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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 Ref
'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.
| 22899 | 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN] |
| 15201 | That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN] |
| 17896 | We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap] |
| 17898 | Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN] |
| 11021 | Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read] |
| 13836 | Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking] |