  Definitions, which seem so peripheral to most logical systems, are in fact key to the potential power of Leśniewski’s logic. The axioms of a system generally use very few semantic categories near the bottom of the recursive hierarchy. It is by definitions that new semantic categories are introduced into the system; once a new category is in, variables for it may be introduced and quantified, a thesis of extensionality formulated for it, and it can provide arguments for further, higher-level functors. So although, unlike a typed logic conceived platonistically, only finitely many types or categories are actually in play in any one system, the potential to go on is restricted only by contingent limitations.