MATHEMATICAL STRUCTURALISM AND PURELY FORMAL THEORY
MATHEMATICAL STRUCTURALISM AND PURELY FORMAL THEORY
Author(s): Marcin CzakonSubject(s): Structuralism and Post-Structuralism, Philosophy of Science, Methodology and research technology
Published by: Editura Universitaria Craiova
Keywords: philosophy of mathematics; mathematical structuralism; structure; structurality of mathematics; deductivity of mathematics; structuralism sui generis; set theory; methodology of mathematics;
Summary/Abstract: In this paper we put a thesis that it is possible to perceive mathematics as a science of structures, where the difference between structure as the object of study and theory as something which describes this object is blurred. We discusses the view of set-theoretical structuralism with a special emphasis placed on a certain gradual development of set theory as a formal theory. We proposes a certain view concerning the methodology of formal sciences, which is an attempt at describing precisely and capturing in a scheme the ways of development of deductive sciences in general, set theory including. We show that the standpoint of sui generis structuralism has some features characteristic of purely formal theory.
Journal: ANALELE UNIVERSITĂȚII DIN CRAIOVA. SERIA FILOSOFIE
- Issue Year: 2/2020
- Issue No: 46
- Page Range: 117-134
- Page Count: 18
- Language: English