Discussing with a philosopher about impossible things existing or being allowed within a particular logic system, he told me:
"This is a funny thing about logically impossible things. You can prove that they exist in any non-consistent or paraconsistent logic system. You might even be able to give a (nonsensical) description that satisfies some specific definition of said thing. But that still doesn't give you anything that makes sense. There, you are asking not only to prove that a very particular impossible thing exists, but you are asking for a detailed description of it to exist as well. I know of no method for doing that" (talking mainly about a solution that makes sense to Russell's set paradox)
So ia it there any method/logic system or anything else where impossible/illogical/inconsistent things would be allowed? For example, If a solution to Russell's set paradox cannot exist and it is impossible to exist, is there any method/logic system or anything else where this solution could exist?