Question

According to David Lewis, the Principal Principle says that "our beliefs about the objective chances of outcomes (typically) determine our rational credences in those outcomes." I’m assuming that this means that on the next roll of a dice, one should have a 1/6 credence in the dice landing on a 1. However, if one has a 1/6 credence for each outcome, then it follows that one should have a 0% credence in any other outcome (such as the dice spontaneously turning into a fly). However, Bayesians who often invoke Cromwell’s rule refuse to assign a zero or 1 prior to anything. Given this, is one supposed to then assign a credence slightly below 1/6 to each outcome of the dice? If so, wouldn’t that then contradict the Principal Principle?

Answer 1

The Principal Principle does not require assigning a 1/6 credence to each outcome of rolling a die. Bayesians may assign a slightly lower credence to each outcome, but this does not contradict the Principal Principle.

Step-by-step explanation:

The Principal Principle, as described by David Lewis, states that our beliefs about the objective chances of outcomes typically determine our rational credences in those outcomes. However, this does not necessarily mean that we should assign a 1/6 credence to each outcome of rolling a fair, six-sided die. The Principal Principle is about rational credences, which may not always align with objective probabilities.

Bayesians who adhere to Cromwell's rule refuse to assign a zero or 1 prior to anything. In the case of rolling a die, they may assign a credence slightly below 1/6 to each outcome, but this does not necessarily contradict the Principal Principle. Rational credences depend on the available evidence and reasoning, which may vary among individuals.