This chapter engages in some ground-clearing. Two concepts have been proposed to play the role of objective probability. One is associated with the idea that probability involves mere counting of possibilities (often wrongly attributed to Laplace). The other is frequentism, the idea that probability can be defined as long-run relative frequency in some actual or hypothetical sequence of events. Associated with the idea that probability is merely a matter of counting of possibilities is a temptation to believe that there is a principle, called the Principle of Indifference, which can generate probabilities out of ignorance. In this chapter the reasons that neither of these approaches can achieve its goal are rehearsed, with reference to historical discussions in the eighteenth and nineteenth centuries. It includes some of the prehistory of discussions of what has come to be known, misleadingly, as Bertrand’s paradox.
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