Evolution: an axiomatic perspective

In this paper we present an axiomatic theory of evolution which is inspired by the reading of a paper written by G.V. Schiaparelli in 1898. Schiaparelli was a famous astronomer, but he also studied the Darwinian ideas. We propose five axioms which can characterize the theory of evolution. We have also written these axioms using the language of the logic of predicates of first order with some constant monadic and dyadic predicates and appropriate functionals. But we can use other types of logic. So we can examine the concepts of species and of speciation. Then we introduce the interesting notion of generation distance. Moreover we give a theorem which establishes a geometrical model of our theory. If we analyze further the fourth axiom (which concerns the notion of generation distance) we can propose an elementary dynamical model by which we can represent possible evolutionary dynamics. These dynamics partially depend on random quantities.