display all the ideas for this combination of texts
2 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
| From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| Full Idea: The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition). | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: [He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way. |