Because in probability based statistics it is always possible to make probability-statements about the same future observations (i.e. make predictions) on basis of different probabilistic theories (or methods) that cannot be true at the same time.

So as an example, we can use lots of sets of probabilistic assumptions and an infinity of estimation methods and surely claim that the probability of rain tomorrow is 0.4, 0.5 or any other probability value. At the same time it is impossible to prove one of the claims or theories definitively wrong.

So it seems to be impossible to collect empirical stochastic knowledge in a Database. In our reasoning there is no stochastic empirical knowledge and a database containing empirical results that are based on stochastic models could include an infinite number of conflicting statements.

One of the major advantages of emergent-law-based statistics therefore is the fact that emergent laws and the simple prediction rule “predict that a pattern that always was true in the past also will become true the next time” cannot result in conflicting predictions. So it becomes possible to collect consistent empirical knowledge in form of emergent laws in databases.

See the power of the resulting KnowledgeWarehouses in the following example:

(Click on the image for fullscreen.)