SUMMARY. — Contrary to the received view, a close connection exists between Brouwer's topological works and his philosophy of mathematics. Brouwer arrived at his main results by abandoning the abstract methods of general (or point-set) topology and opting instead for a combinatorial approach that seeks to make topological concepts arithmetic. In this article I investigate the genesis of Brouwer's notion of the « degree » of a mapping and the discovery of the equivalence of the existence of fixed points in a topological mapping and the existence of singularities in the field of vectors tangent to the sphere.

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Mental states in sight of everybody The meaning of the psychological predicates has to be communicable, thus it cannot be defined by reference to private mental experiences. But these predicates should be only ascribed to creatures who are able to ascribe them to themselves on the ground of their own qualitative experience. The paper deals with the ways of resolving this contradiction.