The following statements are taken from a book:
The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has nothing to do with imperfections of physical coins; it endows nature with memory, or, in our terminology, it denies the stochastic independence of successive trials. Marbe's theory cannot be refuted by logic but is rejected because of lack of empirical support.
Can someone explain both of the reasons why it cannot be disproved logically but rejected out of lack of empirical support?
Is the lack of empirical support related to impossibility to obtain truly, ideally fair coin? Because in my thoughts it is quite true that the more heads I get in a row, the more probable that the next is tail. What is wrong with this reasoning?
What about logical disproof? As the book states general inability of logic to disprove this, I can't understand what is an obstacle in logic to disprove this theory. Thanks in advance!