This essay explores seventeenth- and early eighteenth-century programs of natural inquiry where conjecture—an uncertain category of knowledge—played a vital role in the advancement of the sciences. It shows how early modern investigators used conjectures as a bridge between knowledge and ignorance and the process of conjecturing as a way to expand the mental state of inquiry. In publishing their conjectures, they were heeding Francis Bacon’s call to inspire hope and urge fellow experimenters to continue researching complex natural phenomena. Fellow investigators (...) could help to test, verify, revise, invalidate, or propose new inferences in a dialectical, collaborative process. The author argues that, by the eighteenth century, public conjecturing marked a particular kind of broad-minded experimental philosopher. This essay situates conjectures within agnotology—the study of culturally produced ignorance—and Baconian communication of knowledge and ignorance. It explores the philosophical and moral tensions investigators navigated when specifying nature’s unknowns. (shrink)