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.

chapter 1|24 pages

Origins and Varieties of Logicism

An Overview
ByFrancesca Boccuni, Andrea Sereni

part I|142 pages


chapter 2|28 pages

Frege on Caesar and Hume's Principle

ByPatricia Blanchette

chapter 3|24 pages

The Role of Truth

ByRobert May

chapter 4|40 pages

Anzahlen and Werthverläufe. Are There Objects Other Than Value-Ranges in Frege's Universe?

An Argument From Grundgesetze, §§I.34–40 *
ByMarco Panza

chapter 5|28 pages

Dedekind's Logicism

A Reconsideration and Contextualization
ByErich H. Reck

chapter 6|20 pages

Logical Form and the Development of Russell's Logicism

ByKevin C. Klement

part II|100 pages

Dangerous Liaisons

chapter 7|28 pages

Frege and Hilbert on Conceptual Analysis and Foundations

Some Remarks
ByMichael Hallett

chapter 8|18 pages

The Chimera of Logicism

Husserl's Criticism of Frege 1
ByMirja Hartimo

chapter 9|28 pages

Peano's Philosophical Views between Structuralism and Logicism

ByPaola Cantù

chapter 10|24 pages

Logicism in Logical Empiricism

ByGeorg Schiemer

part III|128 pages

The Roads Ahead

chapter 11|20 pages

Ordinals by Abstraction 1

ByBob Hale

chapter 12|20 pages

Logicism, Separation, and Complement

ByRoy T. Cook

chapter 13|40 pages

Principia Mathematica Redux

ByGregory Landini

chapter 15|23 pages

Frege's Theorem and Mathematical Cognition

ByLieven Decock