CRITERIA OF OBJECTHOOD: INTRINSIC PROPERTIES
Victoria Alekseyevna Sukhareva
Institute of Philosophy and Law, the Ural Branch of the Russian, Yekaterinburg, Russia
Keywords: criteria of objecthood, thesis of incompleteness of mathematical objects, intrinsic properties, criterion of intrinsic properties, mathematical structuralism, mathematical Platonism
Abstract
The article considers the thesis of incompleteness of mathematical objects, from which the criterion of intrinsic properties is explicated. Two justifications of the criterion of intrinsic properties are reconstructed; the necessity and sufficiency of this criterion as an independent metaphysical criterion of objecthood are analyzed. It is shown that both justifications are vulnerable to criticism. The following objections are raised: firstly, objects can have criteria of identity without having intrinsic properties; secondly, not all mathematical objects lack intrinsic determinacy; thirdly, an independent existence and intrinsic properties do not necessarily imply each other. The conclusion is made that the criterion of intrinsic properties in itself can be considered neither a necessary nor a sufficient criterion of objecthood.,
|
