8 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) |
| 7771 | We need 'events' to explain adverbs, which are adjectival predicates of events [Davidson, by Lycan] |
| Full Idea: To deal with the truth conditions for some adverbs, Davidson introduced a domain of 'events', and made adverbs into adjectival predicates of events. | |
| From: report of Donald Davidson (The Logical Form of Action Sentences [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: This seems to be a striking case of a procedure of which I heartily disapprove - deriving you ontology from your semantics. Do all languages have adverbs? |
| 8860 | Language-learning is not good enough evidence for the existence of events [Yablo on Davidson] |
| Full Idea: One needs a better reason for believing in events than the help they provide with language-learning. | |
| From: comment on Donald Davidson (The Logical Form of Action Sentences [1967], §8) by Stephen Yablo - Apriority and Existence §8 | |
| A reaction: I can almost believe in micro-events at the quantum level, but I cannot believe that the Renaissance (made of events within events within events) is an event, even though I may 'quantify over it', and discuss its causes and effects. |
| 15002 | If the best theory of adverbs refers to events, then our ontology should include events [Davidson, by Sider] |
| Full Idea: Davidson argued that the best linguistic theory of adverbial modification assigns truth-conditions quantifying over events; thus we must embrace an ontology of events. | |
| From: report of Donald Davidson (The Logical Form of Action Sentences [1967]) by Theodore Sider - Writing the Book of the World 07.8 | |
| A reaction: Sider is critical and I agree. This is just the sort of linguistic manoeuvre that gets philosophy a bad name. As Yablo remarks, we have a terrible tendency to want to thingify everything. |
| 7495 | Apart from the fear, dying is an easy duty [Montaigne] |
| Full Idea: If our fears did not lend it weight, dying would be one of our lighter duties. | |
| From: Michel de Montaigne (III.12 On physiognomy [1580], p.1191) | |
| A reaction: An Epicurean thought. 'Duties' is nice - presumably death qualifies as a duty, because Nature requires it of us (we each of us 'owe nature a death'). The remark appears to me to be true. |