Federica Melis
University of Bologna
The question of how logic explains has received comparatively little attention in the philosophy of logic. Notable exceptions include Wyatt and Payette (2018) and Martin (2021). These accounts take the validity of arguments to constitute the explanans of a logical explanation. A central line of concern for both the approaches is that traditional models of explanation, in particular the deductive-nomological (DN) model, do not seem well suited to logic. The core difficulty is that applying DN models to logical explanation appears to generate a threat of circularity. The aim of this paper is to challenge this line of thought.
A DN logical explanation proceeds by translating a particular argument A with conclusion b (A;b) into a formal structure (Γ,φ) via conditions C, i.e. translation rules. The laws (L) are given by the semantics or proof theory of a logical system, from which it follows that either Γ⊢φ or Γ⊬φ. A DN explanation derives this consequence from L, showing that (Γ,φ) satisfies the relevant conditions. Given that (Γ,φ) correctly translates A;b and that the laws hold, it follows that A;b is valid. The account appeals to rules of implication that already presuppose a notion of validity or consequence. But «if logicians were to use the DN model, they would be forced to assume what they are seeking to establish—the truth of certain logical laws» (Martin 2021: 607). The aim of this paper is to challenge this line of thought.
First, DN explanations employ rules of implication to derive results from logical laws, but this does not amount to presupposing the truth of those laws. As Martin (2021: 908) notes, rules of implication are not themselves theorems, even if they can be represented as such. Hence, it is not obvious that one must already assume the truth of the relevant logical laws in order to be warranted in making such inferences. Second, both accounts seem to equate explanation and justification of a logical argument. The aim of DN explanations, or more generally of unificationist models, is not to establish the correctness of logical laws, nor to justify a system from an external standpoint, but to explain the validity of a particular argument. The relevant logical laws are not justified within the explanation, but are presupposed as part of the framework in which the explanation operates. I conclude than an epistemic, rather than ontic, conception of explanation is required: to explain why an argument is valid is to yield understanding on how it falls under a more general schema.
Martin, B. (2021). Anti-exceptionalism about logic and the burden of explanation. Canadian Journal of Philosophy, 51(8), 602–618.
Wyatt, N., & Payette, G. (2018). How do logics explain? Australasian Journal of Philosophy, 96(1), 157–167.
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SOPhiA 2026 