Authors
Maarten McKubre-Jordens
Canterbury University
Zach Weber
University of Otago
Abstract
A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent innitesimals. The area of the circle is taken 'up to inconsistency'. The fact that the core of Archimedes's proof still works in a weaker logic is evidence that the integral calculus and analysis more generally are still practicable even in the event of inconsistency.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.26686/ajl.v14i1.4034
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,586
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
Real Analysis in Paraconsistent Logic.Maarten McKubre-Jordens & Zach Weber - 2012 - Journal of Philosophical Logic 41 (5):901-922.
Whither Relevant Arithmetic?Harvey Friedman & Robert K. Meyer - 1992 - Journal of Symbolic Logic 57 (3):824-831.
Inconsistent Models of Arithmetic: Part II: The General Case.Graham Priest - 2000 - Journal of Symbolic Logic 65 (4):1519-1529.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Real Analysis in Paraconsistent Logic.Maarten McKubre-Jordens & Zach Weber - 2012 - Journal of Philosophical Logic 41 (5):901-922.
Negation and Paraconsistent Logics.Soma Dutta & Mihir K. Chakraborty - 2011 - Logica Universalis 5 (1):165-176.
Paraconsistency Everywhere.Greg Restall - 2002 - Notre Dame Journal of Formal Logic 43 (3):147-156.
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
Logic and Aggregation.Bryson Brown & Peter Schotch - 1999 - Journal of Philosophical Logic 28 (3):265-288.
Paraconsistent Logics Included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):442-466.
Contradiction and Contrariety. Priest on Negation.Heinrich Wansing - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):81-93.
A Paraconsistent Model of Vagueness.Z. Weber - 2010 - Mind 119 (476):1025-1045.
A Paraconsistentist Approach to Chisholm's Paradox.Marcelo Esteban Coniglio & Newton Marques Peron - 2009 - Principia: An International Journal of Epistemology 13 (3):299-326.

Analytics

Added to PP index
2017-04-11

Total views
12 ( #729,172 of 2,348,743 )

Recent downloads (6 months)
1 ( #512,546 of 2,348,743 )

How can I increase my downloads?

Downloads

My notes