If S and S' satisfy all functional and structural criteria for ship-identity equally well, the burden of proof lies with Carter to supply a non-arbitrary reason to prefer O's identity with the original, which he does not provide.

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Carter(the specific philosopher being critiqued here): A philosopher (William R. Carter) who wrote about the Ship of Theseus problem and how we determine ship identity.
Functional criteria(the standard used to judge whether animals are truly using concepts): The practical standards or requirements needed to say something actually works or serves a purpose—focusing on what it *does* rather than what it's made of.
Non-arbitrary(describing whether there's a fair, logical way to measure contributions): A way of deciding something that's based on clear, objective reasons rather than just picking whatever you want without justification.
S and S'(used to compare two potential ships): Symbols used in logic to represent two different objects or scenarios being compared; the prime mark (') just means 'another version of S'.

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