We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
What Are Structural Properties?
- Authors
Korbmacher, Johannes; Schiemer, Georg
- Abstract
Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. From this observation we draw some philosophical conclusions about the possibility of a 'correct' analysis of structural properties.
- Subjects
MATHEMATICAL models; NATURAL numbers; PEANO axioms; ORDINAL measurement; DEFINABILITY theory (Mathematical logic)
- Publication
Philosophia Mathematica, 2018, Vol 26, Issue 3, p295
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nkx011