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36 THE EPISTEMOLOGICAL WORKSor to the probability of hypotheses, and to demonstrate that it was wrongto reduce the latter to the former.Classical theory deals with numerical probability—that is, with thequotient obtained by dividing the number of favourable cases by thenumber of possible cases, as in games of chance where the probabilitythat a dice will show the number 5 is 1 in 6. The theory is not univocal,however, and lends itself to a variety of interpretations both subjectivistand objectivist. In the first group, we find the psychologisticinterpretation which measures the sensations of certainty or uncertaintythat may be aroused by the expectation of particular occurrences. Thisacceptation of the term may satisfy us when we have to do with nonnumericalstatements, but it is of no use at all when mathematical valuescome into play.Another variant is the logico-subjective theory, which Popper chieflyidentifies with Keynes and his interesting work A Treatise onProbability (1921). Here too, probability is identified with the ‘degree ofrational belief’, or ‘the amount of trust it is proper to accord to astatement’—but the probability relation is treated as a kind of logicalrelationship between two statements, so that the degree of probability ishighest (=1) when one proposition is derivable from another, and lowest(=0) when the two propositions contradict each other (LSD: 149).Popper rejects this conception as being of no use to science, for ‘thelogical probability of a statement is complementary to its degree offalsifiability: it increases with a decreasing degree of falsifiability. Thelogical probability 1 corresponds to the degree 0 of falsifiability, andvice versa’ (LSD: 119). The aim of science, then, is not to achieve highprobability: if it were, science would have to base itself upon a largenumber of trivialities with an equally high degree of probability.Rather, science is interested in theories with a high content, whoseprobability obviously decreases in proportion to the rise in content(LSD: 286–287). We shall return below to this point, which isparticularly important because it involves a new concept of probabilityto which Popper gives the name ‘corroboration’, to distinguish it fromothers that refer in one way or another to the calculus of probability.Before we explain Popper’s own views, however, let us stay a littlelonger with his survey of ‘subjective’ and ‘objective’ interpretations ofprobability. Whereas ‘the subjective theory of probability springs fromthe belief that we use probability only if we have insufficientknowledge’ (P1:281), objective theories ‘take probabilities as propertiesof certain physical systems—experimental set-ups, for example’ (P1:295). The author of the Logic places in this group the theory of relative