 Lewis called A an ‘undermining’ future; it has a chance of happening, but if it happens the chances are different. The problem with underminers is that they conflict with the Principal Principle. Someone who knows the chance of A should, by the Principal Principle, have credence 1 in 2n that A will happen. But given the chance of A, it is possible to deduce ~A, and hence have credence in A. This looks like an inconsistency, so like any principle that implies a contradiction, the Principal Principle must be false. The most obvious way out is to say that information about the chance of A is inadmissible, since it reveals something about the future, namely that A doesn’t occur. But to say that chances are inadmissible is to make the Principal Principle useless. So given the best systems theory of laws and chances, the Principal Principle is either false or useless. Since the Principal Principle is neither false nor useless, Lewis concluded in these 1980s papers that the best systems theory of laws and chances was false.