The Black Swan Problem

Logic is the fundemental basis of science. Is logic something hard and fast? Can it be brought down to its lowest common denominator? I really dont understand logic to that level. But in a simple framework you tend to use logic itself as a set of rules. The whole number A > whole number B > whole number C => A>C. That is mathematical logic. The Sun has been rising the on the east always, it is almost certain that it will rise in the east t'row.

Philosphically, the Black Swan(seemingly the theory was first put forward by Karl Popper) problem is considered a true blood. If all your life and in science if you only see white swans does mean that Black Swans' do not exist? (Actually they apparetnly were found in Australia). Even more interesting, inductive logic is true only again by induction. That is some logic isnt it?

PS: None of the thoughts above are mine, they belong to a book on infinity.

When does logic fail? Is the application of logic merely a reflection of the amount of information known about a particular subject. Lets say that we suddenly solve the mysteries about the seemingly expanding universe, would logic then apply? I would think so. You cannot really apply logic to things you have no information about.(If aliens have existed all this while, why have not contacted us-Fermi Paradox types, the damn thing being we know a vast little about aliens). That is the problem many of us face with behavioral analysis too, we dont really know the motivations of others so we cant really apply our logic to it. Logic could possibly be the infinite number line, but only when the space is defined. Till then we can even have a colored swan i.e. if the chinese want a colored swan.