History and Philosophy of Logic 41 (1):82-95 (2020)

Authors
Panu Raatikainen
Tampere University
Abstract
The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few rudimentary facts of arithmetic are logically derivable from Hume’s Principle. And that hardly counts as a vindication of logicism.
Keywords Neo-logicism  Second-order logic  Frege's theorem
Categories (categorize this paper)
Reprint years 2020
ISBN(s)
DOI 10.1080/01445340.2019.1680517
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
Through your library

References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Introduction to Mathematical Logic.Alonzo Church - 1944 - London: Oxford University PRess.
Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.

View all 40 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Logicism Revisited.Otávio Bueno - 2001 - Principia 5 (1-2):99-124.
Logicism Reconsidered.Patricia A. Blanchette - 1990 - Dissertation, Stanford University
Aristotelian Logic, Axioms, and Abstraction.Roy T. Cook - 2003 - Philosophia Mathematica 11 (2):195-202.
The Logic in Logicism.Alexander Bird - 1997 - Dialogue 36 (2):341--60.
The Contemporary Interest of an Old Doctrine.William Demopoulos - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:209 - 216.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Finitude and Hume's Principle.Richard G. Heck Jr - 1997 - Journal of Philosophical Logic 26 (6):589 - 617.
Frege, Dedekind, and the Origins of Logicism.Erich H. Reck - 2013 - History and Philosophy of Logic 34 (3):242-265.
Frege, Kant, and the Logic in Logicism.John MacFarlane - 2002 - Philosophical Review 111 (1):25-65.
Logicism as Making Arithmetic Explicit.Vojtěch Kolman - 2015 - Erkenntnis 80 (3):487-503.
On the Origin and Status of Our Conception of Number.William Demopoulos - 2000 - Notre Dame Journal of Formal Logic 41 (3):210-226.

Analytics

Added to PP index
2015-03-22

Total views
1,273 ( #3,842 of 2,462,339 )

Recent downloads (6 months)
46 ( #19,211 of 2,462,339 )

How can I increase my downloads?

Downloads

My notes