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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)
and 24 Related for: Paraconsistent mathematics information
Paraconsistentmathematics, sometimes called inconsistent mathematics, represents an attempt to develop the classical infrastructure of mathematics (e...
Paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating[clarification needed] way. Alternatively, paraconsistent...
Maarten (August 2011). "This is not a carrot: Paraconsistentmathematics". Plus Magazine. Millennium Mathematics Project. Retrieved January 14, 2017. de Swart...
geometry Paraconsistentmathematics sometimes called inconsistent mathematics, it is an attempt to develop the classical infrastructure of mathematics based...
"unreasonable effectiveness of mathematics", paraconsistentmathematics, and the role of mathematical notation in the progress of mathematics. The book was praised...
classical propositional logic and intuitionistic logic, but not in some paraconsistent logics. Stoic logic Type of syllogism (disjunctive, hypothetical, legal...
Costa's international recognition came especially through his work on paraconsistent logic and its application to various fields such as philosophy, law...
Equiconsistency Hilbert's problems Hilbert's second problem Jan Łukasiewicz Paraconsistent logic ω-consistency Gentzen's consistency proof Proof by contradiction...
and false. They thereby reject the principle of bivalence of truth. Paraconsistent logics are logical systems able to deal with contradictions. They do...
translations. Mathematical Logic Quarterly Volume 55, Issue 5, 2009, pages 515-534. W. A. Carnielli (with J. C. Agudelo). Paraconsistent Machines and their...
proposed logics that deny the validity of the law. Logics known as "paraconsistent" are inconsistency-tolerant logics in that there, from P together with...
originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded middle as well as the...
Nicolay Vasilyev, inventor of non-Aristotelian logic, the forerunner of paraconsistent and multi-valued logics Ivan Vinogradov, developed Vinogradov's theorem...
deg. See Star catalogue#Proper motion catalogues Logic of Paradox, a paraconsistent logic LP record, a long-playing 12- or 10-inch (30 or 25 cm) vinyl record...
they may be adopted. Intuitionistic logic is related by duality to a paraconsistent logic known as Brazilian, anti-intuitionistic or dual-intuitionistic...
made to create a paraconsistent logic. Some Soviet philosophers argued that the materialist dialectic could be seen in the mathematical logic of Bertrand...
while paraconsistent logics reject the principle of explosion. Deductive reasoning plays a central role in formal logic and mathematics. In mathematics, it...
following Aristotle, that no dialetheia exist, but they are allowed in some paraconsistent logics. Frank Ramsey drew a distinction between logical paradoxes and...
In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly...
Contradiction – 1937 essay by Mao Zedong Oxymoron – Figure of speech Paraconsistent logic – Type of formal logic without explosion principle Paradox – Statement...
to paraconsistent logic, and made contributions to predicative set theory and geometry. Avron, Arnon (2001). Introduction to Discrete Mathematics (in...
1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be...
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