Theory of Probability

4Conditional Prevision and Probability

4.1 Prevision and the State of Information

We have all at times insisted on making clear the fact that every prevision and, in particular, every evaluation of probability, is conditional; not only on the mentality or psychology of the individual involved, at the time in question, but also, and especially, on the state of information in which he finds himself at that moment.

Those who would like to ‘explain’ differences in mentality by means of the diversity of previous individual experiences, in other words – broadly speaking – by means of the diversity of ‘states of information’, might even like to suppress the reference to the first factor and include it in the second. A theory of this kind is such that it cannot be refuted, but it seems (in our opinion) rather meaningless, being untestable, vacuous and metaphysical; in fact, since two different individuals (even if they are identical twins) cannot have had, instant by instant, the same identical sensations, any attempt at verification or refutation assumes an absurd hypothesis. It is like asking whether or not it is true that had I lived in the Napoleonic era and had participated in the Battle of Austerlitz I would have been wounded in the arm.

As long as we are just referring to evaluations relative to the same individual and state of information, there is no need to make any explicit mention of it; for example instead of P(E), writing something like P(E|H₀), where H₀ stands for ‘everything ...