Origins and Varieties of Logicism

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abstraction principles
abstractionism
analytic philosophy history
Andrea Sereni
arithmetical truths
Bertrand Russell
Bob Hale
Bolzano
Burali Forti's Contradiction
Burali Forti’s Contradiction
Cardinal Number
cardinality
Carnap
Category=PBB
Category=QD
Category=QDHR
Category=QDTL
Collective Combination
Dedekind
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Erich Reck
Fiona Doherty
formalism
Francesca Boccuni
Frege
Frege's Ontology
Frege's System
Frege's View
Frege’s Ontology
Frege’s System
Frege’s View
Genuine Singular Term
Geometric Calculus
Georg Schiemer
Goedel
Gregory Landini
Higher Order Logic
Hilbert
history of mathematics
Hume's Principle
Hume’s Principle
Husserl
Husserl's View
Husserl’s View
Kevin C. Klement
Lieven Decock
logic
logical empiricism
Logical Objects
logicism
logicism in contemporary mathematics
Logicist Thesis
Marco Panza
mathematical cognition
mathematical foundations
Mathematical Practice
Matthias Schirn
Michael Hallett
Mirja Hartimo
Natural Numbers
neo-Fregean theories
neo-Logicism
Number Concepts
numerical cognition research
Ordinal Abstraction
Ordinal Numbers
Paola Cantu
Patricia Blanchette
Peano
Peano Arithmetic
philosophy of logic
philosophy of mathematics
Principia Mathematica
Recursive Analysis
reference
Robert May
Roy T. Cook
Salvatore Florio
set theory
Singular Terms
Stefan Roski
structuralism
Vice Versa
Wittgenstein

Product details

  • ISBN 9781032159102
  • Weight: 576g
  • Dimensions: 152 x 229mm
  • Publication Date: 27 May 2024
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Paperback
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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.

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.