--- Notes on logic and mathematics ---
Nature cares nothing for logic, our human logic: she has her own, which we do not recognize and do not acknowledge until we are crushed under its wheel.
Well, maybe not quite so negative. I don't think Nature is waiting out there to crush us under wheels, but I have said that I don't believe that Nature's primary purpose is not our convenience, so you should watch where you step.
But I don't see logic "out there". Logic characterizes reality to some extent but I've said over and over how "the word isn't the thing" and it's dangerous to forget it. Logic (and mathematics, concepts, models) is a language that we use to understand how things work in the world, and it is a very useful tool as long as we keep a firm hold on it's limitations. It is not the be all and end all of analysis. It will not allow us to formulate all knowledge (as the logical positivists hoped).
Our binary Western logic isn't even complete. There are things that doesn't fit into a nice, neat dichotomous scheme - true/false, extant/nonextant. For instance, my favorite example - the circle (Plato preferred the right triangle - whatever). It doesn't exist - it cannot exist. It's a curve which is everywhere equidistant to a single point, but such a curve would have no width. But so much of our society is built on a circle. Architectural designs, machines, symbols (anybody ever been in the winner's circle or sat in a support group?), so many circles! They don't exist but they certainly affect society as if they did. Circles exist powerfully in our minds. They exist as information, something that is nonexistence-in-existence. Eastern logic recognizes many categories of existence and can deal with categories such as information better than we can in the West.
Logic and mathematics are languages composed of words. They don't exist out there but are powerful tools of the mind to span the dimensions of reality.