What Follows from all that Data?\\Logic in the Methodology of Data-Intensive and AI-Driven Science

There is no foreseeable future in which science is not about data and the inferences data license. For centuries, logic has been the tool to analyse inference. And yet, logic is vastly underappreciated in the current methodology of data-driven science, as we argue in this paper. We first outline two historical reasons behind this mismatch, then highlight the need to bridge it by examining a widely used form of scientific inference: Null Hypothesis Significance Testing. Finally, we argue that the question: what follows from data?\ is ripe to be tackled by logicians. We submit that this will help lay a sound methodological foundation for the practice of data-intensive and AI-driven science.