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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.
This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.
The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.
A founder of modern analytic philosophy and one of the most important logicians of the twentieth century, Bertrand Russell has influenced generations of philosophers. The Bloomsbury Companion to Bertrand Russell explores this influence in detail and responds to renewed interest in Russell's philosophical approach, presenting the best guide to research in Russell studies today. Bringing new insights into Russell's relationship with his contemporaries, a team of experts explore his life-long battles with important philosophical issues. They consider how he influenced thinkers and schools of thought, from Schröder, Frege and Meinong to Wittgenstein and the Vienna Circle, while also covering his impact on individual issues in epistemology, logic, metaphysics, philosophy of mind, philosophy of language, and political philosophy. Importantly this companion discusses often overlooked topics. Focusing on Russell's later views, including his moral philosophy and his politics, reveals that Russell did make significant contributions to ethics - both theoretical and practical - in the course of his career. Through a combination of enlightening historical background and sustained focus on Russell's impact on contemporary areas of philosophy, The Bloomsbury Companion to Bertrand Russell demonstrates why Russell continues to influence philosophers of language, mathematics, epistemology and metaphysics.
These essays apply the core conceptual innovation underlying Frege's theory of number to the general analysis of theoretical knowledge.
This systematic and historical treatment of Russell's contributions to analytic philosophy, from his embrace of analysis in 1898 to his landmark theory of descriptions in 1905, draws important connections between his philosophically motivated conception of analysis and the technical apparatus he devised to facilitate analyses in mathematics
This book repairs and revives the Theory of Knowledge research program of Russell’s Principia era. Chapter 1, 'Introduction and Overview', explains the program’s agenda. Inspired by the non-Fregean logicism of Principia Mathematica, it endorses the revolution within mathematics presenting it as a study of relations. The synthetic a priori logic of Principia is the essence of philosophy considered as a science which exposes the dogmatisms about abstract particulars and metaphysical necessities that create prisons that fetter the mind. Incipient in The Problems of Philosophy, the program’s acquaintance epistemology embraced a multiple-relation theory of belief. It reached an impasse in 1913, having been itself retrofitted with abstract particular logical forms to address problems of direction and compositionality. With its acquaintance epistemology in limbo, Scientific Method in Philosophy became the sequel to Problems. Chapter 2 explains Russell’s feeling intellectually dishonest. Wittgenstein’s demand that logic exclude nonsense belief played no role. The 1919 neutral monist era ensued, but Russell found no epistemology for the logic essential to philosophy. Repairing, Chapters 4–6 solve the impasse. Reviving, Chapters 3 and 7 vigorously defend the facts about Principia. Studies of modality and entailment are viable while Principia remains a universal logic above the civil wars of the metaphysicians.
This book offers new perspectives on the history of analytical philosophy, surveying recent scholarship on the philosophical study of mind, language, logic and reality over the course of the last 200 years. Each chapter contributes to a broader engagement with a wider range of figures, topics and disciplines outside of philosophy than has been traditionally associated with the history of analytical philosophy. The book acquaints readers with new aspects of analytical philosophy’s revolutionary past while engaging in a much needed methodological reflection. It questions the meaning associated with talk of 'analytic' philosophy and offers new perspective on its development. It offers original studies on a range of topics – including in the philosophy of language and mind, logic, metaphysics and the philosophy of mathematics – and figures whose relevance, when they is not already established as in the case of Russell, Moore and Wittgenstein, are just now beginning to become the topic of mainstream literature: Franz Brentano, William James, Susan Langer as well as the German and British logicians of the nineteenth century.
To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.