Did Frege commit a cardinal sin?

Analysis 75 (3):379-386 (2015)
  Copy   BIBTEX

Abstract

Frege’s _Basic Law V_ is inconsistent. The reason often given is that it posits the existence of an injection from the larger collection of first-order concepts to the smaller collection of objects. This article explains what is right and what is wrong with this diagnosis

Categories

Keywords

Reprint years

DOI

10.1093/analys/anv046

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,227

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A set theory with Frege-Russell cardinal numbers.Alan McMichael - 1982 - Philosophical Studies 42 (2):141 - 149.
Frege on cardinality.Lila Luce - 1988 - Philosophy and Phenomenological Research 48 (3):415-434.
Frege on Existence and Non‐existence.Karen Green - 2015 - Theoria 81 (4):293-310.
How tarskian is Frege?Joan Weiner - 2008 - Mind 117 (466):427-450.
The development of arithmetic in Frege's Grundgesetze der Arithmetik.Richard Heck - 1993 - Journal of Symbolic Logic 58 (2):579-601.
Hans Sluga (ed.), The philosophy of Frege. A four-volume collection of scholarly articles on all aspects of Frege's philosophy, vol.1: General assessments and historical accounts of Frege's philosophy, vol.2: Logic and foundations of mathematics in Frege's philosophy, vol.3: Meaning and ontology in Frege's philosophy, vol.4: Sense and reference in Frege's philosophy. [REVIEW]Jan Wolenński - 1997 - Erkenntnis 46 (3):407-410.
Frege, Carnap, and Explication: ‘Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science’.Gregory Lavers - 2013 - History and Philosophy of Logic 34 (3):225-41.
On the consistency of the Δ11-CA fragment of Frege's grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
Wittgenstein on Circularity in the Frege-Russell Definition of Cardinal Number.Boudewijn de Bruin - 2008 - Philosophia Mathematica 16 (3):354-373.
Concepts, extensions, and Frege's logicist project.Matthias Schirn - 2006 - Mind 115 (460):983-1006.
Frege on Vagueness and Ordinary Language.Stephen Puryear - 2013 - Philosophical Quarterly 63 (250):120-140.
Are truth values objects?Robert Ray - 1979 - Philosophical Studies 35 (2):199 - 211.
Cardinality, Counting, and Equinumerosity.Richard G. Heck - 2000 - Notre Dame Journal of Formal Logic 41 (3):187-209.
Frege's Notion of Logical Objects.Marco Antonio Caron Ruffino - 1996 - Dissertation, University of California, Los Angeles
Unsaturatedness: Wittgenstein's challenge, Frege's answer.Mark Textor - 2009 - Proceedings of the Aristotelian Society 109 (1pt1):61-82.

Analytics

Added to PP
2015-07-08

Downloads
76 (#219,061)

6 months
15 (#170,787)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

A. C. Paseau
University of Oxford

Citations of this work

Impredicativity and Paradox.Gabriel Uzquiano - 2019 - Thought: A Journal of Philosophy 8 (3):209-221.
The concept horse is a concept.Ansten Klev - 2018 - Review of Symbolic Logic 11 (3):547-572.
Russell’s Paradox and Free Zig Zag Solutions.Ludovica Conti - 2020 - Foundations of Science 28 (1):185-203.
Russell’s Paradox and Free Zig Zag Solutions.Ludovica Conti - 2020 - Foundations of Science 28 (1):1-19.
Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientiae:189-206.

View all 6 citations / Add more citations

References found in this work

Principia Mathematica.Morris R. Cohen - 1912 - Philosophical Review 21 (1):87.
Reason’s Nearest Kin.Michael Potter - 2000 - History and Philosophy of Logic 21 (3):231-234.
Saving Frege from contradiction.George Boolos - 1987 - Proceedings of the Aristotelian Society 87:137--151.

View all 8 references / Add more references