Re: Pienso, luego Dudo – Capítulo 18b

An alternative to the realist view of chance and probability is the subjectivist

doctrine. This is also known as Bayesianism because of its heavy reliance on a

certain interpretation of Bayes’s theorem. Bayesianism is the opinion that

probabilities are just opinions: that every probability value is a measure of the

strength of the belief of a person in a fact or in a statement. (See, e.g., de Finetti

1972, Jeffreys 1975, Keynes 1957, and Savage 1954.) This opinion was held

by no less than Jacques and Daniel Bernoulli, Pierre Simon Laplace, Augustus

De Morgan, and John Maynard Keynes.

More precisely, Bayesianism holds that (a) probabilities are properties of

beliefs, propositions, or statements, rather than of facts of a certain kind; and

(b) “probability measures the confidence that a particular individual has in the

truth of a particular proposition, for example, the proposition that it will rain

tomorrow” (Savage 1954: 3).

[…]

A third reason for adopting Bayesianism is the mistaken belief that it is the

only respectable alternative to the frequency doctrine proposed by such eminent

empiricists as John Venn (1962) and Richard von Mises (1926). According

to it, probability is definable in terms of long-run relative frequency. This

view is intuitively appealing to experimental scientists because it conflates

chance (or randomness) with its tests–an instance of the operationist confusions

of definition with test, and reference with evidence. Indeed, to determine

whether a given set of data is random, one looks for certain fairly constant

global properties of the set, particularly the shape and scatter (variance) of a

distribution, such as the bell curve. In particular, when observed frequencies

are available, one contrasts them with the corresponding calculated probabilities.

But one should remember that probabilities (and probability densities) are

properties of individuals, whereas the statistical parameters are properties of

aggregates. Besides, statistics are restricted to past events, the only ones on

which statistical parameters, such as frequencies and variances, can be counted.

(More in Bunge 1981a and 1988.) Last, but not least, the frequency theory of

probability happens to be mathematically flawed (Ville 1939).

So, the frequency theory of probability must be discarded. However, contrary

to popular belief, Bayesianism is not the sole alternative to it. Indeed, as

suggested in the previous section, there is a tertium quid, namely, the objectivist

(or realist or “propensity”) interpretation, the one usually employed in

theoretical physics and biology. For example, the probability distributions

calculated in classical statistical mechanics are deemed to be objective properties

of the systems concerned. Furthermore, those distributions depend on the

system’s energy and temperature, neither of which can be estimated by counting

frequencies. When such a count is possible, its serves to test probability

estimates, not to assign them meanings.