 In the early 1940s, Fitch explored a purely positive (negationless) combinatory system \(K\) with the explicit aim of defining a sort of universal formal system, where every system of logic could be represented. Later he was able to strengthen his approach to include forms of negation and implication, insofar as he provided a simultaneous generation of truth and falsehood, and this actually amounts to conceive truth as a partial predicate. Fitch’s approach is radically intensional: classes are always classes of expressions \(M\) in some language (say, of the basic logic) and they are identified with attributes, while membership is essentially reduced to truth in the sense of \(K\). Thus, that \(M\in T\) holds, essentially means that \(M\) truly falls under the property specified (or expressed) by \(T\) (see also the entry on  combinatory logic).  Logical systems, along similar lines, were also proposed and proved consistent via proof theoretic methods by Schütte in the early fifties (see Schütte 1960 for a comprehensive treatment).