Danny Ayers calls the relationship between tags and formal systems a false dichotomy:

Tagging terms are are only imprecise when you throw away the contextual information - i.e. who did the tagging and when. This information can be captured transparently to the user (and is, by tools like del.icio.us).

I'm not sure I fully agree, however I for sure disagree with Clay Shirky's classical piece on this theme (some details on my opinion can be found in this post).

An interesting way to add more structure to social (bottom-up) tagging systems, is to provide a feature that allows users to organize tags in a (socially defined) hierarchical (multi-)taxonomy, such as Wikipedia's category system. I find it astonishing how (globally) accurate and complete this structure has become.