Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of geometry was sustained (...) by Russell compels us to question the meaning of logicism: how is it possible to reconcile Russell's global reductionist standpoint with his local defence of the specificities of geometry? * This paper was first presented at the conference ‘Qu'est ce que la géométrie aux époques modernes et contemporaines?’, organized by the Universität Köln and the Archives Poincaré. I would like to thank Philippe Nabonnand for having enlightened me about the issues relative to projective geometry. I would like also to thank Nicholas Griffin, Brice Halimi, Bernard Linsky, Marco Panza, Ivahn Smadja for their helpful discussions. Many thanks also to the two anonymous referees for their useful suggestions. CiteULike Connotea Del.icio.us What's this? (shrink)

In a world shaped by contradictions, uncertainties, and evolving paradigms, Neutrosophic Philosophy emerges as a groundbreaking framework that transcends binary thinking. Rooted in the study of neutralities, contradictions, and their dynamic interplay, this philosophy redefines classical logic, epistemology, and ontology, offering a comprehensive approach to understanding reality. Through the lens of Neutrosophy, this book collects papers exploring fundamental concepts such as the continuum of neutralities, equilibrium of ideas, thesis-antithesis-neutrothesis, challenging traditional dialectical structures. It expands the boundaries of philosophy by integrating (...) mathematization, many-valued logics, and transdisciplinary approaches to knowledge. From quantum mechanics and artificial intelligence to ethics, sociology, and literature, the applications of Neutrosophy are vast and transformative. Whether reinterpreting paradoxes, reshaping philosophical foundations, or exploring the infinite nature of truth, this work paves the way for a new way of thinking—one that embraces ambiguity, indeterminacy, and the coexistence of opposites. By bridging disciplines and introducing innovative principles such as Neutrosophic Logic, Neutrosophic Social Evolution, and Neutrosophic Materialism, this book serves as both a theoretical foundation and a practical guide for scholars, researchers, and thinkers seeking a deeper understanding of complexity in the modern world. Neutrosophic Philosophy is not just an exploration of knowledge—it is an invitation to rethink the very essence of truth, reality, and human understanding. (shrink)

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.