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Full Idea
For a demonstration to be cogent it is necessary that the passage from step to step involve a recognition of truth at each line.
Gist of Idea
A successful proof requires recognition of truth at every step
Source
Michael Dummett (The Justification of Deduction [1973], p.313)
Book Ref
Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.313
A Reaction
Dummett cited Quine (esp. 1970) as having an almost entirely syntactic view of logic. Rumfitt points out that logic can move validly from one falsehood to another. Even a 'proof' might detour into falsehood, but it would not be a 'canonical' proof!
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| 1885 | Proof moves from agreed premises to a non-evident inference [Sext.Empiricus] |
| 8627 | Leibniz is inclined to regard all truths as provable [Leibniz, by Frege] |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| 2898 | Anything which must first be proved is of little value [Nietzsche] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |