Browse/search for people

Publication - Professor Hannes Leitgeb

    Criteria of Identity and Structuralist Ontology


    Leitgeb, H & Ladyman, J, 2008, ‘Criteria of Identity and Structuralist Ontology’. Philosophia Mathematica, vol 16., pp. 388-396


    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.

    Full details in the University publications repository