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? |
| 1474 | Moral evil may be acceptable to God because it allows free will (even though we don't see why this is necessary) [Plantinga, by PG] |
| Full Idea: Moral evil may be acceptable to a benevolent God because it is the only way to allow genuine free will, which may have a supreme value in creation (even if we are unsure what it is). | |
| From: report of Alvin Plantinga (Free Will Defence [1965], Pref.) by PG - Db (ideas) |
| 1475 | It is logically possible that natural evil like earthquakes is caused by Satan [Plantinga, by PG] |
| Full Idea: Physical evil (e.g. earthquakes) may be attributable to a fallen angel (Satan), who is the enemy of God, and this is enough to retain the idea that God is omnipotent and benevolent, and yet evil exists. | |
| From: report of Alvin Plantinga (Free Will Defence [1965], III) by PG - Db (ideas) |