On Sep 2, 2010, at 11:35 PM, Henning Thielemann wrote:

But in the lattice example the roles of 0 and 1 are interchangeable, aren't they?

Sort of. If you try to interchange the roles of 0 and 1, you are interchanging the roles of the meet and join operations. In short, you are constructing the dual lattice. A mirror image is a good analogy for this construction. So, 0 and 1 are interchangeable. In the same way that "True" and "False" are. And "Top" and "Bottom". And "Left" and "Right". Arbitrary structurally, but with a history of consistency across domains.