Emil Post has shown that classical propositional logic (CPL) is functionally complete, i.e., all connectives definable by binary truth-functions are definable in CPL. Moreover, he has shown that CPL is maximal in the sense that its connectives cannot be strengthened. Some philosophers, like Quine, have used such results to support the claim that CPL is the best logic in the world. However, many connectives, truth-functional or not, cannot be defined in CPL, and CPL can be extended in many different ways. For example, modal logic S5 is a strict conservative extension of CPL. One can wonder if there are logics which are absolutely maximal in the sense that they cannot be extended in any non trivial way. In this talk I will define the concept of absolute maximality using concepts from the theory of combination of logics and universal logic, and show, using a technique inspired by the Lindenbaum lemma, that any logic can be extended into an absolute maximal one.