The supporting argument assumes the consistency of arithmetic as a fixed, established fact, but Gödel's second incompleteness theorem entails this consistency cannot itself be proven within the system.

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Arithmetic: Arithmetic is the branch of mathematics dealing with basic number operations—addition, subtraction, multiplication, and division. It's the foundation of math that you use in everyday life, like calculating change at a store, splitting a bill, or figuring out measurements. Essentially, it's the practical math skill everyone learns early in school to work with numbers in simple, straightforward ways.
Consistency (in logic/math)(describing whether arithmetic has internal contradictions): When a system of rules doesn't contradict itself—meaning you can't prove that something is both true and false at the same time.
Gödel(as a historical figure in mathematical logic): Kurt Gödel was a 20th-century mathematician and logician who proved that any consistent formal system (a set of logical rules) is incomplete—meaning there are true statements it can't prove.
Incompleteness theorem(Gödel's key discovery about system limitations): A fundamental result showing that in any mathematical system complex enough to describe arithmetic, there are true statements that cannot be proven using the rules of that system.

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