 The idea which, has just re-surfaced in our discussion, apropos of Garson, that the natural deduction introduction and elimination rules together, or perhaps just the introduction rules alone (Gentzen’s preferred  position),[19]  somehow fix the meanings of the connectives they govern, often goes hand in hand with considerations of the existence and the uniqueness of a connective answering to the said rules, considerations first raised by H. Hiż, according to Belnap (1962). Belnap was replying to Prior (1960) in which the idea that any old set of rules could be stipulated to fix the meaning of a proposed connective, was contested with the aid of the subsequently much-discussed example Tonk, a supposed binary connective for which an introduction rule allowed the passage from (arbitrary) φ to φ Tonk ψ, as with ∨-introduction from the first disjunct, and an elimination rule allowed the passage from φ Tonk ψ to ψ, as with ∧-elimination to the second conjunct. (This was the point anticipated in §2 when the Tonk problem was mentioned apropos of the dual to hybridizing conjunction and disjunction.) Since this allowed, by successively applying (Tonk-I) and then (Tonk-E), any ψ to be derived from any φ, Prior took this to show that no coherent meaning had been conferred on Tonk by the proposed rules, and to refute the general thesis that the meaning of a connective can be fixed by means of rules governing it. (Prior saw Popper and Kneale as the targets of his argument, which does not touch Gentzen’s view that the meaning is fixed by the totality of introduction rules for a connective, coupled with the fact that these are the totality of such rules. Since there is only the one way of introducing Tonk, namely that provided by (Tonk-I), where the premiss is φ the meaning of φ Tonk ψ is simply that of φ and the appropriate elimination rule is not that given by Prior but rather one licensing an elimination to the first “tonkjunct”.) Belnap responded that what was wrong with Prior’s Tonk rules was that a proof system antecedently endorsed for the connectives in use would be non-conservatively extended by the enrichment of the language with Tonk in tandem with supplementing the proof system with the (Tonk-I) and then (Tonk-E), since they allow the derivation of the sequent φ ≻ ψ even for Tonk-free φ,  ψ.[20]  Later in this section, we return to Tonk and examine its behaviour in a sequent calculus setting.