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Full Idea
It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place.
Gist of Idea
We must be clear about every premise and every law used in a proof
Source
Gottlob Frege (Logic in Mathematics [1914], p.212)
Book Ref
Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.212
A Reaction
Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step.
| 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] |