It is a commonplace by now that there are two theories of reism: the semantic and the material theory. This distinction was introduced by Ajdukiewicz (1930) in his review of Kotarbinski’s (1929) Elementy. (Kotarbinski’s book appeared in English under the unrecognizable title of Gnosiology; a Scientific Approach to the Theory of Knowledge, 1966; this translation sometimes does not do justice to the original text). Today, the difference can be formulated in familiar terms: semantic reism states the conditions for sentences to be well formed and to say something whereas material reism limits the models of such sentences. A model is a structure composed of the primary objects, of functions from one, two, three, etc., such objects to the logical values (truth and falsity), of functions from such functions to the logical values, and so on. At first, this description of a model, seems not to be stated in a reistic language. It may be argued, however, that this definition of a model is acceptable to a reist and that according to material reism only such models are allowed which take things alone as the primary objects. Semantic reism states that well formed primary sentences use names of things. The rest of a primary sentence, those parts of it which are not names of things, jointly constitute a functor. The functor, together with names of things as its arguments, forms a true or false sentence. There may also be sentences, no longer primary, which have as arguments not names of things but the functors just mentioned; as functors these sentences have a new kind of expressions which form sentences with primary functors as their arguments. Generally: (1) N1,N2, … are names of things; (2) If F(Nj, 1, Ni, 2, …, Nj,x) is a sentence, then F is a functor of the first order; (3) If Fi, 1, Fi,2, …, Fi,y are functors of order m and if G (Fi, 1, Fi, 2, …, Fi,y) is a sentence, then G is a functor of the m+1 order.