Ramified Frege Arithmetic

Journal of Philosophical Logic 40 (6):715-735 (2011)
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Abstract

Øystein Linnebo has recently shown that the existence of successors cannot be proven in predicative Frege arithmetic, using Frege’s definitions of arithmetical notions. By contrast, it is shown here that the existence of successor can be proven in ramified predicative Frege arithmetic

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10.1007/s10992-010-9158-y

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Richard Kimberly Heck
Brown University

Citations of this work

Predicative Frege Arithmetic and ‘Everyday’ Mathematics.Richard Heck - 2014 - Philosophia Mathematica 22 (3):279-307.
Frege meets Brouwer.Stewart Shapiro & Øystein Linnebo - 2015 - Review of Symbolic Logic 8 (3):540-552.
A Logic for Frege's Theorem.Richard Heck - 1999 - In Richard G. Heck (ed.), Frege’s Theorem: An Introduction. The Harvard Review of Philosophy.
The Basic Laws of Cardinal Number.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 1-30.

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References found in this work

Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
Logic, Logic, and Logic.George Boolos - 1998 - Cambridge, Mass: Harvard University Press. Edited by Richard C. Jeffrey.
Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
The Julius Caesar objection.Richard Heck - 1997 - In Richard G. Heck (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 273--308.

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