 Brouwer was not alone in his doubts concerning certain classical forms of reasoning. This is particularly visible in descriptive set theory, which emerged as a reaction to the highly nonconstructive notions occurring in Cantorian set theory. The founding fathers of the field, including Émile Borel and Henri Lebesgue as two of the main figures, were called semi-intuitionists, and their constructive treatment of the continuum led to the definition of the Borel hierarchy. From their point of view a notion like the set of all sets of real numbers is meaningless, and therefore has to be replaced by a hierarchy of subsets that do have a clear description. 