Rudolf Carnap spent much of the last 25 years of his career developing an inductive logic: a logic of reasoning from the known to the unknown that is derived from first principles and, at the same time, faithful to how scientists evaluate hypotheses and make predictions based on observations. In my talk, I will review what I take to be the main contribution of Carnap's inductive logic. I will then connect it to developments in Bayesian statistics, in particular probabilistic symmetries and invariance principles and developments in predictive inference, and suggest ways in which it can be enriched to supply a more comprehensive account of scientific inference. I will end with some philosophical reflections on the kind of model of scientific reasoning that inductive logic gives rise to.