“Paraconsistent mathematics”的意思、由来-开放百科全书

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Paraconsistent mathematics

释义

References
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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

3 : Philosophy of mathematics|Proof theory|Paraconsistent logic

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