If Foucault has been describing the study of discourse in general, why has he only used examples from the 'imprecise' sciences of medicine, economics, and grammar? What about mathematics or physics, or, for that matter, literature or philosophy? First, it is important to consider that archeology does not deal with disciplines, except as a starting-point for the description of discursive formations that exceed them. In Madness and Civilization, for example, Foucault set out to describe the conditions for the emergence of psychiatry in the early nineteenth century. But the discursive formation that turned out to establish those conditions was found to extend through aspects of a number of other disciplines and practices. The formation also extended back into the eighteenth and seventeenth centuries, when there was no identifiable 'discipline' of psychiatry.
Discursive positivities, then, do not coincide with sciences, nor are they unorganized precursors to future sciences, nor again do they exclude sciences altogether (clinical medicine is not itself a science, but it is intimately bound to a number of 'perfectly constituted,' formal sciences). What, then, is the relation between positivities and sciences? It is not a relation defined by knowledge as such; discursive positivities are, at the archeological level, neither systems of knowledge nor collections of bits of more or less true knowledge. Rather, they constitute the conditions under which something may become knowledge; thus, organized sciences are established on the basis of discursive positivities.
Knowledge is 'that of which one can speak in a discursive practice.' It is thus constituted not just of things judged to be true, but also of practices, of a space in which the subject of knowledge speaks, of concepts and their modes of integration, and of possibilities for use or appropriation. On this model, 'there is no knowledge without a particular discursive practice,' and a discursive practice 'may be defined by the knowledge that it forms.' Whereas the history of ideas understands knowledge as connaissance and is therefore dependent upon an empirical or transcendent subject of knowledge, archeology takes knowledge as savior, thereby positing only a subject that is 'situated and dependent' (see the entry on 'knowledge' in the terms list for a discussion of the French terms). This view of knowledge as more than just a set of propositions proved is precisely what enables archeological 'territories' that deal with science to extend to literature or philosophy.
Science is engaged with ideology precisely because science is a localized set of discursive practices within a larger, discursively formulated range of knowledge. In describing the ways in which a science is ideologically infused, then, we must turn to its discursive relations rather than to the relative truth-value or rigor of its claims. A science does not become less ideological the more rigorously true it becomes; though gaps in the science's theoretical structure may point us toward the operation of ideology, this operation must ultimately be examined solely at the level of discursive positivity.
In becoming a science, a discursive formation crosses a number of thresholds: that of positivity (when it is first put into operation), that of epistemologization (when it begins to dominate and systematically rearrange knowledge), that of scientificity (when it formulates its own rules of articulation), and that of formalization (when it fully formalizes its own principles, axioms, and methods). This series does not, however, obey strict chronological laws, nor does it even maintain this order of thresholds. Archeology comes in to describe the variations in the sequence. Mathematics is the only discourse to have crossed all these thresholds at once; for this very reason, to take mathematics as a model for understanding all other scientific discourse erases the great variety of the sequence of thresholds in those discourses.
Different methods within the history of ideas describe different thresholds. 'Recurrential' analyses work in terms of the threshold of formalization, describing the history of a science in terms of the development of its formalized systems. 'Epistemological' histories are concerned with the threshold of scientificity, and define the history of a discipline in terms of its progress toward the level of established science. Archeological analysis, in contrast to these methods, takes the threshold of epistemologization as its 'point of attack,' describing how a science takes shape as 'knowledge' within a discursive formation; it treats the history of sciences at the level of knowledge (as defined above).