Material Structure and Mathematical Structure

Abstract

My theme is the relation between material structures and mathematical structures. In the ‘Theses’ composed for this Symposium definitions are given of what is to be understood by ‘mathematical structure’ and ‘material structure’ (there called ‘structure in the physical object region’). Yet no statement can be found concerning the relation between the two. True, Thesis Seven says that when the physical content is disregarded physical structures are identical to mathematical ones; however, we are left guessing what is meant by ‘physical structure’. If material structure is meant the thesis is wrong if not nonsense. If the structure of a physical theory is meant the thesis is true in a trivial sense and does not say anything about the relation between material and mathematical structure.

Translated from ‘Über das Verhältnis von Realstruktur und mathematischer Struktur’, Wiss. Z. Humboldt-Univ. Berlin, Math.-Nat. R. 16 (1967) 871–2.

Paper read at the Symposium ‘Struktur und Prozess in den Naturwissenschaften und der Technik’ organized by the Section Philosophische Probleme der modernen Naturwissenschaften of the Institut für Philosophie of the Humboldt University at Berlin and held on 21–22 November, 1966.