In ([3]; [5], Ch. 8) Graham Priest argues that classical reasoning can be made compatible with his preferred (paraconsistent) logical theory (LP) by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favor of the one in [4], I shall suggest that due to the fact that the Derivability Adjustment Theorem holds for several Logics of Formal (In)consistency (cf. [2]), these paraconsistent logics are particularly well-suited to accommodate classical reasoning by means of (a version of) that maxim – yielding, thus, an enthymematic account of classical recapture.

References

[1] BEALL, J. C. A Simple Approach Towards Recapturing Consistent Theories in Paraconsistent Settings. Review of Symbolic Logic 6 (2013), 1–10.

[2] CARNIELLI, W. A., AND CONIGLIO, M. E. Paraconsistent Logic: Consistency, Contradiction and Negation. Springer, 2016.

[3] PRIEST, G. The Logic of Paradox. Journal of Philosophical Logic 8 (1979), 219–241.

[4] PRIEST, G. Minimally Inconsistent LP. Studia Logica 50 (1991), 321–331.

[5] PRIEST, G. In Contradiction, 2nd ed. Oxford University Press, 2006.