On Logic

Some have thought that logic will one day be completed and all its problems solved. Now we know it is an endless task

…When one just looks at such ordinary cases, one can get the impression that logic has only a limited number of argument forms to deal with, so that once they have all been correctly classified as valid or as invalid, logic has completed its task, except for teaching its results to the next generation. Philosophers have sometimes fallen into that trap, thinking that logic had nothing left to discover. But it is now known that logic can never complete its task. Whatever problems logicians solve, there will always be new problems for them to tackle, which cannot be reduced to the problems already solved. To understand how logic emerged as this open-ended field for research, we need to look back at how its history has been intertwined with that of mathematics.

https://aeon.co/essays/more-than-argument-logic-is-the-very-structure-of-reality