I agree that in order to assess biodiversity such that it translates into science-based policy, we need clarity and definitions at every step of the process. However, I think that the most urgent need is for an understanding of, and consensus about, the concept of biodiversity itself. So far, there has been few attempts to formalize and define biodiversity beyond the all-encompassing definition from the Rio summit. I believe that definition is not a measurable entity. Wether in the end we will use indicators of biodiversity, or assess it directly, we need to both define AND be able to measure biodiversity.
Biodiversity is the diversity of life-forms.
An assemblage of dead objects can not have biodiversity, although they may be the result of life processes. Diversity is indeed an emergent property of an assemblage of objects. The relevance of biodiversity is in the differences among life-forms, and to measure biodiversity is to measure those differences. The genetic code is arguably the most fundamental property of life, so biodiversity would be based on genetic differences among life-forms. If taxonomic classifications reflect genetic differences, they can be used to estimate such differences for a defined assemblage of life-forms, in a certain place, at a certain time.