  Almost all metalogical ways of dealing with logical systems are platonistic. They assume that the simple and complex expressions are abstract types, that they are infinite in number, that an axiom system has infinitely many logical theorems, and so on. Leśniewski can admit none of this. So he has to find a way to deal with logical systems as something organic, growing and changing with time. He does so by employing a complex system of metalogical definitions, which he calls ‘terminological explanations’, and inference rules, which he calls ‘directives’. In effect Leśniewski gives a schematic grammatical and logical framework for an indefinitely extensible language, decades in advance of the advent of formal descriptions of computer programming languages, which are the nearest equivalent elsewhere.