 Peirce’s paper was in many respects far ahead of its time. His sharp distinction between propositional, first-intentional, and second-intentional logical systems was not to be equaled in clarity until Hilbert in his lectures of 1917/18. Peirce was also prescient in viewing the quantifiers as (possibly infinite) sums and products, a notation which Löwenheim was to credit with making possible the discovery of the Löwenheim-Skolem theorem, and which was to play a significant role in the formulation of Hilbert’s proof-theoretic program in the 1920s. (Peirce’s logical ideas were well-known in continental Europe, having been taken up by Ernst Schröder and given wide circulation in the three volumes of his Algebra der Logik (1890–95).) 