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Fourteenth-century logicians define formal consequences as consequences that remain valid under uniform substitutions of categorematic terms, but they say little about the significance of this distinction. Why does it matter whether a consequence is formal or material? One possible answer is that, whereas the validity of a material consequence depends on both its structure and “the nature of things”, the validity of a formal consequence depends on its structure alone. But this claim does not follow from the definition of formal consequence by itself, and the fourteenth-century logicians do not give an argument for it. For that we must turn to Abelard, who argues explicitly that consequences that hold under uniform substitutions of their terms take their validity from their construction alone, and not from “the nature of things”. I will look at Abelard’s argument in its historical context. If my reconstruction is correct, the argument, and hence also the significance of the distinction between formal and material consequence depends on a conception of “the nature of things” that we can no longer accept. This should give pause to contemporary thinkers who look to medieval notions of formal consequence as antecedents of their own.