Origins and Varieties of Logicism On the Logico-Philosophical Foundations of Mathematics Routledge Studies in the Philosophy of Mathematics and Physics Series

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.