6 ideas
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| Full Idea: The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate. | |
| From: George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind | |
| A reaction: Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!). |
| 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? |
| 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. |
| 19068 | Causation interests us because we want to explain change [Mumford] |
| Full Idea: Like Aristotle, the reason we are really interested in causation is because we want to be able to explain change. | |
| From: Stephen Mumford (Contemporary Efficient Causation: Aristotelian themes [2014], 8) | |
| A reaction: This pinpoints a very important and simple idea. It raises the question (among others) of whether we have just invented this thing called 'causation', because no explanation of change was visible. Hume certainly couldn't see any explanation. |