It's totally necessary to specify the preorder set in which you're taking the meet, and not just when you're taking the meet of the empty set! The definitions of meet and join (definition 1.60 in the book) use the preorder set in the definitions. For example, the meet of \$$\emptyset\$$ when our preorder set is \$$\\{1,2\\}\$$ with the usual numerical meaning of \$$\leq\$$ is \$$\\{1,2\\}\$$, while the meet of \$$\emptyset\$$ when our preorder set is \$$\\{1,2,3\\}\$$ is \$$\\{1,2,3\\}\$$.