 Suppose Sophia does not know much about wine. By the principle of indifference, her degree of belief that an Austrian Schilcher is a white wine and her degree of belief that it is a red wine should both be .5. Contrast this with the following case. Sophia is certain that a particular coin is fair, i.e. that the objective chance of the coin landing heads and the objective chance of the coin landing tails are both exactly .5. The principal principle (Lewis, 1980) requires roughly that, conditional on the objective chances, one’s subjective probability should equal the objective probability (see Briggs, 2009b). By the principal principle, her degree of belief that the coin will land heads on the next spin should also be .5. Although Sophia’s subjective probabilities are alike in these two scenarios, there is an important difference. In the first case a subjective probability of .5 represents complete ignorance. In the second case it represents certainty about objective chances.