Originally Posted by Jaz 
It's a matter of definition. I (for example) love Bach, but he is a Baroque composer and thus not a 'true' Classical composer of the Vienna period (which was truly short, as Beethoven - the last in line - was more of predecessor of the Romantics than anything else).
I used classical with a little "c" to refer to the genre, which encompasses the periods of Baroque, Classical, Romantic and Contemporary.