Generics, Frequency Adverbs, and Probability

intended for, we need to discuss the restriction of partitions to “suitable”
ones.
Salmon notes that there are two trivial cases of homogeneous reference
classes: when all ψs are φs and when no ψs are φs. In the former case, the
probability of φ given any subset of the reference class would be equal to 1,
and in the latter case to 0. He observes that, if every partition is considered
suitable, homogeneity would only be satisfied in the trivial cases, since a
partition which violates homogeneity can always be found in any non-trivial
case. Suppose that at least one ψ is a φ, and at least one ψ is not a φ;
now let Ω = {φ, ψ ∧ ¬φ}. Ω is clearly a partition of ψ; moreover, it violates
homogeneity, since P (φ|ψ ∧ φ) = 1 and P (φ|ψ ∧ (ψ ∧ ¬φ)) = 0. Clearly,
then, not every conceivable way to partition the reference class ought to be
considered; the class of possible partitions must be constrained in some way,
so that only suitable ones be considered, if the concept of homogeneity is to
play any useful role at all.
3.1 F-Admissibility
A natural way to partition the domain of a generic or a frequency adverb is
according to time. Let us redefine the admissibility of histories in such a way
that only histories in which a homogeneous sequence of individuals occurs
will be admissible. We will require that for every “sufficiently long” time
interval, the relative frequency of φs among ψ during this interval should be
equal to the relative frequency over the history as a whole.
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