This article examines Henri Poincaré’s philosophical conceptions of generality in mathematics and physics, and more specifically his claim that induction in experimental physics does not consist in extending the domain of a predicate. It first considers Poincaré’s view that generalization is not a means to reach generality and that the issue of infinity is related to the theme of generality. It then shows how generality in mathematics and physics is construed by Poincaré in a very specific way and how he analyzes empirical induction in physics. It also analyzes the distinction suggested by Poincaré between generalizations used in mathematical physics and generalizations used by ‘naturalists’. In particular, it explains the distinction between mathematical generality and the so-called predicative generality. Finally, it compares Poincaré’s concern regarding empirical induction with Nelson Goodman’s ‘new riddle of induction’, arguing that ‘the new riddle of induction’ was originally formulated by Poincaré half a century earlier.