7 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 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? |
| 20721 | Punctuality and justice in dealings are excellent for raising a man in the world [Franklin] |
| Full Idea: After industry and frugality, nothing contributes more to raising a young man in the world than punctuality and justice in all his dealings. | |
| From: Benjamin Franklin (Advice to a Young Tradesman [1748], p.87-), quoted by Max Weber - The Protestant Ethic and the Spirit of Capitalism 2 | |
| A reaction: A perfect illustration of the self-interest that drives morality in the social contract view. |
| 20720 | Time is money, ..credit is money, ..and money breeds more money [Franklin] |
| Full Idea: Remember that time is money, …and that credit is money, …and that money can beget money. | |
| From: Benjamin Franklin (Advice to a Young Tradesman [1748], p.87-), quoted by Max Weber - The Protestant Ethic and the Spirit of Capitalism 2 | |
| A reaction: [snippets] A wonderful quotation rescued by Max Weber, showing that Franklin understood capitalism with crystal clarity, before it had even barely begun |