Kripke's necessity of identity entails that if A and B are numerically distinct, this is so necessarily, meaning the scratch scenario merely reveals a contingent difference insufficient to ground metaphysical distinctness independently of haecceitism.
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Necessity of Identity(Used in Adams's modal argument to derive that possible identity entails possibly necessary identity)
The modal principle that if two objects are identical, then their identity holds necessarily — i.e., if A = B then necessarily A = B
contingent difference(contrasting with necessary, unchangeable differences)
A difference that just happens to exist in our world but could have been otherwise—like how you happened to wear a blue shirt today, but you could have worn red.
numerically distinct(Used to characterize the parts of the Form that must exist separately in each participant)
Being distinct in the sense of being different individual tokens, not merely different in kind or quality.
scratch scenario(an example used to probe whether something is necessarily or contingently true)
A thought experiment (a made-up imaginary situation) used to test philosophical ideas—in this case, imagining scratching something to see if it changes what it is.