Logic is the science not of external forms of thought, but of the laws of development "of all material, natural and spiritual things", i. e., of the development of the entire concrete content of the world and of its cognition, i. e., the sum-total, the conclusion of the History of knowledge of the world.
Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?