Gödel's incompleteness theorem and the philosophy of open systems

In Daniel Miéville (ed.), Kurt Gödel: Actes du Colloque, Neuchâtel 13-14 Juin 1991, pp. 103-127. Travaux de logique N. 7, Université de Neuchâtel (1992)
In recent years a number of criticisms have been raised against the formal systems of mathematical logic. The latter, qualified as closed systems, have been contrasted with systems of a new kind, called open systems, whose main feature is that they are always subject to unanticipated outcomes in their operation and can receive new information from outside at any time [cf. Hewitt 1991]. While Gödel's incompleteness theorem has been widely used to refute the main contentions of Hilbert's program, it does not seem to have been generally used to point out the inadequacy of a basic ingredient of that program - the concept of formal system as a closed system - and to stress the need to replace it by the concept of formal system as an open system.
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