 To a certain extent, the ideas of Fitch can be regarded as introducing the view that the basic predicates of truth and membership have to be partial or, if you like, three-valued. Bochvar (1937) outlines a proposal based on the introduction of a three-valued logic, where, besides the standard truth values T (truth) and F (false), there exists a third value N, to be interpreted as “meaningless”. His logical analysis leads to the conclusion that the paradoxes involve meaningless statements. A characteristic feature of Bochvar’s formalism is that it distinguishes two types of connectives, roughly corresponding to two different modes of assertion. A statement \(A\) in itself assumes exactly one among the prescribed values (true, false or meaningless); but the internal three-valued logical operations are also equipped with external logical operations, which correspond to statements on the metalevel and allow the use of classical logic in dealing with non-classical statements. Formally, he described three valued truth tables for the main propositional internal connectives &amp; (and), \(\sim\) (negation), \(\vee\) (or), \(\rightarrow\) (implication), \(\leftrightarrow\) (logical equivalence). The truth values of \(\sim A, A \amp B\), etc., coincide with their classical values if \(A, B\) assume classical values; they are meaningless (assume value N) if one among \(A, B\) has value N (strictness). No formula built up with the standard connectives can be valid (or a tautology, i.e., is true under all possible assignments), as \(A \rightarrow A\) has value N, if \(A\) is meaningless. But there are connectives allowing the formation of metatheorical statements such as \(\vdash A, \neg A, \downarrow A\), to be read as “\(A\) is true”, “\(A\) is false”, “A is meaningless” (in the given order). The value of \(\vdash A (\neg A)\) is true if \(A\) is true (false), false (true) otherwise. Bochvar describes a version of the extended type-free logical calculus of Hilbert-Ackermann (1928), and, in order to dispose of the paradoxes, he restricts substitution and hence the comprehension schema of the form