I still don't see a point in assuming every statement to be true. It seems more like a gimmick than anything else. Even without the principle of explosion, there must be a distinction between what is proved to be not false and what isn't. What use is there in assuming everything to be true?

I see no point in this theory. The application to MWI doesn't really make sense, and even if it did, that's no reason to give this proposition any credence. The Tegmark hypothesis is also misunderstood; it states that all well-formed mathematical structures complex enough to have self-aware systems subjectively exist to those systems. I am not sure this can be proven, but I see even less of a connection to "destructive mathematics" than MWI.

How is this useful to logic?