3 ideas
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| Full Idea: Gödel proved the completeness of first order predicate logic in his doctoral dissertation of 1930. | |
| From: report of Kurt Gödel (Completeness of Axioms of Logic [1930]) by Michal Walicki - Introduction to Mathematical Logic History E.2.2 |
| 9226 | If mathematical theories conflict, it may just be that they have different subject matter [Field,H] |
| Full Idea: Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects. | |
| From: Hartry Field (Recent Debates on the A Priori [2005], 7) | |
| A reaction: For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect. |
| 16705 | Whiteness isn't created in an alteration, because it is just this-being-white [Oresme] |
| Full Idea: If it is said that whiteness begins to be through alteration, this does not hold, because whiteness is nothing other than this-being-white. | |
| From: Nicole Oresme (On 'Generation and Corruption' [1349], I.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.3 | |
| A reaction: This innocent-looking remark is dynamite, because it rejects the separability of qualities, which threatens the doctrine of Transubstantiation. |