[hmkpoker]

Perfect logic exists in a vacuum.

For example, yes, we can take a simple zero-sum game (let's say something like tic-tac-toe) and deduce that a certain choice is unequivocally most correct. However, add a little more complexity into it (say, the opening move of a chess game) and it becomes more difficult to deduce a perfect move.

These are simple games with few variables and perfectly understood principles. We live in a world of seemingly infinite complexity, and we do not fully understand it. Logic breaks down, as we have neither the means nor the practical method to solve real problems perfectly. To analyze a real world (i.e., not in a vacuum, like our chess game) problem with logic, we must convert X into ~X, where ~X is something infinitely easier to understand, and able to be entered into our formula.

Logic is useful, but practically very infallible.