| 1917 | works |
| p.125 | 15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification | |
| Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain. | |||
| From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3 | |||
| A reaction: Lavine summarises this as 'first-order logic with parameters'. |
| 1949 | Phil of Mathematics and Natural Science |
| 25-7 | p.160 | 10246 | The limit of science is isomorphism of theories, with essences a matter of indifference |
| Full Idea: A science can determine its domain of investigation up to an isomorphic mapping. It remains quite indifferent as to the 'essence' of its objects. The idea of isomorphism demarcates the self-evident boundary of cognition. | |||
| From: Hermann Weyl (Phil of Mathematics and Natural Science [1949], 25-7), quoted by Stewart Shapiro - Philosophy of Mathematics | |||
| A reaction: Shapiro quotes this in support of his structuralism, but it is a striking expression of the idea that if there are such things as essences, they are beyond science. I take Weyl to be wrong. Best explanation reaches out beyond models to essences. |