What is a new possibility in theoretical biology?

Biological evolution involves the appearance of new traits, new phenotypes and new processes but the mathematical understanding of such novelties is still lacking. In this paper, I argue that the notion of a new possibility should be and can be a fundamental notion in biology. This idea has been used in several models but it still lacks a proper mathematical, theoretical and epistemological framework. The notion of new possibility should be analyzed carefully since, like for the notion of probability, points of view a priori and a posteriori cannot be conflated. Moreover possibilities are virtual and it seems at first sight that adding possibilities by a retrospective theoretical move does not change the state of an object. In order to define precisely the notion of new possibilities, I will first discuss a positive notion of possibility which pertains to properties that are properly defined theoretically. This will lead us to a more precise discussion than the set-theoretic language to describe possibilities and enable us to define a robust notion of new possibilities.