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) |
| 9052 | Vague predicates lack application; there are no borderline cases; vague F is not F [Unger, by Keefe/Smith] |
| Full Idea: In a slogan, Unger's thesis is that all vague predicates lack application ('nihilism', says Williamson). Classical logic can be retained in its entirety. There are no borderline cases: for vague F, everything is not F; nothing is either F or borderline F. | |
| From: report of Peter Unger (There are no ordinary things [1979]) by R Keefe / P Smith - Intro: Theories of Vagueness §1 | |
| A reaction: Vague F could be translated as 'I'm quite tempted to apply F', in which case Unger is right. This would go with Russell's view. Logic and reason need precise concepts. The only strategy with vagueness is to reason hypothetically. |
| 16070 | There are no objects with proper parts; there are only mereological simples [Unger, by Wasserman] |
| Full Idea: Eliminativism is often associated with Unger, who defends 'mereological nihilism', that there are no composite objects (objects with proper parts); there are only mereological simples (with no proper parts). The nihilist denies statues and ships. | |
| From: report of Peter Unger (There are no ordinary things [1979]) by Ryan Wasserman - Material Constitution 4 | |
| A reaction: The puzzle here is that he has a very clear notion of identity for the simples, but somehow bars combinations from having identity. So identity is simplicity? 'Complex identity' doesn't sound like an oxymoron. We're stuck if there are no simples. |
| 7294 | No crime and no punishment without a law [Roman law] |
| Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law. | |
| From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws? |