Probability as a quasi-theoretical concept — J.V. Kries' sophisticated account after a century

Conclusion

These arguments are fairly well known today. It is interesting to note that v. Kries already knew them, and that they have been ignored by Reichenbach and v. Mises in their original account of probability.²

This observation leads to the interesting question why the frequency theory of probability has been adopted by many people in our century in spite of severe counterarguments. One may think of a change in scientific attitude, of a scientific revolution put forward by Feyerabendarian propaganda- and who would deny that Reichenbach was an excellent propagandist!

My suggested explanation is the following:

J. v. Kries is still a mentalist in the tradition of Descartes and Locke. This can be shown very well from his logic, which he wrote even much later (1916). A mentalist does not pose semantical questions in a proper sense: he rather asks which ideas in the human mind make up a concept. And studying probability in this way, he will find in any case that what is in the human mind is first of all an expectation. Therefore, his analysis of the concept of probability will be centered around the concept of expectation.

People tended to approach the problem in quite a different way after the scientific revolution which led from mentalism to lingualism. They tended in many cases to use operationalism and to ask how probabilities are determined in science, if they wanted to clear up the meaning of probability. This new aspect of probability, which was caused by looking at it from a new position or standpoint, suggested it to be the limit of relative frequencies in the first instance. This suggestion was so strong that all objections were ignored, and all counterarguments encountered deaf ears.

Of course I have used here an oversimplification. Neither was J. v. Kries untouched by Poincaré's conventionalism, which is essentially a movement leading to the breakdown of mentalism; nor was Reichenbach, when he wrote his thesis in 1915, already a lingualist in any respect.

Nevertheless, I think that the lingualist revolution, which took place particularly in mathematics and physics, has also changed the attitude towards probability. It would be interesting to corroborate this thesis by extensive study of the history of science in the late 19th century.

Besides this historical aspect of v. Kries' theory, there is a systematic one which should be noticed. Though his theory still has a mentalist outlook, many of v. Kries' statements can be translated into the present lingualist idiom and then become most interesting contributions to the present discussion. We shall then state that for v. Kries probabilities appear first of all in probabilistic hypotheses which may or may not be confirmed by empirical data. Therefore, they have a role similar to theoretical concepts.³

But that is not the only predominant feature of v. Kries' theory. He is approaching objective probability in a way which is quite unfamiliar to present day philosophers or mathematicians. Objective probabilities are connected with other concepts in three different ways. First of all, probabilistic hypotheses are confirmed by empirically found relative frequencies in a finite series of events. Secondly, they serve as an aid for decisions. And finally, there is a third relationship. Probabilities have to be explained by theories which are in many cases not formulated in probabilistic terms themselves. We can try to understand probability in one of the first two ways via their connection to other concepts. That is what is usually done by interpretations in terms of frequencies or decisions. A third approach, however, is to understand the nature of probability by the way probabilities are explained, and that is what v. Kries does. Such an approach does not seem unusual at all. In many cases the nature of a kind of objects is characterized by giving an explanation. If somebody asks what an eclipse of the moon is, we shall answer - as Aristotle already proposed - by giving an explanation of it. Thus it is quite natural to answer a question as to the nature of probability by describing the general type of explanation of probability distributions in natural or social science. The answer given by v. Kries is - as we know today — of limited validity. Quantum mechanical probabilities are not explainable by Spielräume. V. Kries solution, however, is remarkable in one important respect. It accounts for the time direction of objective probabilities, which are always predictive or forward probabilities, while retrodictive or backward probabilities are always subjective. The relation of objective probabilities to time direction is surely of utmost importance for natural philosophy. I do not know of any other philosophical foundation of probability which takes into account this deep-rooted relation. Therefore, v. Kries' interpretation may help us to understand one of the most intricate puzzles of philosophy. It may be nearly one hundred years old, but is by no means out of date.