6 ideas
| 6564 | To affirm 'p and not-p' is to have mislearned 'and' or 'not' [Quine] |
| Full Idea: To affirm a compound of the form 'p and not-p' is just to have mislearned one or both of these particles. | |
| From: Willard Quine (From Stimulus to Science [1995], p.23), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Quoted by Fogelin. This summarises the view of logic developed by the young Wittgenstein, that logical terms are 'operators', rather than referring terms. Of course the speaker may have a compartmentalised mind, or not understand 'p' properly. |
| 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) |
| 13440 | Causation is the power of one property to produce another, and this gives time its direction [Esfeld] |
| Full Idea: The metaphysics of causation in terms of powers is linked with an intrinsic direction of time. There is a causal connection if an F-property produces a G. One can argue that causation thus is the basis for the direction of time. | |
| From: Michael Esfeld (Humean metaphysics vs metaphysics of Powers [2010], 7.2) | |
| A reaction: I think this is my preferred metaphysic - that both time and causation are primitive, but the direction of time is the result of the causal process. Viewing some new world, we would just say that time went in whichever direction the causation went. |