 Perhaps there is a reason to allow the notion of logical consequence to apply even more broadly. In Gentzen’s proof theory for classical logic, a notion of consequence is defined to hold between multiple premises and multiple conclusions. The argument from a set \(X\) of premises to a set \(Y\) of conclusions is valid if the truth of every member of \(X\) guarantees (in the relevant sense) the truth of some member of \(Y\). There is no doubt that this is formally perspicuous, but the philosophical applicability of the multiple premise—multiple conclusion sense of logical consequence remains an open philosophical issue. In particular, those anti-Realists who take logical consequence to be defined in terms of proof (such as Michael Dummett) reject a multiple conclusion analysis of logical consequence. For an Anti-realist, who takes good inference to be characterised by the way warrant is transmitted from premise to conclusion, it seems that a multiple conclusion analysis of logical consequence is out of the question. In a multiple conclusion argument from \(A\) to \(B, C\), any warrant we have for \(A\) does not necessarily transmit to \(B\) or \(C\): the only conclusion we are warranted to draw is the disjunction \(B\) or \(C\), so it seems for an analysis of consequence in terms of warrant we need to understand some logical vocabulary (in this case, disjunction) in order to understand the consequence relation. This is unacceptable if we hope to use logical consequence as a tool to define that logical vocabulary. No such problems appear to arise in a single conclusion setting. (However, see Restall (2005) for a defence of multiple conclusion consequence for Anti-realists; and see Beall (2011) for a defence of certain sub-classical multiple-conclusion logics in the service of non-classical solutions to paradox.)