Abstract

There is a broad debate in contemporary philosophy of logic on the informativeness of proofs. In this context, informative proofs are demonstrations whose premises do not include the content of the conclusion. D’Agostino and Floridi (Synthese 167(2):271–315, 2009) claimed that proofs are informative if they use _virtual information_. In their terminology, this is the data carried by _dischargeable hypotheses_, assumptions entertained during proof and eliminated before concluding. Although these authors capture several cases of informative demonstrations, they do not explain the nature of virtual information. Why does the use of dischargeable hypotheses increase the informativeness of a demonstration? Following a Kantian inspiration, D’Agostino and Floridi claim that virtual information adds a synthetic feature to our proofs. However, this appeal to Kantianism is misleading: for Kant, mathematics is synthetic because it requires the construction of concepts in pure intuition. On the other hand, the entertainment of provisional hypotheses does not seem to involve the construction of figures in (transcendental) imagination. Exploring a _dialogical_ characterization of logic, I suggest that virtual information results from the dynamics between a reasoner and her audience. When a reasoner provisionally assumes _P_, she enacts potential interlocutors who commit to _P_. Thus, “virtual information” denotes the content of some assumptions of the possible audience of a demonstration. This process of departing from one’s original premises to embrace the suppositions of other people is informative, but it is not synthetic: in this way, the reasoner does not entertain intuitions but only needs to reason through the conceptual content of other people’s premises.