Ideas from 'The Runabout Inference Ticket' by Arthur N. Prior [1960], by Theme Structure

[found in 'Philosophical Logic' (ed/tr Strawson,P.F.) [OUP 1973,0-19-875004-8]].

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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example
                        Full Idea: Prior dislike the holism inherent in the claim that the meaning of a logical connective was determined by the inference patterns into which it validly fitted. ...His notorious example of 'tonk' (A → A-tonk-B → B) was a reductio of the view.
                        From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Stephen Read - Thinking About Logic Ch.8
                        A reaction: [The view being attacked was attributed to Gentzen]
Maybe introducing or defining logical connectives by rules of inference leads to absurdity
                        Full Idea: Prior intended 'tonk' (a connective which leads to absurdity) as a criticism of the very idea of introducing or defining logical connectives by rules of inference.
                        From: report of Arthur N. Prior (The Runabout Inference Ticket [1960], 09) by Ian Hacking - What is Logic?
We need to know the meaning of 'and', prior to its role in reasoning
                        Full Idea: For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion.
                        From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132
                        A reaction: The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives.
Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B
                        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.
                        From: comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink 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.