Questions of logical principle in the investigation of the foundations of mathematics
The development of mathematics in the last hundred years and the theoretical reflections to which this has given rise have produced results that seem apt to bring about a complete overturning of traditional conceptions of logic. It is not only the epistemological significance of logical principles that is drawn into the debate in order to elucidate the origins of a validity that is not as such denied — as was for example the case in the controversy over psychologism — but the very principles themselves are put in question. Thus the antinomies that appear in Cantor's theory of manifolds — of which some can be applied to logic in the narrow sense as well-have helped to undermine our conviction that logic is consistent. In the course of the critique of method that was thereby provoked, the universal validity of the principle of excluded middle was challenged and restricted to finite domains.
Kaufmann, F. (1978). Questions of logical principle in the investigation of the foundations of mathematics, in The infinite in mathematics, Dordrecht, Springer, pp. 188-224.
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