8 ideas
| 10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
| Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition. | |
| From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3 | |
| A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle. |
| 10467 | Individuals consist of 'compresent' tropes [Bacon,John] |
| Full Idea: 'Qualitons' or 'relatons' (quality and relation tropes) are held to belong to the same individual if they are all 'compresent' with one another. | |
| From: John Bacon (Tropes [2008], §4) | |
| A reaction: There is a perennial problem with bundles - how to distinguish accidental compresence (like people in a lift) from united compresence (like people who make a family). |
| 10464 | A trope is a bit of a property or relation (not an exemplification or a quality) [Bacon,John] |
| Full Idea: A trope is an instance or bit (not an exemplification) of a property or a relation. Bill Clinton's eloquence is not his participating in the universal eloquence, or the peculiar quality of his eloquence, but his bit, and his alone, of eloquence. | |
| From: John Bacon (Tropes [2008], Intro) | |
| A reaction: If we have identified something as a 'bit' of something, we can ask whether that bit is atomic, or divisible into something else, and we can ask what are the qualities and properties and powers of this bit, we seems to defeat the object. |
| 10465 | Trope theory is ontologically parsimonious, with possibly only one-category [Bacon,John] |
| Full Idea: A major attraction of tropism has been its promise of parsimony; some adherents (such as Campbell) go so far as to proclaim a one-category ontology. | |
| From: John Bacon (Tropes [2008], §2) | |
| A reaction: This seems to go against the folk idiom which suggests that it is things which have properties, rather than properties ruling to roost. Maybe if one identified tropes with processes, the theory could be brought more into line with modern physics? |
| 13230 | Particular essence is often captured by generality [Steiner,M] |
| Full Idea: Generality is often necessary for capturing the essence of a particular. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.36) | |
| A reaction: The most powerful features of an entity are probably those which are universal, like intelligence or physical strength in a human. Those characteristics are powerful because they compete with the same characteristic in others (perhaps?). |
| 10466 | Maybe possible worlds are just sets of possible tropes [Bacon,John] |
| Full Idea: Meinongian tropism has the advantage that possible worlds might be thought of as sets of 'qualitons' and 'relatons' (quality and relational tropes). | |
| From: John Bacon (Tropes [2008], §3) | |
| A reaction: You are still left with 'possible' to explain, and I'm not sure that anything is explain here. If the actual world is sets of tropes, then possible worlds would also have to be, I suppose. |
| 13229 | Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M] |
| Full Idea: Maybe to deduce a theorem as an instance of a generalization is more explanatory than to deduce it correctly. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.32) | |
| A reaction: Steiner eventually comes down against this proposal, on the grounds that some proofs are too general, and hence too far away from the thing they are meant to explain. |
| 13231 | Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M] |
| Full Idea: My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.34) | |
| A reaction: He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing. |