## ABSTRACT

We should keep in mind that mathematics is not a property of nature. Although some physicists may disagree, I think that there are some phenomena that are “mathematical” and other phenomena which are not. Whenever we express an idea through order relations among its components, we are expressing it mathematically. The basic meaningful unit of this artifi cial language is the idea of quantity. More than a property or characteristic in itself, it is a kind of property: certain entities have “quantities” of

something. These are those properties of entities expressing a gradation or intensity. Therefore, quantities will be the opposite of qualities: those characteristic features that do not imply gradations, and cannot be expressed in terms of relations of order. The only thing we can say about a quality is that it is “present” or “absent”. Quantities allow the ordering of objects or phenomena in terms of relations of order:

A is greater than B in q A is equal to B in q A is less than B in q

By extension, I suggest that a phenomenon that can only be expressed quantitatively, in terms of intensities and orderings, is a mathematical phenomenon, not because it has a different nature, but because if described in verbal terms it would add too much ambiguity and misunderstanding. Mathematics is simply an artifi cial language used to represent ideas that cannot be expressed in another language. Therefore, there is not a “quantitative” archaeology that may be distinguished from another “qualitative” archaeology. I am just saying that we can do better archaeology using quantifi cation. This is what Nicolucci and colleagues consider in Chapter 3: “data cannot be compared, if the data structures have no clear semantics and the provenance of knowledge is not transparent.” Mathematics, as an artifi cial and formal language should be considered as an attempt to make explicit and well-defi ned in formal terms the many current archaeological (subjective) implicit terms and concepts. Nicolucci, Hermon and Doerr clarify the archaeological concepts and terms that can be formalized, although they give no details about the way mathematics can be used to disambiguate the description of archaeological primary data, that is, archaeological observables.