Atomistic structuralism: elements are completely specified apart from their role in a system (grammar: needs only rules and elements).
In archaeology, statements cannot be detached from the system because they are constituted as such by the rules of the enunciative field (a truth game). Therefore, atomistic structuralism and archaeology have nothing in common.
Holistic structuralism: what counts as a possible element is defined apart from the system, but what counts as an actual element is a function of the whole system.
Such an analysis would require Foucault to identify types of possible statements, then leave it to individual systems to actualize them. This would work for a structuralist working with meaningless elements, but what is Foucault doing that is different? Although he brackets meaning, he relies on statements being meaningful for users. Statements are both individuated by the entire system and can only be identified as elements in a system in which they make sense.
Atomistic structuralism identifies and individuates isolated elements and equates the whole with the sum of its parts.
Holistic structuralism identifies elements in isolation and asserts that the system individuates. Whole is less than the sum of its possible parts.
Archaeology asserts that the whole determines what can count as possible. The whole is fundamental and more than the sum of its parts, and the parts only exist within the field which individuates and identifies them (obvious parallel to the Deleuzian distinction between the virtual and the actual).
“While the structuralist claims to find cross-cultural, ahistorical, abstract laws defining the total space of possible permutations of meaningless events, the archaeologist only claims to be able to find the local, changing rules which at a given period in a particular discursive formation define what counts as an identical meaningful statement.”
What are these rules? The ways the statements are actually related. Foucault: “The fact of [the statement’s] belonging to a discursive formation and the laws that govern it are one and the same thing…” (Archaeology of Knowledge, 116).
These systems are emergent and cannot be determined in advance. Instead, one can only describe the systems and their statements. Structuralism studies possibilities while archaeology studies the existence of conditions that make structuralist analyses possible.