Foucault's task in the face of the history of ideas is, as elsewhere, to 'maintain discourse in all its many irregularities. As usual, he is intensely, rigorously suspicious of any received notions about historical continuity. Here, such suspicions aim beyond the level of the long, logical totalities of history that were excoriated in the Introduction. Foucault rejects not only 'continuity' here, but also 'contradiction' and even 'change' itself, two ideas that don't initially seem to force history into systematic molds.
Even as innocuous a concept as 'contradiction' is quite controversial here. Foucault's own method depends on describing the 'differential' nature of discourse, the 'uniqueness' of statements over and against other statements. Thus, contradiction is by no means foreign to archeological analysis altogether. What Foucault rejects, then, is contradiction as some sort of uniform principle, an idea that defines all discourse either in its role as the obstacle to be overcome (in analyses that attempt to find the overall spirit of a discourse) or in its role as the principle of difference that is the fundamental cause of discourse. On Foucault's method, there is no single principle of contradiction; it must be described anew in the context of each discourse or sub-discourse examined.
Comparison (of one statement or discourse to another) is criticized along the same lines. In the history of ideas, comparison is generally of two or more things of the same order: two successive schools of philosophy, for example, or two eighteenth-century sciences. Such comparisons tend to depend on (or even to generate) a kind of homogeneous background on which the compared items rest: a gradual progression of philosophy, or an overall worldview of eighteenth-century science. What Foucault finds at fault, then, is not comparison itself, but the assumptions of homogeneity that are built into the particular form of comparison used. In archeological comparison, elements are compared at and across a great variety of different levels (the level of statements, the level of discursive objects or strategies, the level of discourse, etc). The result is, again, a greater attention to detail, variety, and difference.
Finally, the bulky, homogeneous principle of 'change' is replaced by the notion of 'transformations,' for similar reasons and with similar effects. A key point here, which we've heard before, is that the various levels of discourse, like the various aspects of language, can interact and transform independently of each other. Just as the propositional content can remain the same when a sentence is repeated in a totally different enunciative framework, an entire discourse can be transformed or replaced even while many of its objects, concepts, subject positions, and strategies do not (and, of course, vice-versa). The general principle of 'change' in the history of ideas is not sensitive to such complex transformations.
In these chapters, Foucault is lending more detail to his overall insistence that archeology describes the positivities of discourse with the greatest possible attention to difference. Difference becomes not only something to pay attention to in the study of discourse, but also a crucial factor in designing the analytical tools that archeology will use. The notion of change, as it is traditionally conceived, is a blunt tool in this sense; if it is more general than the set of different tools that fall under the notion of 'transformations,' it will fail to uncover the full range of differences present in the archive.