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When Bertrand Russell discovered an unresolvable contradiction in Gottlob Frege's (1848-1925) logical system, the effect was calamitous, embittering Frege and overshadowing his important work in analytical philosophy. Frege's student, Rudolf Carnap, took detailed notes of his lectures that show how Frege tried to address the contradiction and how he integrated his later doctrine of sense and reference into his exposition of logic. Reproduced in the original German with facing translations, these rare documents are published here for the first time.