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) |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 23888 | Knowledge is beyond question, as an unavoidable component of thinking [Weil] |
| Full Idea: The speaker refuses to pose the question of knowledge, since knowledge is a given that is mixed with thought, and that no thinking being can get away from. | |
| From: Simone Weil (Philosophy [1941], p.42) | |
| A reaction: On the whole I favour belief-first, but I take the primary purpose of minds to be navigation, and that needs facts, not hopeful beliefs. Weil's thought pushes me a bit towards the knowledge first view. |
| 23887 | Art (like philosophy) establishes a relation between world and self, and between oneself and others [Weil] |
| Full Idea: Isn't true art a method for establishing a certain relation between the world and the self, and between oneself and others, and isn't that the equivalent of philosophy? | |
| From: Simone Weil (Philosophy [1941], p.38) | |
| A reaction: I hope the definition of 'true' art doesn't have to conform to achieving this relation. I suppose each good work of art shows you a distinctive way of relating to the world. An interesting thought (as so often with this thinker). |