It is probably the most fundamental tenet of philosophy that any inquiry requires a method or a system, as – as Descartes also notice (AT 10:371, CSM 1:15f) – a haphazard approach to inquiry can never guarantee for its findings. A philosophical system is traditionally defined by two structural pillars: consistency (the absence of contradictions) and closure under specific rules, most notably modus ponens. This is because, classically, a single contradiction makes any system logically trivial. For this reason in the last decades many paraconsistent logics have been devised (like the one proposed by Fagin and Halpern [1988]) to offer strategies to allow for a contradiction in a logical systems and still contain such “explosions” semantically.

The interpretation of this kind of works has changed in the last years, when an approach first suggested in Priest [1982] started to gain more traction: Priest suggests that certain contradictions may be real metaphysical features of the world rather than mere errors and, for this reason, paraconsistent logic has to be adopted as the new standard logic, as it is more suitable to describe the world.

We argue that such proposals to revise logic based on empirical observation faces some issues: a rational agent cannot simply “adopt” a new logical rule without already possessing a pre-existing logical framework, as Kripke [2023] observes, and recent takes on the logic on belief seems to fall in the same pitfall (see Williamson [2024]). Ultimately, logic remains fundamentally non-revisable in its core structure, because the criteria for such a revision must be extra-logical. Consequently, classical logic functions not merely as one algebraic option among many, but as the foundational structure upon which all systematic implementations – including alternative ones – must necessarily insist.

Keywords: Adoption problem, Logic revision, Hyperintensionality, Paraconsistency

References:

Descartes, R. Rules for the Direction of the Mind (AT 10:371, CSM 1:15f).

Fagin, R., & Halpern, J. (1988). “Belief, awareness and limited reasoning.” Artificial Intelligence, 34, pp. 39–76.

Kripke, S. A. (2023). “The Question of Logic.” Mind, 133(529), pp. 1–36.

Priest, G. (1982). “To Be and Not to Be: Dialectical Tense Logic.” Studia Logica, 41(2-3), pp. 249–268.

Williamson, T. (2024). Heuristics and Overfitting in Philosophy. New York: Oxford University Press.