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) |
| 16620 | A chair is wood, and its shape is the form; it isn't 'compounded' of the matter and form [Hobbes] |
| Full Idea: Nothing can be compounded of matter and form. The matter of a chair is wood; the form is the figure it has, apt for the intended use. Does his Lordship think the chair compounded of the wood and the figure? | |
| From: Thomas Hobbes (Letter to Bramhall [1650], 4:302), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1 | |
| A reaction: Aristotle does use the word 'shape' [morphe] when he is discussing hylomorphism, and the statue example seems to support it, but elsewhere the form is a much deeper principle of individuation. |
| 16622 | Essence is just an artificial word from logic, giving a way of thinking about substances [Hobbes] |
| Full Idea: Essence and all other abstract names are words artificial belonging to the art of logic, and signify only the manner how we consider the substance itself. | |
| From: Thomas Hobbes (Letter to Bramhall [1650], 4:308), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 | |
| A reaction: I sympathise quite a lot with this view, but not with its dismissive tone. The key question I take to be: if you reject essences entirely (having read too much physics), how are we going to think about entities in the world in future? |
| 16718 | Primary qualities are the cause of all the other sensible qualities [Albertus Magnus] |
| Full Idea: The primary qualities of tangible things are the cause of all the other sensible qualities. | |
| From: Albertus Magnus (On 'Generation and Corruption' [1261], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 21.2 | |
| A reaction: This makes the primary qualities sound suspiciously like the essence. |