Well, I think it's hard to strictly and generally define what "quantity of matter" is. I would say that is a good non-relativistic heuristic about what mass is. In relativistic physics mass is defined by [tex]m=\frac{1}{c^2}\sqrt{E^2-p^2c^2}[/tex]
E and p are of course frame-dependent, but it turns out that m is not, so it is a good and non-problematic generalisation of Newtonian mass. Contrary to what is known as "relativisitc mass"...