Paraconsistent Mathematics

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 interesting 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. Interestingly, the theory of differentiation turned out to have these advantages, while the theory of integration did not. (2)

Famous quotes containing the word mathematics:

    Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
    Simone Weil (1909–1943)