popper-logic-scientific-discovery

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some structural components of a theory of experience
event. Thus the probability that an individual man k will die within a
given period of time may assume very different values according to
whether we regard him as a member of his age-group, or of his occupational
group, etc. It is not possible to lay down a general rule as to
which out of several possible reference-classes should be chosen. (The
narrowest reference-class may often be the most suitable, provided that
it is numerous enough to allow the probability estimate to be based
upon reasonable statistical extrapolation, and to be supported by a
sufficient amount of corroborating evidence.)
Not a few of the so-called paradoxes of probability disappear once
we realize that different probabilities may be ascribed to one and the
same occurrence or event, as an element of different reference-classes.
For example, it is sometimes said that the probability αP k(β) of an event
before its occurrence is different from the probability of the same event after
it has occurred: before, it may equal 1/6, while afterwards it can only
be equal to 1 or 0. This view is, of course, quite mistaken. αP k(β) is
always the same, both before and after the occurrence. Nothing has
changed except that, on the basis of the information k εβ (or k εβ - )—
information which may be supplied to us upon observing the
occurrence—we may choose a new reference-class, namely β (or β - ),
and then ask what is the value of βP k(β). The value of this probability is
of course 1; just as β -P k(β) = 0. Statements informing us about the actual
outcome of single occurrences—statements which are not about some
frequency but rather of the form ‘k εφ’—cannot change the probability
of these occurrences; they may, however, suggest to us the
choice of another reference-class.
The concept of a formally singular probability statement provides a
kind of bridge to the subjective theory, and thereby also, as will be shown
in the next section, to the theory of range. For we might agree to
interpret formally singular probability as ‘degree of rational belief’
(following Keynes)—provided we allow our ‘rational beliefs’ to be
guided by an objective frequency statement. This then is the information
upon which our beliefs depend. In other words, it may happen that
we know nothing about an event except that it belongs to a
certain reference-class in which some probability estimate has been
successfully tested. This information does not enable us to predict what
the property of the event in question will be; but it enables us to