If two distinct properties can share an extension, then co-extension is insufficient to establish property identity.

In an effort to provide identity conditions for properties, one could mimic those for sets, or equate the former with the latter (as in class nominalism; see note 3), and provide the following extensionalist identity conditions: two properties are identical iff they are co-extensional. This criterion can hardly work, however, since there are seemingly distinct properties with the same extension, such as having a heart and having kidneys, and even wildly different properties such as spherical and