   One of Leśniewski’s most lasting contributions to the metatheory of logic is his theory of semantic categories. This replaced the theory of simple types which he developed in 1921, about which he wrote, “[E]ven as I was constructing my theory of types, I considered it to be only an inadequate stop-gap […] In 1922 I outlined a concept of semantical categories as a replacement for the hierarchy of types, which is quite unintuitive to me” (Collected Works, 421). In type theory, expressions belonging to different logical types cannot be substituted for one another without turning grammatical or well-formed expressions into ungrammatical or ill-formed ones. Only well-formed or grammatical expressions may have a sense or meaning. The theory was developed by Bertrand Russell as a way of blocking set-theoretic paradoxes, though there were anticipations in the work of Ernst Schröder and Gottlob Frege. In type theory it is usually assumed that variables at each type range over a domain of entities specific to that type, and that all such domains are mutually disjoint. In Frege for instance the domains were objects and functions of various levels, while in Russell they are usually taken to be a hierarchy of propositional functions. This presumptively platonistic and ontologically inflationary position was naturally uncongenial to the nominalist Leśniewski, and he readjusted the notion of category, turning categories from classes of entities (with their attendant expressions) to classes of expressions alone. His inspiration was in part the traditional syntactic theory of different parts of speech, and in part Husserl’s theory of Bedeutungskategorien (meaning categories) from the latter’s Logical Investigations. Where Husserl’s categories were of abstract meanings, Leśniewski, ever the nominalist, substituted categories of (concrete) expressions. Although like later writers he could have called the classes of expressions ‘syntactic categories’, he deliberately chose the expression ‘semantic categories’ in order to emphasize that the expressions combined grammatically are all meaningful, unlike the meaningless marks proposed by formalist writers of the Hilbert School.