A SUMMARY IN ENGLISH by EditorThe problem is to find out whether mathematical propositions are analytical, and if so, or if not, to what extent.Kant defined the analyticity in terms of Cartesianres extensa, exemplified by“A body is extended”, while he considered, because of such examples, mathematical propositions to be synthetic. The recent studies in set theory by Gödel, P.J.Cohen, etc., indicate, however, that such a proposition as the continuum hypothesis is certainly not“analytic (tautological)”in the strict sense of logicists. Rather a small portion, comparatively speaking, of mathematical propositions must therefore be considered analytic relative to the definitions of fundamental conrepts in logic. Axioms, for example, areper definitionemnon-analytic. Other problems that demand reöxaminations are, for instance:1. Why is thereonly oneunique series of the natural numbers?2. On which ground is the factual eminence of Euclidean geometry to be founded?etc. The two assertions that mathematical propositions are analytic and that they are synthetic aprioriare thus not at all contradictory; they are, to begin with, not even mutually exclusive Poss
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