Single Idea 17898

[catalogued under 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives]

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.