Generics, Frequency Adverbs, and Probability

3 Homogeneity
In order to answer this question, we ought to consider more carefully the
evaluation of probability judgments. Since it is impossible to observe arbitrarily
long histories in the actual world, these must be extrapolated from the
actual history that transpired and was observed. For this extrapolation to
be of use, we need to assume that the observed instances provide a good statistical
sample. That is to say, we need to assume that the relative frequency
over the sample we do have is close to the value of the probability, i.e. the
relative frequency over arbitrarily long sequences. In order for us to believe
this, any history we consider ought to be such that any sufficiently large
sample taken from it is a good sample. Then, if our sample is sufficiently
large, we can extrapolate from it with some confidence.
This idea has already been explored by von Mises, who requires an admissible
sequence to be random, in the sense that every sub-sequence selected
from it and satisfying some constraints 9 must have the same relative frequency
as that of the original sequence.
A random sequence, then, is one in which the relative frequency of a
certain outcome over all sufficiently large sub-sequences approximates the
probability for that outcome. A random sequence does not admit of long
“chunks” where the relative frequency of φs among ψs differs from the relative
frequency in the sequence as a whole. In the words of Fisher (1959), it must
9 Von Mises and subsequent researchers have made a number of proposals regarding the
appropriate constraints; see Salmon (1977) for an overview.
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