3 ideas
6558 | A foolish consistency is the hobgoblin of little minds [Emerson] |
Full Idea: A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. | |
From: Ralph Waldo Emerson (Self-Reliance [1841], p.37) | |
A reaction: A remark to warm the hearts of pragmatists, Wittgensteinians, Nietzscheans and the post-modern mob. But pay careful attention to the word "foolish". Robert Fogelin gives a very balanced view of the matter (e.g. Idea 6557). |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'. | |
From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3 | |
A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality. |