Giorgio Israel – författare

Determinism, holism and complexity: three epistemological attitudes that have easily identifiable historical origins and developments. Galileo believed that it was necessary to "prune the impediments" to extract the mathematical essence of physical phenomena, to identify the math­ ematical structures representing the underlying laws. This Galilean method was the key element in the development of Physics, with its extraordinary successes. Nevertheless the method was later criticized because it led to a view of nature as essentially "simple and orderly", and thus by choosing not to investigate several charac­ teristics considered as an "impediment", several essential aspects of the phenomenon under investigation might be left out. The Galilean point of view also contains an acknowledgement of the central role played by the causal nexus among phenomena. The mechanistic-deterministic de­ scription of reality - for instance, a la Laplace - although acknowledging that it is not possible to predict phenomena exactly owing to unavoid­ able measurement error, is based on the recognition of the their causal nature, even in an ontological sense. Consequently, deterministic predic­ tion became the methodological fulcrum of mathematical physics. But although mechanistic determinism has had and, in many cases, still has, considerable success in Physics, in other branches of science this situa­ tion is much less favourable.

Determinism, holism and complexity: three epistemological attitudes that have easily identifiable historical origins and developments. Galileo believed that it was necessary to "prune the impediments" to extract the mathematical essence of physical phenomena, to identify the math­ ematical structures representing the underlying laws. This Galilean method was the key element in the development of Physics, with its extraordinary successes. Nevertheless the method was later criticized because it led to a view of nature as essentially "simple and orderly", and thus by choosing not to investigate several charac­ teristics considered as an "impediment", several essential aspects of the phenomenon under investigation might be left out. The Galilean point of view also contains an acknowledgement of the central role played by the causal nexus among phenomena. The mechanistic-deterministic de­ scription of reality - for instance, a la Laplace - although acknowledging that it is not possible to predict phenomena exactly owing to unavoid­ able measurement error, is based on the recognition of the their causal nature, even in an ontological sense. Consequently, deterministic predic­ tion became the methodological fulcrum of mathematical physics. But although mechanistic determinism has had and, in many cases, still has, considerable success in Physics, in other branches of science this situa­ tion is much less favourable.

Determinism, holism and complexity: three epistemological attitudes that have easily identifiable historical origins and developments. Galileo believed that it was necessary to "prune the impediments" to extract the mathematical essence of physical phenomena, to identify the math­ ematical structures representing the underlying laws. This Galilean method was the key element in the development of Physics, with its extraordinary successes. Nevertheless the method was later criticized because it led to a view of nature as essentially "simple and orderly", and thus by choosing not to investigate several charac­ teristics considered as an "impediment", several essential aspects of the phenomenon under investigation might be left out. The Galilean point of view also contains an acknowledgement of the central role played by the causal nexus among phenomena. The mechanistic-deterministic de­ scription of reality - for instance, a la Laplace - although acknowledging that it is not possible to predict phenomena exactly owing to unavoid­ able measurement error, is based on the recognition of the their causal nature, even in an ontological sense. Consequently, deterministic predic­ tion became the methodological fulcrum of mathematical physics. But although mechanistic determinism has had and, in many cases, still has, considerable success in Physics, in other branches of science this situa­ tion is much less favourable.

Foreword The modern developments in mathematical biology took place roughly between 1920 and 1940, a period now referred to as the "Golden Age of Theoretical Biology". The eminent Italian mathematician Vito Volterra played a decisive and widely acknowledged role in these developments. Volterra''s interest in the application of mathematics to the non physical sciences, and to biology and economics in particular, dates back to the turn of the century and was expressed in his inaugural address at the University of Rome for the academic year 1900/01 (VOLTERRA 1901). Nevertheless, it was only in the mid-twenties that Volterra entered the field in person, at the instigation of his son in law, Umberto D''Ancona, who had confronted him with the problem of competition among animal species, asking him whether a mathematical treatment was possible. From that time on, until his death in 1940, Volterra produced a huge output of publications on the subject. Volterra''s specific project was to transfer the model and the concepts of classical mechanics to biology, constructing a sort of "rational mechanics" and an "analytic mechanics" of biological associations. The new subject was thus to be equipped with a solid experimental or at least empirical basis, also in this case following the tried and tested example of mathematical physics. Although very few specific features of this reductionist programme have actually survived, Volterra''s contribution was decisive, as is now universally acknowledged, in en­ couraging fresh studies in the field of mathematical biology.

Foreword The modern developments in mathematical biology took place roughly between 1920 and 1940, a period now referred to as the "Golden Age of Theoretical Biology". The eminent Italian mathematician Vito Volterra played a decisive and widely acknowledged role in these developments. Volterra's interest in the application of mathematics to the non physical sciences, and to biology and economics in particular, dates back to the turn of the century and was expressed in his inaugural address at the University of Rome for the academic year 1900/01 (VOLTERRA 1901). Nevertheless, it was only in the mid-twenties that Volterra entered the field in person, at the instigation of his son in law, Umberto D'Ancona, who had confronted him with the problem of competition among animal species, asking him whether a mathematical treatment was possible. From that time on, until his death in 1940, Volterra produced a huge output of publications on the subject. Volterra's specific project was to transfer the model and the concepts of classical mechanics to biology, constructing a sort of "rational mechanics" and an "analytic mechanics" of biological associations. The new subject was thus to be equipped with a solid experimental or at least empirical basis, also in this case following the tried and tested example of mathematical physics. Although very few specific features of this reductionist programme have actually survived, Volterra's contribution was decisive, as is now universally acknowledged, in en­ couraging fresh studies in the field of mathematical biology.

Foreword The modern developments in mathematical biology took place roughly between 1920 and 1940, a period now referred to as the "Golden Age of Theoretical Biology". The eminent Italian mathematician Vito Volterra played a decisive and widely acknowledged role in these developments. Volterra's interest in the application of mathematics to the non physical sciences, and to biology and economics in particular, dates back to the turn of the century and was expressed in his inaugural address at the University of Rome for the academic year 1900/01 (VOLTERRA 1901). Nevertheless, it was only in the mid-twenties that Volterra entered the field in person, at the instigation of his son in law, Umberto D'Ancona, who had confronted him with the problem of competition among animal species, asking him whether a mathematical treatment was possible. From that time on, until his death in 1940, Volterra produced a huge output of publications on the subject. Volterra's specific project was to transfer the model and the concepts of classical mechanics to biology, constructing a sort of "rational mechanics" and an "analytic mechanics" of biological associations. The new subject was thus to be equipped with a solid experimental or at least empirical basis, also in this case following the tried and tested example of mathematical physics. Although very few specific features of this reductionist programme have actually survived, Volterra's contribution was decisive, as is now universally acknowledged, in en­ couraging fresh studies in the field of mathematical biology.

Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.