 According to Ramsey, the antinomies of the first group (such as Russell’s, or Burali-Forti’s) can be avoided by referring to a universe of mathematical objects which is structured into types of individuals, functions of individuals, functions of functions of individuals, etc. Quantification over arbitrary types is legitimate and hence types are closed under impredicative comprehension, which is considered necessary for mathematics. Types are intrinsic to logical and mathematical objects and the logical paradoxes are exactly those which require type distinctions to be solved (e.g., self-membership is blocked for objects in the type-theoretic hierarchy). In order to solve the semantical antinomies (e.g., the Liar, Berry’s), Ramsey proposes to distinguish several notions of meaning. In light of later developments, it is interesting to note that for him semantics is not a viable universal notion: in particular, it is impossible to obtain “an all-inclusive relation of meaning for propositional functions. Whatever one we take there is still a way of constructing a symbol to mean in a way not included in our relation. The meanings of meaning form an illegitimate totality” (Ramsey 1926, p. 372). This yields the clue to the solution of Grelling’s paradox (see 3.3.2). Let \(R\) be the meaning relation linking an adjective \(f\) to the corresponding propositional function denoted by \(F\) (so that \(f R F\) holds). In the definition of “heterological” we do use the relation \(R: x\) is heterological iff there exists \(F\) such that \(F\) does not apply to \(x\) and \(x R F\). Now, there exists a propositional function, say \(H\), which is the meaning of the adjective “heterological”. Ramsey’s point is that this sense of meaning cannot be the same as that given by \(R\) and this blocks the contradiction, when we apply \(H\) to “heterological” (ibid.,p. 370). So one needs a new meaning relation depending on the given fixed \(R\). These ideas foreshadow those of Tarski. (For an analysis of semantical antinomies in a ramified context, compare also the later contribution of Church 1976, also reconsidered and criticized in Martino 2001.).