 The direct acquaintance theorist does presuppose the intelligibility of a world that has “structure” independent of any structure imposed by the mind. Without facts that are independent of the thoughts and judgments that represent them, one could not make sense of a relation of acquaintance between a person and a fact, a relation that grounds foundational justification. More radical contemporary rejections of foundationalism may well involve dissatisfaction with the foundationalist’s implicit commitment to a strong realistic correspondence conception of truth as involving some relation to mind-independent facts. A discussion of problems with the correspondence conception and alternatives would take us far afield, however. (For more, see the entry on the  correspondence theory of truth.)