Synthese 191 (13):3063-3078 (2014)

Jean Paul Van Bendegem
Vrije Universiteit Brussel
No one will dispute, looking at the history of mathematics, that there are plenty of moments where mathematics is “in trouble”, when paradoxes and inconsistencies crop up and anomalies multiply. This need not lead, however, to the view that mathematics is intrinsically inconsistent, as it is compatible with the view that these are just transient moments. Once the problems are resolved, consistency (in some sense or other) is restored. Even when one accepts this view, what remains is the question what mathematicians do during such a transient moment? This requires some method or other to reason with inconsistencies. But there is more: what if one accepts the view that mathematics is always in a phase of transience? In short, that mathematics is basically inconsistent? Do we then not need a mathematics of inconsistency? This paper wants to explore these issues, using classic examples such as infinitesimals, complex numbers, and infinity
Keywords Mathematics  Paraconsistency  Infinitesimals  Complex numbers  Strict finitism
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DOI 10.1007/s11229-014-0474-6
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References found in this work BETA

Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.

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