Despite Adminnemooseus' accusation of babbling, this is actually an excellent topic that Mike has stumbled upon, and a very important field of study in logic, mathematics, and extreme theoretical physics - not to mention in more casual philosophy and also electronic/computer design.
Mike's opening questions are spot on:
"Is it science? Is it part of science. Is it important? Did the likes of Darwin and Einstein observe such laws as the excluded middle?"
Now Mike may have just been having a dig at the use of logic, but given that his questions have good answers it would seem a pity not to promote this - obvious destination is "Is it science?"