HINTIKKA’S THEOREM DOES NOT HOLD IN NON-AXIOMATIC LOGIC

Abstract

Hintikka’s theorem relates what is impossible to what is forbidden. It provides that if something is impossible, that cannot be permitted. There are logical demonstrations of the theorem. Those demonstrations follow requirements of classical, modal, and deontic logics. However, there are also accounts based on psychological theories trying to explain why people’s tendency should be to reject it. I will attempt to account for the probable rejection of the theorem by people too. But my explanation will resort to Non-Axiomatic Logic. I will argue that, from the latter logic, linking possibility and prohibition is preferable to linking impossibility and prohibition. So, Hintikka’s theorem does not hold in Non-Axiomatic Logic.