"So much data. Who needs probability?" Have we been here before?

Statisticians have been dealing with the paradoxes of ever more data since the French Revolution. The bigger the data, the more we know, and the more we think we know. Do we still need probability to tell us what we don't know? And what ever made us think, in the first place, that statistics needs probability? This text is adapted from an after-dinner talk given at the Fifth Bayesian, Fiducial, and Frequentist Conference, University of Michigan, May 7, 2018. [ABSTRACT FROM AUTHOR]