The Completeness Theorem

All five of these axioms are intuitively not just desirable to make a system fair but essential for it to be rational. Yet they are inconsistent. How can you be rational yet inconsistent? Well this is a matter of logic as well and it is reminiscent of Goethe's incompleteness theorem by the way. In this different kinds of logic let's not go too much into the details. The simplest kind of logic is sentential logic. You can prove that everything that's provable within that system of logic is true. And this is true for sentential logic for the simplest of all logic.