Note 48

We must realize that this 'formalization' is only a formalization in the broader sense :  In a strict formalization of a given system only the elements of the system itself are allowed to be used in enunciating the propositions (axioms, theorems, etc.) of the argument. Nothing from outside the system should be used. This means that in TARSKI's example the english words should not be used. What these words express should be stated by means of the system's own elements. Only then we obtain a purely and genuine formal system.

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