Before revision:  We  also show that the VC-dimension is unbounded for pairwise disjoint convex sets in \mathbb{R ^d , for d \geq 3.
After revision:  We provide a quadratic lower bound in the number of pairs of intersecting sets in a shattered family of convex sets in the plane. We also show that the VC-dimension is unbounded for pairwise disjoint convex sets in \mathbb{R ^d , for d \geq 3.