Pre-intuitionism

In the philosophy of mathematics, the pre-intuitionists is the name given by L. E. J. Brouwer to several influential mathematicians who shared similar opinions on the nature of mathematics. The term was introduced by Brouwer in his 1951 lectures at Cambridge where he described the differences between his philosophy of intuitionism and its predecessors:^[1]

Of a totally different orientation [from the "Old Formalist School" of Dedekind, Cantor, Peano, Zermelo, and Couturat, etc.] was the Pre-Intuitionist School, mainly led by Poincaré, Borel and Lebesgue. These thinkers seem to have maintained a modified observational standpoint for the introduction of natural numbers, for the principle of complete induction [...] For these, even for such theorems as were deduced by means of classical logic, they postulated an existence and exactness independent of language and logic and regarded its non-contradictority as certain, even without logical proof. For the continuum, however, they seem not to have sought an origin strictly extraneous to language and logic.