The argument presupposes that 'strongly represents' the proof relation in F suffices to transfer facts about standard numerals to all elements of non-standard models, but this inference requires the metatheory to already privilege the standard model.

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Metatheory(as the foundational framework underlying a logical system): The background rules and assumptions you need to use in order to study or reason about a logical system—like the scaffolding needed to build a house.
Presupposes(as describing what Plantinga's argument takes for granted): Assumes something to be true without proving it—like how an argument might presuppose that logic works, without first arguing that logic is valid.
non-standard models(as used in mathematical logic): Alternative mathematical structures that follow the same formal rules as the standard system but contain different kinds of objects (like infinite numbers that don't exist in regular arithmetic).
privilege(Used to distinguish protected interests that do not rise to the level of rights): An interest or opportunity that the state ought to protect but that cannot be claimed as a matter of right, as distinct from a right proper.

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