Infeasible inconsistency

[Kreinovich, Vladik]

As a partial answer to this question, it is probably worth mentioning an easy-to-prove fact that for many ZF statements S, we can add, to arithmetic,

·         all arithmetic consequences of S AND

·         all arithmetic consequences of “not S”,
and still get a consistent theory, see e.g.,

Olga Kosheleva and Vladik Kreinovich, "Contradictions do not
  necessarily make a theory inconsistent", Journal of Innovative
  Technology and Education, 2017, Vol. 4, No. 1, pp. 59-64.
http://www.cs.utep.edu/vladik/2017/tr17-27.pdf


From: FOM <fom-bounces at cs.nyu.edu> On Behalf Of Joe Shipman


The reason I am concerned about the lack of examples is that paraconsistent logic doesn’t seem to be worth much unless there is such a system that it could be applied to.

— JS
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