Recent BIO-tagging-based neural semantic role labeling models are very high performing, but assume gold predicates as part of the input and cannot incorporate span-level features. We propose an end-to-end approach for jointly predicting all predicates, arguments spans, and the relations between them. The model makes independent decisions about what relationship, if any, holds between every possible word-span pair, and learns contextualized span representations that provide rich, shared input features for each decision. Experiments demonstrate that this approach sets a new state of the art on PropBank SRL without gold predicates.