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.
1. Origins and Varieties of Logicism: An Overview Francesca Boccuni and Andrea Sereni Part I. Origins 2. Frege on Caesar and Hume’s Principle Patricia Blanchette 3. The Role of Truth Robert May 4. Anzahlen and Werthverläufe. Are there Objects other than Value-Ranges in Frege’s Universe? An Argument from Grundgesetze, §§ I.34-40 Marco Panza 5. Dedekind’s Logicism: A Reconsideration and Contextualization Erich Reck 6. Logical Form and the Development of Russell’s Logicism Kevin C. Klement Part II. Dangerous Liaisons 7. Frege and Hilbert on Conceptual Analysis and Foundations: Some Remarks Michael Hallett 8. The Chimera of Logicism: Husserl’s Criticism of Frege Mirja Hartimo 9. Peano’s Philosophical Views between Structuralism and Logicism Paola Cantù 10. Logicism in Logical Empiricism Georg Schiemer Part III. The Roads Ahead 11. Ordinals by Abstraction Bob Hale 12. Logicism, Separation, and Complement Roy T. Cook 13. Principia Mathematica Redux Gregory Landini 14. The Ontology of Abstraction, from Neo-Fregean to Neo-Dedekindian Logicism Fiona Doherty 15. Frege’s Theorem and Mathematical Cognition Lieven Decock
Francesca Boccuni is Associate Professor at Vita-Salute San Raffaele University, Milan. She published articles in scientific journals and collected volumes, edited collections in the philosophy of mathematics and logic. Andrea Sereni is Associate Professor at the School for Advanced Studies IUSS Pavia. He has published essays and books, as well as edited special issues and collections in the epistemology and philosophy of mathematics and logic.
Reviews for Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Mathematics
This volume promises to expand the discussion of logicism both historically and theoretically. It proposes an original and overdue re-examination of logicism and its import in the philosophy of mathematics. - Pieranna Garavaso, University of Minnesota Morris, USA
