Adams's anti-haecceitist position holds that all genuine modalfactssupervene on qualitative facts, so two spheres indiscernible in all qualitative respects occupy the same modal profile and therefore the same identity.
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When two things are so similar that you cannot tell them apart based on any observable or describable difference. If two things are indiscernible in all qualitative respects, they're identical in every way you could measure or describe.
Modal facts(as what supervene on counterpart relations)
Facts about what is possible, necessary, or could have been different—basically, facts about how things could be other than they actually are.
Supervene/Supervenes(as used in metaphysics)
When a higher-level property is completely determined by lower-level details—meaning if all the basic facts stay the same, the bigger picture must stay the same too.
modal profile(comparing whether God and God's existence have the same logical structure)
A description of all the different ways something could or must exist—basically, a map of what's possible and impossible for that thing.
qualitative facts(Grounding relation for identity facts)
Facts about the qualitative character of the world, as opposed to facts about which specific individuals bear which properties