Giorgio Israel

The Science of Complexity: Epistemological Problems and Perspectives

For several decades now a set of researches from a wide range of different sectors has been developed which goes by the name of “science of complexity” and is opposed point by point to the paradigm of classical science. It challenges the idea that world is “simple.” To the reductionist idea that each process is the sum of the actions of its components it opposes a holistic view (the whole is more than the sum of the parts). The aim of the present article is to analyze the epistemological status attributed in the science of complexity to several fundamental ideas, such as those of scientific law, objectivity, and prediction. The aim is to show that the hope of superseding reductionism by means of concepts such as that of “emergence” is fallacious and that the science of complexity proposes forms of reductionism that are even more restrictive than the classical ones, particularly when it claims to unify in a single treatment problems that vary widely in nature such as physical, biological, and social problems.

The Poincaré-Volterra theorem: a significant event in the history of the theory of analytic functions

Summaries In this article we have reconstructed the history of the Poincare-Volterra theorem (which asserts that the set of values of an analytic function in a point of its domain of definition is a set of countable power at most). For this purpose we have made use of unpublished material from the Volterra archives, conserved in the Accademia Nazionale dei Lincei. The appendixes provide transcripts of correspondence between Vito Volterra and Georg Cantor, of correspondence between Volterra and Giulio Vivanti, and a manuscript by Volterra. The history of the Poincare-Volterra theorem clarifies some developments in the theory of analytic functions toward the end of the nineteenth century. In particular, we have shown that the attitude of some of the greatest mathematicians of the period toward Riemanns geometric theory was quite negative, while Weierstrass arithmetical theory was regarded as fully satisfactory.

Qualitative and numerical analysis of a class of prey-predator models

We consider a problem of the dynamics of prey-predator populations suggested by the content of a letter of the biologist Umberto D’Ancona to Vito Volterra. The main feature of the problem is the special type of competition between predators of the same species as well as of different species. Two classes of cases are investigated: a first class in which the behaviour of the predator is ‘blind’ and the second one in which the behaviour is `intelligent’. A qualitative analysis of the dynamical systems under consideration is followed by a numerical analysis of the most significant cases.