文章基本信息

标题：Paraconsistent Measurement of the Circle
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作者：Zach Weber ; Maarten McKubre-Jordens
期刊名称：Australasian Journal of Logic
印刷版ISSN：1448-5052
电子版ISSN：1448-5052
出版年度：2017
卷号：14
期号：1
语种：English
出版社：Philosophy Department, University of Melbourne
摘要：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.