Open AccessEstructuras y representaciones
Author(s) -
Adolfo García de la Sienra
Publication year - 1990
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.101
H-Index - 6
ISSN - 1870-4905
DOI - 10.22201/iifs.18704905e.1990.733
Subject(s) - metaphysics , axiom , representation (politics) , parallelepiped , representation theorem , mathematics , pure mathematics , homomorphism , algebra over a field , uniqueness , connection (principal bundle) , set (abstract data type) , basis (linear algebra) , epistemology , computer science , philosophy , mathematical analysis , geometry , politics , political science , law , programming language
The aim of the present paper is to set a philosophical basis in order to discuss the type of representation that holds between mathematical structures and those aspects of the real world which they represent. It is maintained that an actualized version of Aristotelian metaphysics is suited for this purpose. The connection between the abstract, rigid concepts of mathematics, and the concepts of metaphysics is attempted through the concept of a fundamental measurement. The existence and degree of uniqueness of a fundamental measurement is established as a representation theorem asserting the existence of a homomorphism from what I call an ontological structure into a numerical one. An ontological structure contains as elements real beings, and its relations represent —in a sense made precise thereof— real relations among these beings. The role of metaphysics in the establishment of a representation theorem is to provide the conceptual apparatus required to discuss and formulate the ontological axioms required to derive the theorem. The paper contains a very complete example of a fundamental measurement in the sense described, namely, the measurement of the height of a physical parallelepiped and that of its potential parts.