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Ideas for 'fragments/reports', 'Lectures on Ethics' and 'Logic for Philosophy'

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9. Objects / F. Identity among Objects / 7. Indiscernible Objects

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.