 | The topic of this article may not meet Misplaced Pages's general notability guideline. Please help to demonstrate the notability of the topic by citing reliable secondary sources that are independent of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be merged, redirected, or deleted. Find sources: "Paraconsistent mathematics" – news · newspapers · books · scholar · JSTOR (February 2019) (Learn how and when to remove this message) |
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (February 2014) (Learn how and when to remove this message) |
Paraconsistent mathematics, sometimes called inconsistent mathematics, represents an attempt to develop the classical infrastructure of mathematics (e.g. analysis) based on a foundation of paraconsistent logic instead of classical logic. A number of reformulations of analysis can be developed, for example functions which both do and do not have a given value simultaneously.
Chris Mortensen claims (see references):
- One could hardly ignore the examples of analysis and its special case, the calculus. There prove to be many places where there are distinctive inconsistent insights; see Mortensen (1995) for example. (1) Robinson's non-standard analysis was based on infinitesimals, quantities smaller than any real number, as well as their reciprocals, the infinite numbers. This has an inconsistent version, which has some advantages for calculation in being able to discard higher-order infinitesimals. The theory of differentiation turned out to have these advantages, while the theory of integration did not. (2)
References
- McKubre-Jordens, M. and Weber, Z. (2012). "Real analysis in paraconsistent logic". Journal of Philosophical Logic 41 (5):901–922. doi: 10.1017/S1755020309990281
- Mortensen, C. (1995). Inconsistent Mathematics. Dordrecht: Kluwer. ISBN 0-7923-3186-9
- Weber, Z. (2010). "Transfinite numbers in paraconsistent set theory". Review of Symbolic Logic 3 (1):71–92. doi:10.1017/S1755020309990281
External links
- Entry in the Internet Encyclopedia of Philosophy
- Entry in the Stanford Encyclopedia of Philosophy
- Lectures by Manuel Bremer of the University of Düsseldorf
 | This mathematical logic-related article is a stub. You can help Misplaced Pages by expanding it. |