Multi-valued conditional events avoid lewis' triviality result

Abstract

The concept of conditional event dealt with here is that given by Coletti and Scozzafava in a series of paper: a detailed account of the relevant theory is in their book "Probabilistic Logic in a Coherent Setting", Kluwer (2002). In this paper, our aim is to show that relying on this definition many of the (putative) inconsistencies and flaws concerning this concept disappear. In particular, the well-known Lewis' triviality principles can be looked on, in this framework, under a different perspective, also due to the circumstance that the concept of "indicative conditionals" (as put by Lewis, and also by Adams) is a very particular case of this general concept of conditional event. A crucial role is played, in our approach, by conditional events of probability 0 and 1.