Massimiliano Badino

There are two basic approaches to the problem of induction:the empirical one, which deems that the possibility of induction depends on how theworld was made (and how it works) and the logical one, which considers the formation(and function) of language. The first is closer to being useful for induction, whilethe second is more rigorous and clearer. The purpose of this paper is to create an empiricalapproach to induction that contains the same formal exactitude as the logical approach.This requires: (a) that the empirical conditions for the induction are enunciatedand (b) that the most important results already obtained from inductive logic are againdemonstrated to be valid. Here we will be dealing only with induction by elimination,namely the analysis of the experimental confutation of a theory. The result will bea rule of refutation that takes into consideration all of the empirical aspect of theexperiment and has each of the asymptotic properties which inductive logic has shown tobe characteristic of induction.

Boltzmann’s equilibrium theory has not received by the scholars the attention it deserves. It was always interpreted as a mere generalization of Maxwell’s work or, in the most favorable case, a sketch of some ideas more consistently developed in the 1872 memoir. In this paper, I try to prove that this view is ungenerous. My claim is that in the theory developed during the period 1866-1871 the generalization of Maxwell’s distribution was mainly a mean to get a more general scope: a theory of the equilibrium of a system of mechanical points from a general point of view. To face this issue Boltzmann analyzed and discussed probabilistic assumptions so that his equilibrium theory cannot be considered a purely mechanical theory. I claim also that the special perspective adopted by Boltzmann and his view about probabilistic requirements played a role in the transition to the non equilibrium theory of 1872.