To supplement the already given answer (although the post is a bit old), which touches many important issues, is the fact that each domain might (and usualy does) require its own logic (in the sense of descriptions of its own processes and interactions) and usualy these domain-specific or organic logics are not of the classical flavor.
This is manifested in modern mathematics and physics as well (surprisingly) in domains or toposes (places, spaces) which have their internal/organic logic of the processes and interactions and these are different from classical logic (mostly of the intuitionistic flavor, where the law of excluded-middle is actually rejected). However this should not seem surprising, that a positive science like physics or mathematics arrives at such notions, since if there is even a remote chance of this being realizable then all forms of knowledge should encounter it at some time.