Taxonomy of Probability


The classical theory of probability applies to equally probable events, such as the outcomes of tossing a coin or throwing dice; such events were known as "equipossible".

probability = number of favourable equipossibilies / total number of relevant equipossibilities.


  • Circular reasoning: For events to be "equipossible", we have already assumed equal probability.
  • Limited scope: It is not always appropriate to assign equal probabilities (such as theories), or cases where the alternatives are not obviously finite and definite in number.


'According to the classical interpretation, the probability of an event, e.g. heads on a coin toss, is equal to the ratio of the number of "equipossibilies" (or equiprobable events) favourable to the event in question to the total number of relevant equipossibilities.'
Audi (1999)

"The classical theory of probability was that probability judgments describe sets of so-called equipossible alternatives. The initial judgment of equipossibility, in the hands of writers such as James Bernoulli and LAPLACE, would be made through using the principle of INDIFFERENCE. This is not satisfactory as an account of the meaning of ‘probable’, since ‘equipossibility’ disguises a judgment of equal probability. Nor does it suggest a very comprehensive way of coming to know probability judgments; for although some investigations may proceed by initially assigning equal probability to various events, not all do. For example, the probability of a male Englishman being between five and six feet tall is judged simply from the empirically given distribution of heights in the population."
Flew and Priest (2002)

'The classical theory defines an event's probability as the proportion of alternatives, among all those possible in a given situation, that include the event in question. There are 36 possible results of tossing two dice, of which 11 include at least one six, so the probability of getting at least one six in a throw of two dice is 11/36. But the alternatives must be equiprobable (equally probable) – or equispecific, if ‘equiprobable’ seems question-begging in an analysis of ‘probable’. This is hard to ensure. Attempts to ensure it have often used the principle of INDIFFERENCE. Other difficulties concern the probability of theories, such as Darwinism, and cases where the alternatives are not obviously finite and definite in number, e.g. the probability that all swans including future ones are white; since we can breed swans the number of future swans could depend on our very probability calculations. Also BERTRAND'S PARADOX and BERTRAND'S BOX PARADOX become relevant here. Kneale's ‘range’ theory attempts to answer some of these difficulties. Range is used elsewhere too. For Carnap a proposition's range is the set of state-descriptions compatible with it. See CONFIRMATION.'
Lacey (1996)