6 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] |
13550 | To be always happy is to lack knowledge of one half of nature [Seneca] |
Full Idea: To be always happy and to pass through life without any mental distress is to lack knowledge of one half of nature. | |
From: Seneca the Younger (On Providence [c.60], §4) | |
A reaction: These kind of paradoxes plague virtue theory, and any theory which aims at an ideal. Heaven, for example, seems to have no problems to solve, which spells boredom. The fascination of corrupt people is their superior knowledge of the world. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
13549 | Nothing bad can happen to a good man [Seneca] |
Full Idea: Nothing bad can happen to a good man. | |
From: Seneca the Younger (On Providence [c.60], §2) | |
A reaction: This is a pithy summary of a well know ancient attitude - one that is rejected by Aristotle, but defended by Socrates. It depends what you mean by 'bad' - but that is a rather modern response. |
13548 | The ocean changes in volume in proportion to the attraction of the moon [Seneca] |
Full Idea: The waves increase by degrees, approaching to the hour and day proportionately larger or smaller in volume as they are attracted by the star we call the moon, whose power controls the ocean's surge. | |
From: Seneca the Younger (On Providence [c.60], §1) | |
A reaction: ....just in case anyone thought that Isaac Newton had invented gravity. |