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Abstrakt

In this paper the logical systems used in the principles of mathematics are treated, concretely the intuitionalist and constructivist approach to the logical construction of mathematics. Intuitionism as well as constructionism at the criticism of classical mathematics refuse first of all the transference of the methods of elementary logic to non-elementary situations, where e. g. the infinite quantities are treated. The difference between intuitionism and constructionism does not consist so much in the approach to logic as in the use of the notions “constructibility” and “intuitive clarity”. A considerable recent elaboration of constructive mathematics and intuitionism gives a prospect to both of these trend in the principles of mathematics.