Formal Logic

Formal logic is sort of terrible. It requires a definiteness to logical principles that don't occur in nature, and therefore is sort of hollow. For example, what if an event p only implies q 60 percent of the time. In the financial world our experience of working systems at that level of complexity is less than 100 years old - we know that the odds of a crisis occurring given a predefined set of conditions is probabilistic, rather than deterministic. But, suppose someone predicted with absolute certainty the stock market would crash in a week. By necessity then, the stock market would crash today as everyone attempts to get out before the dooms day scenario. So we have a system that is not only probabilistic, but indeterminably so given all implicative p's. In actual fact, using formal logic to make predictive statements of the world is limited for this very reason. Which, practically, limits formal logic as constructive in the real world.

There are other pretty huge holes as well. What if two objects are not equivalent - one apple plus another apple does not make two equivalent apples if we consider their unique characteristics. We have Bertrand Russel's paradox, we have Godel's Incompleteness theorem. Really formal logic is trying to make sense of a disordered universe and failing pretty hard.