5 ideas
| 19433 | The universe is infinitely varied, so the Buridan's Ass dilemma could never happen [Leibniz] |
| Full Idea: The Buridan's Ass case of perfect equilibrium is chimerical. ...The universe has no centre and its parts are infinitely varied; thus it will never happen that all will be perfectly equal and will strike equally from one side or the other. | |
| From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
| A reaction: Can the great Leibniz have missed the point? Surely all that matters is that the ass cannot distinguish the two options - not that they actually are identical in every detail? If the ass is short-sighted, that should be easy to set up. |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 19434 | There may be a world where dogs smell their game at a thousand leagues [Leibniz] |
| Full Idea: There will perhaps be a world in which dogs will have sufficiently good noses to scent their game at a thousand leagues. | |
| From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
| A reaction: Wonderful. This should immediately replace Lewis's much repeated example of a world containing a talking donkey. We should always honour the first person to suggest an idea. That is one of the motivations for this collection of ideas. |
| 6649 | Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe] |
| Full Idea: Chomsky now contends that not only the syntax of natural language but also the concepts expressible in it have an innate basis. | |
| From: report of Noam Chomsky (Chomsky on himself [1994]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.7 n25 | |
| A reaction: This seems to follow Fodor, who has been mocked for implying that we have an innate idea of a screwdriver etc. Note that Chomsky says concepts have an innate 'basis'. This fits well with modern (cautious) rationalism, with which I am happy. |