 To make further progress in these debates, an important element is arguably the historical development of the notion of (logical) consequence over the centuries, so that we may come to understand where the informal notion(s) of logical consequence come(s) from. Engaging in an exercise of ‘conceptual history’ may allow for a better grasp of the reasons why this notion (now widely endorsed) established itself as such in the first place. If these are compelling reasons, then they may count as arguments in favor of the centrality of formality and necessary truth-preservation; but if they rest on disputable, contentious assumptions, then the analysis may provide elements for a critical evaluation of each of these two components as truly constitutive of the concept of logical consequence.