13 ideas
| 1403 | A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG] |
| Full Idea: A rational donkey faced with two totally identical piles of hay would be unable to decide which one to eat first, and would therefore starve to death | |
| From: report of Jean Buridan (talk [1338]) by PG - Db (ideas) | |
| A reaction: also De Caelo 295b32 (Idea 19740). |
| 15380 | Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging [Vervloesem] |
| Full Idea: Intuitively, the Barcan formula says that nothing comes into existence when moving from a possible world to an alternative world. The converse says that nothing goes out of existence. Together they say the domain of quantification is fixed for all worlds. | |
| From: Koen Vervloesem (Barcan Formulae [2010]) | |
| A reaction: Stated so clearly, they sound absurd. The sensible idea, I suppose, is that you can refer to all the things from any world, but that doesn't mean they are possible. Shades of Meinong. 'Square circles' are not possible. |
| 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. |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects. | |
| From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| Full Idea: Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'. | |
| From: report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality | |
| A reaction: An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied. |
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions. | |
| From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4 |
| 16678 | Without magnitude a thing would retain its parts, but they would have no location [Buridan] |
| Full Idea: If magnitude were removed from matter by divine power, it would still have parts distinct from one another, but they would not be positioned either outside one another or inside one another, because position would be removed. | |
| From: Jean Buridan (Questions on Aristotle's Physics [1346], I.8 f. 11va), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 | |
| A reaction: This shows why Quantity is such an important category for scholastic philosopher. |
| 16793 | A thing is (less properly) the same over time if each part is succeeded by another [Buridan] |
| Full Idea: Less properly, one thing is said to be numerically the same as another according to the continuity of distinct parts, one in succession after another. In this way the Seine is said to be the same river after a thousand years. | |
| From: Jean Buridan (Questions on Aristotle's Physics [1346], I.10, f. 13vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 29.3 | |
| A reaction: This is a rather good solution to the difficulty of the looser non-transitive notion of a thing being 'the same'. The Ship of Theseus endures (in the simple case) as long as you remember to replace each departing plank. Must some parts be originals? |
| 16726 | Why can't we deduce secondary qualities from primary ones, if they cause them? [Buridan] |
| Full Idea: The entire difficulty in this question is why through a knowledge of the primary tangible qualities we cannot come to a knowledge of flavors or odors, since these are their causes, since we often go from knowledge of causes to knowing their effects. | |
| From: Jean Buridan (Questions on Aristotle's Posterior Analytics [1344], I.28c), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.2 | |
| A reaction: He is commenting on Idea 16725. Still a nice puzzle in the philosophy of mind. Will neuroscientists ever be able to infer to actual character of some quale, just from the structures of the neurons? |
| 16577 | Induction is not demonstration, because not all of the instances can be observed [Buridan] |
| Full Idea: Inductions are not demonstrations, because they do not conclude on account of their form, since it is not possible to make an induction from all cases. | |
| From: Jean Buridan (Questions on Aristotle's Physics [1346], I.15 f. 18vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 02.3 | |
| A reaction: Thus showing that demonstration really is meant to be as conclusive as a mathematical proof, and that Aristotle seems to think such a thing is possible in physical science. |
| 16576 | Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan] |
| Full Idea: Induction should be regarded as a principle of natural science. For otherwise you could not prove that every fire is hot, that all rhubarb is purgative of bile, that every magnet attracts iron. | |
| From: Jean Buridan (Questions on Aristotle's Physics [1346], I.15 f. 18vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 02.3 | |
| A reaction: He is basing this on Aristotle, and refers to 'Physics' 190a33-b11. |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
| Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose. | |
| From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2 | |
| A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts. |