There has been an interesting step forward on this subject in 1999:
Jean-Louis Krivine, a french researcher in mathematical theories concerning AI, managed to prove that both mathematics and natural languages are subsets of
Lambda calculus. It means that the human brain is an aggregate of many "neuron circuits" which each perform a basic Lambda Calculus function. This brings a quite shocking consequence: that what we call logic is a human construct. But in a sense, it is independent from the human mind, since such construct spontaneously emerges from the interconnection of neurons. The brain appears as a machine programmed in Lambda-Calculus, but it's physical laws that do the programming.
By connecting the two we get the idea that logic is a consequence of physical laws.
This result goes against the theories of dialectics that suppose that the concepts lying in mathematics and logic are independent from matter, and would exist (or still be true) even if the Universe did not exist.