"On the other hand": conventional implicatures

We have elaborated on Grice's example (adapted):

"My uncle is a drunkard; on the other hand, I like to spend my vacations in Normandie".

Grice wants to say that nothing has been asserted by the use of 'on the other hand'. To look for some contrast will be neither nor there. "on the other hand" works not on the ground-floor of things. It's a meta-device. On the other hand, there's Steven Wright, who said:

On the other hand, you have different fingers.