In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do we have (...) (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes. (shrink)

The paper critically discusses two prominent arguments against closure principles for knowledge. The first one is the “argument from aggregation”, claiming that closure under conjunction has the consequence that, if one individually knows i premises, one also knows their i-fold conjunction—yet, every one of the premises might exhibit interesting positive epistemic properties while the i-fold conjunction might fail to do so. The second one is the “argument from concatenation”, claiming that closure under entailment has the consequence that, if one knows (...) a premise, one also knows each of its remote consequences one arrives at—yet, again, the premise might exhibit interesting positive epistemic properties while some of its remote consequences might fail to do so. The paper firstly observes that the ways in which these two arguments try to establish that the relevant closure principle has the relevant problematic consequence are strikingly similar. They both crucially involve showing that, given the features of the case, the relevant closure principle acts in effect as a soritical principle, which is in turn assumed to lead validly to the relevant problematic consequence. There are however nontransitive logics of vagueness where soritical principles do not have any problematic consequence. Assuming that one of these logics is the correct logic of vagueness, the paper secondly observes that both arguments describe situations where knowledge is arguably vague in the relevant respects, so that a tolerant logic should be used in reasoning about it, with the effect that the relevant soritical principle no longer validly leads to the relevant problematic consequence. This shows an interesting respect in which the gap between validity and good inference that arguably arises in a transitive framework can be bridged in a tolerant one, thereby approximating better certain features of our epistemic lives as finite subjects. Moreover, even for those who do not subscribe to tolerant logics, the paper’s two observations jointly indicate that, for all the arguments from aggregation and concatenation show, the status of the relevant closure principles should be no worse than that assigned by one’s favoured theory of vagueness to soritical principles, which only rarely is plain falsity and can indeed get arbitrarily close to full truth. (shrink)