Please forgive me if this question sounds too naive... Well, in mathematics a *formal theory* consists of a collection of axioms $T$ (such as Peano arithmetics, or Group Theory, or ZFC), which essentially are certain structured chains of symbols, and theorems can be derived from them by applying certain deduction rules (or "inference laws"). These deduction rules are themselves formalizable by some axioms $\Lambda$ (such as the Hilbert-Frege deduction system).

Gödel's second incompleteness theorem states, roughly, that we cannot *prove* (and, to be able to *prove* something, we leave some fixed inference laws $\Lambda$ as understood) the consistency of any set of axioms $T$ (working within $T$).

What about the consistency of the inference system $\Lambda$ itself alone? That is, does Gödel's theorem apply somehow also to $\Lambda$ so that nobody is able to "prove" that it will not lead to a contradiction?