I'm thinking every logical derivation as something like all the derivations in the Principle of Explosion - really everything.
It could just be a helpful interpretation, not trying to get super deep into ontological commitments. I guess I really do mean there is a "world" where 1=2, or 1=2 is helpful to some situation (I really prefer the latter, it seems to avoid a lot of ontological commitments as to what 1=2 is even saying, and what exists).
In a way I guess it would help reinforce the empirical stance/side of knowledge (at least for me temporarily) like Quine did about set theory and physics, i.e. set theory is part of our greatest overall empirical theory, and could still be abstract/platonic.
I don't think its paraconistent or dialetheism. If it's pluralism, does it have a name? Explosive pluralism? Or have I missed some obvious and trivial step, that of course we think all derivations "exist" as the backdrop to (our) logical and mathematical knowledge.
*Another misstep I may have made is I just don't know how to define logic and math. (Then, is there a modern conception of them which still makes this wondering possible?)