display all the ideas for this combination of texts
1 idea
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
Full Idea: The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property. | |
From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) | |
A reaction: Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different. |