 It was obviously necessary to clarify the foundations of set theory, but the overall situation did not make this an easy task. The different competing viewpoints were widely divergent. Cantor had a metaphysical understanding of set theory and, although he had one of the sharpest views of the field, he could not offer a precise foundation. It was clear to him (as it had been, somewhat mysteriously, to Ernst Schröder in his Vorlesungen über die Algebra der Logik, 1891) that one has to reject the idea of a Universal Set, favoured by Frege and Dedekind. Frege and Russell based their approach on the principle of comprehension, which was shown contradictory. Dedekind avoided that principle, but he postulated that the Absolute Universe was a set, a “thing” in his technical sense of Gedankending; and he coupled that assumption with full acceptance of arbitrary subsets.