defending pluralism in mathematics, in particular Errett Bishop's constructive approach to mathematics ('Foundations of Constructive Analysis, 1967), more systematic than Brouwer's program of intuitionistic mathematics. (..) defending that classical, constructive, computer assisted and various forms of finitistic mathematics can coexist. (..) In different frameworks the answer to a question may be different, but this in no way implies that one or the other is 'right' (anti-Platonistic) (..) In classical math the [Exist-sign] refers to Platonic existence, but Bishop used it to refer to the production of an algorith for constructing the relevant quantity (sc stricter conditions for its application). (..) Surprisingly Bishop could develop much analysis without using the least upperbound principle or the law of the exlcuded middle. |