tonk

tonk a sentential connective whose meaning and logic are completely characterized by the two rules (or axioms) (1) [P P (P tonk Q)] and (2) [(P tonk Q) P Q]. If (1) and (2) are added to any normal system, then every Q can be derived from any P. Arthur Prior invented ‘tonk’ to show that deductive validity must not be conceived as depending solely on arbitrary syntactically defined rules or axioms. We may prohibit ‘tonk’ on the ground that it is not a natural, independently meaningful notion, but we may also prohibit it on purely syntactical grounds. E.g., we may require that, for every connective C, the C-introduction rule [(xxx) P (. . . . . .)] and the C-elimination rule [( — — — C — — -) P (yyy)] be such that the (yyy) is part of (xxx) or is related to (xxx) in some other syntactical way. See also RELEVANCE LOGI. D.H.

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