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Subjective probability and statistical physics

Statistical physics has a history stretching back 150 years. The subjective view on probability goes back three centuries. Any paper, such as this one, that aims to survey the interplay between these two themes in just a few pages must therefore necessarily be selective, and also subjective in its choice. Before discussing the role of the subjective view on probability in statistical physics, it should be clear what is meant by ”subjective”. Particularly, because there are at least two main variants of the subjective/objective dichotomy. We shall meet both variants in our discusion of probability below. A first sense in which a quantity, quality, attribute or predicate of a physical system (or event, or state) my be called ‘objective’ is that it corresponds to a property of the object (or event or state). For example, the mass, charge, position, etc. of a system are thought to be properties which are either inherent to the system or determined by the state of the system itself. Such attributes do not depend on us, the subjects who consider or observe such systems. Of course one may counter that the numerical values by which we measure mass, charge, position etc., do depend on a coordinate frame of reference, a choice of units and so on, so that, strictly speaking we are not dealing with properties of a system by itself, but rather with a relation between the system and some such a system of reference or units. But this does not alter the point that, even if so conceived, attributes of the kind just mentioned are are then determined by a factual relation between the system in and some given reference system. Whether this relation holds (or not) is considered a fact which does not depend on the beholder. By contrast, when we say that a painting is beautiful, a piece of music is passionate, or a dish tasty, this is not thought to express an objective state of affairs, but rather a judgment or attitude from the person who considers it. Beauty, as the saying goes, is in the eye of the beholder. Subjective attributes of an object thus seem to reside in the mind perceiving or contemplating such objects rather than inherent in the object itself, or in relations of the object with fixed referential systems. This is the first main variant of the subjective/objective dichotomy.