> all theorems about a certain statement being true must be reducible to a single irreducible logical chain of argument. Why is this necessarily true? We know

> all theorems about a certain statement being true must be reducible to a single irreducible logical chain of argument. Why is this necessarily true? We know that true statements in topology (for example) don't all reduce down to being equivalent (eg if I have a loop that goes through the ring of a donut/toroid it doesn't reduce the same as if I have a loop on the surface of the donut/toroid so establishing facts about one wouldn't tell me facts about the other). So how do we know that statements in logic reduce? Could the space of logical statements not have topological characteristics like that?