Deep and shallow uncertainty are defined and contrasted with regard to messaging the uncertainty about climate change. Deep uncertainty is often traced back to the writings of Frank Knight, where in fact it simply meant subjective probability. Although Knight envisioned a scientifically grounded quantification of subjective uncertainty, deep uncertainty is frequently invoked to disable uncertainty quantification, with attendant problems in communicating and propagating uncertainty through chains of reasoning. These issues, together with science-based uncertainty quantification, are illustrated with recent applications to ice sheet dynamics. The issues of performance assessment and validation are addressed.