lunes, 19 de febrero de 2007

The Propensity Interpretation of Probability

Kart R Popper
The British Journal for the Philosophy of Science,

By an interpretation of probability Popper means an interpretation of such a statement as ‘The probability of 'a' given ‘b’ is equal to ‘r’:
‘p (a, b) = r’

The frequency interpretation sees that formula as a statement that can, in principle, be objectively tested, by means of statistical test. Here, ‘r’ describes the relative frequency with which the outcome ‘a’ is estimated to occur in any sufficiently long sequence of experiments characterized by the experimental conditions ‘b’.

Popper argues with the frequency interpretation, -especially which refers to singular events (The probability of a singular event can be nothing but the relative frequency within the sequence in question) - and proposes that the propensity interpretation of probability help us to explain, and to predict, the statistical properties of certain sequences. Propensities are defined as possibilities which are endowed with tendencies or dispositions to realize themselves, and which are taken to be responsible for the statistical frequencies with which they will in fact realize themselves in long sequences of repetitions of an experiment.

The propensity interpretation says that the probability is a property of the generating conditions –or the experimental arrangements- and if it is therefore considered as depending upon these conditions. Here the conditions are endowed with a tendency to produce sequences whose frequencies are equal to the probabilities. In this way, a singular event may have a probability even though it may occur only once, for its probability is a property of its generating conditions. The justification of this new idea is made just by an appeal to its usefulness for physical theory.