4 ideas
| 17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
| Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers. | |
| From: Nicholas P. White (What Numbers Are [1974], V) |
| 17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
| Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege. | |
| From: Nicholas P. White (What Numbers Are [1974], IV) | |
| A reaction: [He adds Quine 1960:268 as a reference] |
| 12694 | Essence is the distinct thinkability of anything [Leibniz] |
| Full Idea: (Essence) is the distinct thinkability (cogitabilitas) of anything. | |
| From: Gottfried Leibniz (Notes on John Wilkins [1672], A6.2.487-8), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1 | |
| A reaction: A very original remark from the young Leibniz. It is neutral as to whether this is a real feature of objects, or a feature of human mental capacities. Presumably accidental features are thinkable, so 'distinct' is the key word. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |