Thinking about random events from a logical point of view

Abstract

The purpose of this essay is to identify a meaningful property of random events by using a theorem introduced in an unconventional symbolic language, which we shall call ℒ_u. More precisely, we attempt to show that every random event must occur at least once. The method, which we use, consists in defining, by means of sentences of the language ℒ_u, the concept of random event, after showing that some statements about the structural proprieties of the sentences of ℒ_u can be translated into sentences of the language ℒ_u itself. Thanks to this peculiar feature of ℒ_u, we achieve an important gain in facilitating the identification of the propriety looked for. In fact, it is easier to deal with sentences of a formal system, free of concealed assumptions and possibly misleading associations of meaning, than with true and false statements.