5 ideas
| 15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine] |
| 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'. |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |