Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form $$\varGamma \models \varphi $$ Γ ⊧ φ —to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form $$\varGamma \not \models \psi $$ Γ ⊭ ψ to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic.

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According to tradition, logic is normative for reasoning. According to many contemporary philosophers of logic, there is more than one correct logic. What is the relationship between these two strands of thought? This paper makes two claims. First, logic is doubly normative for reasoning because, in addition to constraining the combinations of beliefs that we may have, logic also constrains the methods by which we may form them. Second, given that logic is doubly normative for reasoning, a wide array of logical pluralisms are inconsistent with the normativity of logic as they entail contradictory claims about how agents ought to reason. Thus, if logic is normative for reasoning, these pluralisms are untenable.