Kategoria BISAC: Science >> Philosophy & Social Aspects

The Art of Science steers a course between two important and contradictory...

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane s work in the early 1940 s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a...

Like any goal-oriented procedure, experiment is subject to many kinds of failures. These failures have a variety of features, depending on the particulars of their sources. For the experimenter these pitfalls should be avoided and their effects minimized. For the historian-philosopher of science and the science educator, on the other hand, they are instructive starting points for reflecting on science in general and scientific method and practice in particular. Often more is learned from failure than from confirmation and successful application. The identification of error, its source, its...

Bruno de Finetti (1906 1985) is the founder of the subjective interpretation of probability, together with the British philosopher Frank Plumpton Ramsey. His related notion of exchangeability revolutionized the statistical methodology. This book (based on a course held in 1979) explains in a language accessible also to non-mathematicians the fundamental tenets and implications of subjectivism, according to which the probability of any well specified fact F refers to the degree of belief actually held by someone, on the ground of her whole knowledge, on the truth of the assertion that F...

Why is our world comprehensible? This question seems so trivial that few people have dared to ask it. In this book we explore the deep roots of the mystery of rationality. The inquiry into the rationality of the world began over two-and-a-half-thousand years ago, when a few courageous people tried to understand the world with the help of reason alone, rejecting the comforting fabric of myth and legend.

After many philosophical and theological adventures the Greek concept of rationality laid the foundations of a revolutionary way of thinking: the scientific method, which transformed...

The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of...

"La cosa piu incomprensibile del mondo e il fatto che sia comprensibile," ebbe a dire un giorno Albert Einstein. A ben pensarci, non e stupefacente che l Universo abbia un intima essenza razionale e matematica, tale da abilitare la mente umana a indagarlo e a conoscerlo?

Questo libro tratta dell evoluzione storica del concetto di razionalita, dal mondo greco classico fino ai nostri giorni, passando attraverso i contributi, spesso sottovalutati o mal compresi, dei Padri della Chiesa e dei teologi medievali. Se non si tengono nel giusto conto i risultati del costruttivo e serrato...