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) |
| 7413 | Without confidence in our beliefs, how should we actually live? [Tuck] |
| Full Idea: The central question for sceptics is if we lose confidence in the truth of most existing beliefs, then how do we actually live? | |
| From: Richard Tuck (Hobbes [1989], Ch.4) | |
| A reaction: Scepticism is not, of course, all or nothing. You can lead a 'normal' life in a virtual reality machine. I find it much more of a struggle to live if I lose faith in values, than if I lose faith in tables. |
| 21947 | Power is localised, so we either have totalitarian centralisation, or local politics [Foucault, by Gutting] |
| Full Idea: Foucault's analysis suggests that meaningful revolution, hence genuine liberation, is impossible: the only alternative to the modern net of micro-centres of power is totalitatian domination. Hence his politics, even when revolutionary, is always local. | |
| From: report of Michel Foucault (Discipline and Punish [1977]) by Gary Gutting - Foucault: a very short introduction 8 | |
| A reaction: It is hard to disagree with this. |
| 21946 | Prisons gradually became our models for schools, hospitals and factories [Foucault, by Gutting] |
| Full Idea: Foucault's thesis is that disciplinary techniques introduced for criminals became the model for other modern sites of control (schools, hospitals, factories), so that prison discipline pervades all of society. | |
| From: report of Michel Foucault (Discipline and Punish [1977]) by Gary Gutting - Foucault: a very short introduction 8 | |
| A reaction: Someone recently designed Foucault Monopoly, where every location is a prison. All tightly controlled organisations, such as a medieval monastery, or the Roman army, will inevitably share many features. |