Generics, Frequency Adverbs, and Probability

Q(ψ, φ) is true iff
⎧
P (φ|ψ) = 1
P (φ|ψ) = 0
if Q = always
if Q = never
⎪⎨
⎪⎩
P (φ|ψ) > 0
P (φ|ψ) > 0.5
P (φ|ψ) > 0.5
if Q = sometimes
if Q = usually
· · ·
if Q = gen
As it stands, definition 1 does not really give us truth conditions. For it
to do so, we need to specify the meaning of the probability judgment P (φ|ψ).
What does it mean to say, for example, that the probability that a fair coin
comes up “heads” is 0.5?
The mathematical probability calculus, as developed by Kolmogorov and
subsequent researchers, will not help us here, since any function which satisfies
its axioms is considered to be just as good as any other function. The
meaning of probability has been the topic of much debate among philosophers
since at least the time of Laplace, and many different theories have
been proposed. It is not my goal here to provide a general solution to this
philosophical problem; the aim of this paper is a considerably more modest
one. I will follow L. J. Cohen (1989), who argues that there is no single “correct”
interpretation of probability: different interpretations are appropriate
for different types of probability judgment. In this paper I will propose an
account of that specific kind of probability judgment which is expressed by
generics and frequency statements.
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