monster drop.

If magic did not exist, how would there be a magic sword?