The foundations of probability theory have many aspects, and Dr. Geiringer has covered a wide spectrum of the questions involved. I will comment only on a selection of points that, in my opinion, ought to be of interest to the physicist. Actually physicists have been showing little interest in the foundations of probability theory, although they are extensive users of the calculus itself. For this there are many reasons. Traditionally, physicists have been using differential equations in their fundamental theories. Probabilistic techniques were admitted only as an expediency in such cases in which the ‘correct’ method became unmanageably complicated. Since the probabilistic methods were ‘second best’, by definition, there seemed little interest in putting them on a sounder basis. Another factor may be the forbidding subtlety of modern mathematical arguments. The point I wish to make is that the foundation of probability theory has conceptual aspects that can be appreciated even in a simplified form. Evidently I am running the risk of being considered pedantic by physicists and pedestrian by mathematicians.
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- 1.L. Tisza, ‘The Logical Structure of Physics’, in Boston Studies in the Philosophy of Science, vol. I (ed. M. Wartofsky), Dordrecht 1961–1962, p. 55.– L. Tisza, Generalized Thermodynamics, Cambridge, Mass., 1966, pp. 333, 368.Google Scholar
- 2.The German 4 Merkmalraum’ is usually translated as sample space. Since this term is suggestive of statistical sampling, I believe that Dr. Geiringer is right to prefer label space in probability theory. If the ‘events’ are the possible states of physical system the term system space might be even more appropriate.Google Scholar
- 3.Reading, Mass., and London 1965.Google Scholar