5 ideas
| 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. |
| 14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
| Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you. |
| 14285 | A possible world is the ontological analogue of hypothetical beliefs [Stalnaker] |
| Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven! |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |