Non-classical logic concepts of Hugh MacColl

In this article we attempt to review the main ideas of non-classical logic of Hugh MacColl, logician, mathematician and philosopher (1837–1909). Based on the ideas of G. Boole MacColl impressively advanced in the fields of studying implication and the nature of inference. This research led the Scottish scholar to an idea that there can be more than two traditional truth-values, 1 and 0, respectively. And by the same time MacColl discovered and defined different types of modalities. Thus, his investigations were breaking-through for his time and anticipated some of milestone innovations in logic of the XX century. His works caused combative debates when released. Most famous logicians of his time criticized all his initiatives, sometimes even calling them ‘useless complication’. However, his ideas inspired C.I. Lewis for his first systems of modal logic and his strict implication. But in his later works Lewis did all not to mention MacColl. The second half of the XX century is a period of some kind of interest for the Scottish logician’s works revival. Still, the ideas of MacColl are not that familiar in Russia.