Title：Bishop's View of Mathematical Constructions

Speaker：Bruno Bentzen (School of Philosophy, Zhejiang University)

Time: 2024/10/15 15:10-18:00 Location: Room 206, Building of Geometry (地学楼), Peking University

Abstract：

Constructions are the primary objects of study in constructive mathematics, but little is known about them against the background of Bishop’s influential brand of constructivism. My aim in this talk is to develop Bishop’s view of constructibility as effective calculability. I argue that a development of his reflections on computation, open-endedness and generality results in a form of “construction structuralism”, the view that constructions are completely determined by the effective rules that relate them to one another in a system of rules proposed by the constructing intelligence. I examine the resulting no nonstructural property and ontological dependency theses of this structuralism and some of its implications.