The Crisis in Contemporary Mathematics
Errett Bishop · 2019
There is a crisis in contemporary mathematics, and anybody who has not noticed it is being willfully blind. The crisis due to our neglect of philosophical issues. The courses in the foundations of mathematics as taught in the universities emphasize the mathematical analysis of formal systems, at the expense of philosophical substance. A similar situation undoubtedly held in the dispute between Kronecker and Weierstrass, about the validity of the real number system as it existed in those days. So there was a violation of the general philosophical principle not to discuss questions of truth until one settles questions of meaning. Many mathematicians regard the theory of computation as a branch of recursive function theory. It is true that many constructivists, for instance the school of Markov in Russia, are re-cursivists. Brouwer, of course was not. The recursive constructivists seem to be motivated by the desire to avoid such vague terms as “rule” and “set.”.