The very fact that Jerzy Neyman considers she might have been playing a “mischievous joke” on Harold Jeffreys (concerning probability) is enough to intrigue and impress me (with Hosiasson!). I’ve long been curious about what really happened. Eleonore Stump, a leading medieval philosopher and friend (and one-time colleague), and I pledged to travel to Vilnius to research Hosiasson. I first heard her name from Neyman’s dedication of Lectures and Conferences in Mathematical Statistics and Probability: “To the memory of: Janina Hosiasson, murdered by the Gestapo” along with around 9 other “colleagues and friends lost during World War II.” (He doesn’t mention her husband Lindenbaum, shot alongside her.) Hosiasson is responsible for Hempel’s Raven Paradox, and I definitely think we should be calling it Hosiasson’s (Raven) Paradox for much of the lost credit to her contributions to Carnapian confirmation theory[i].
But what about this mischievous joke she might have pulled off with Harold Jeffreys? Or did Jeffreys misunderstand what she intended to say about this howler, or? Since it’s a weekend and all of the U.S. monuments and parks are shut down, you might read this snippet and share your speculations…. The following is from Neyman 1952:
“Example 6.—The inclusion of the present example is occasioned by certain statements of Harold Jeffreys (1939, 300) which suggest that, in spite of my
insistence on the phrase, “probability that an object A will possess the
property B,” and in spite of the five foregoing examples, the definition of
probability given above may be misunderstood.
Jeffreys is an important proponent of the subjective theory of probability
designed to measure the “degree of reasonable belief.” His ideas on the
subject are quite radical. He claims (1939, 303) that no consistent theory of probability is possible without the basic notion of degrees of reasonable belief.
His further contention is that proponents of theories of probabilities alternative to his own forget their definitions “before the ink is dry.” In
Jeffreys’ opinion, they use the notion of reasonable belief without ever
noticing that they are using it and, by so doing, contradict the principles
which they have laid down at the outset.
The necessity of any given axiom in a mathematical theory is something
which is subject to proof. …
However, Dr. Jeffreys’ contention that the notion of degrees of reasonable
belief and his Axiom 1are necessary for the development of the theory
of probability is not backed by any attempt at proof. Instead, he considers
definitions of probability alternative to his own and attempts to show by
example that, if these definitions are adhered to, the results of their application would be totally unreasonable and unacceptable to anyone. Some
of the examples are striking. On page 300, Jeffreys refers to an article of
mine in which probability is defined exactly as it is in the present volume.
The first definition is sometimes called the “classical” one, and is stated in much
modern work, notably that of J. Neyman.
However, Jeffreys does not quote the definition that I use but chooses
to reword it as follows:
If there are n possible alternatives, for m of which p is true, then the probability of
p is defined to be m/n.
He goes on to say: Continue reading