Full Idea
Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B.
Clarification
'Conservative' means only adding what that connective implies
Gist of Idea
Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B
Source
comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135
Book Reference
'Philosophical Logic', ed/tr. Strawson,P.F. [OUP 1973], p.135
A Reaction
Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction.