If one adopts Nelson's ultrafinitism, the supporting arguments' P2 begs the question by presupposing a completed infinite domain over which exponentiation's rate of growth is assessed.

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Completed infinite domain(as a mathematical concept): The idea of treating infinity as a finished, whole collection that you can work with all at once—like saying 'all infinite numbers exist as a complete set.'
Exponentiation(as used in mathematics): A mathematical operation where you multiply a number by itself a certain number of times, like 2³ = 2 × 2 × 2.
Nelson's ultrafinitism(as a school of thought in mathematics and logic): A mathematical philosophy developed by David Nelson arguing that we should only accept numbers and mathematical objects that can actually be constructed or computed, rejecting the idea of infinitely large completed collections.
P2(Provides the truth conditions for proposition (7), identified as proposition (7): George Bush does not exist.): The principle that proposition (7) is true if and only if George Bush does not exist — a modalized instance of the Tarski truth-schema 's is true iff s'.

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