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] |
| 5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
| Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'. | |
| From: Xenophon (Symposium [c.391 BCE], 3.5) | |
| A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue |
| 8338 | A phenomenalist about objects has to be a regularity theorist about causation [Strawson,G] |
| Full Idea: If you are a phenomenalist about objects, then there is an important sense in which you ought to be a Regularity theorist about what causation is, in such objects. | |
| From: Galen Strawson (The Secret Connexion [1989], App C) | |
| A reaction: Strawson is denying that Hume is a phenomenalist. One might go a little further, and say that a phenomenalist should abandon the idea of causation (as Russell did). |