Abstract I discuss Sir David Cox's views of the nature and importance of statistical foundations and their relevance to today's controversies about statistical inference, particularly in using statistical significance tests. A central theme in Cox's statistical philosophy is the importance of calibrating methods by considering their behavior in (actual or hypothetical) repeated sampling. Two key questions are open to philosophical controversy: How can the frequentist calibration be used as an evidential or inferential assessment?How can we ensure that the hypothetical long-run used in calibration is relevant to the specific data? I will discuss the answers that emerge from Cox's work and our jointly written papers, Mayo and Cox (2006) and Cox and Mayo (2010) on statistical significance testing, objectivity in statistics, and conditioning.