Criteria of Identity and Structuralist Ontology

Leitgeb, Hannes and Ladyman, James (2008): Criteria of Identity and Structuralist Ontology. In: Philosophia Mathematica, Vol. 16, No. 3: pp. 388-396

Abstract

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view.

• Item Type: Journal article
• Keywords: PII, identity, structuralism, ontology of mathematics, graph theory, structures
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 160 Logic
• ISSN: 0031-8019
• Language: English