A collection of articles originally presented at two conferences, the first at Ventura Hall, Stanford, in April 1998; and the second at the University of Bologna in September 1999.

The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary (...) particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status.Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics.In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox. (shrink)

The difference between carnap's and de finetti's conceptions of probability does not consist of a couple of requirements, As carnap asserted in a letter to de finetti. The paper is intended to give a theoretical justification for this denial. In order to do this, The author stresses the difference between (tolerant) objectivism and (radical) subjectivism. The difference is discussed in statistical terms. The discussion is faced with respect to predictive inferences, A type of statistical inference that both carnap and de (...) finetti advocate in many occasions. (shrink)